Home

Phase modulating interferometry with stroboscopic illumination for

Contents

1. 10 Za 0 Timeout bd amera control settings Attached camera id numbers Operating camera id number rror flow Fig D 7 Default event when there has been no changes on the user interface continue program with all prior settings 126 amera control settings FEATURE FLAG MANUAL 0x00000002 7 ttached Camera id numbers Sess Wie ch Suppen i P E El True cK E g S d b Geen fees perating camera 1d number GN ol B ISSS S ISSS SSSL ELA H Bee Fig DS Event structure la when the gamma has been adjusted Stop the camera feed while adjusting the camera gamma value and restart the camera feed 27 fal fi Gamma Mouse Up e 1 Camera control settings Attached camera id numbers Operating camera id number P Si i Error flow Fig D 9 Event structure 1b when the gamma has been adjusted adjusting the camera gamma value when the camera is not providing an image feed 128 GE wi Shutter value Change S f 1 Camera control settings Attached camera id numbers FEATURE FLAG MANUAL Ox00000002 v Operating camera id number Error flow Fig D 10 Event structure 2 if the shutter exposure time has been adjusted send the new value to the camera system This setting is not read when the camera is operating in Low Integrate trigger mode 129 amera control settings TG Attached camera id numbers rig Update CD Operating camera id number Trig
2. A FireWIRE bus must be installed for control of the PixeLINK PL 741 monochrome CMOS camera General control software for the camera system comes with device purchase however integration with the LabVIEW programming environment requires installation of VI libraries available from either the camera developers or included in the attached data CD A list of these VI libraries is given in Table E 2 Table E 2 Programming control blocks required for operation of the PixeLINK PL 741 monochrome CMOS camera system PxLLabVIEW dll ACQUISITION IIb CAMERA FEATURES IIb Debug Examples 7 1 1lb Debug Examples lb Demo Examples 71 lb Demo Examples llb DESCRIPTOR CONTROL IIb DETECTION IIb ERROR REPORTING IIb GENERIC IIb IDENTIFICATION IIb INITIALIZATION IIb LabVIEW 6 1 IMAQ for IEEE 1394 Examples llb PREVIEW llb TRANSLATION IIb The developed code may work for other monochrome PixeLINK cameras however all other brands will require the replacement of the PixeLINK control blocks with code 144 available from that particular camera s developer Control of the exposure cycle of the camera system requires the subsequent installation of National Instruments PCI 6713 analog voltage output card Installation software is available with purchase of this card It is assumed that this card is connected to the interferometer as outlined in Table 4 1 After installation of the required LabVIEW control libraries the developed code may
3. Phase modulating interferometry with stroboscopic illumination for characterization of MEMS A Thesis submitted to the faculty of the Worcester Polytechnic Institute as a partial fulfillment of the requirements for the Degree of Master of Science in Mechanical Engineering by Matthew T Rodgers 15 December 2006 L HE i Ee Cosme FA es Majors Beet E AG VLMa Prof Ry Gh Rey hutiew ez Member Thesis Committee PAEA AAA Prof Gfetar oe Meunier Thesis Committee Mr Mark gd GE K Corporation Member Thesis Committee Prof Mark Richman Gradnate Committee Representative Phase modulating interferometry with stroboscopic illumination for characterization of MEMS A Thesis submitted to the faculty of the Worcester Polytechnic Institute as a partial fulfillment of the requirements for the Degree of Master of Science in Mechanical Engineering by Matthew T Rodgers 15 December 2006 Approved Prof Cosme Furlong Major Advisor Prof Ryszard J Pryputniewicz Member Thesis Committee Prof Gretar Tryggvason Member Thesis Committee Mr Mark Koslowske Ceranova Corporation Member Thesis Committee Prof Mark Richman Graduate Committee Representative Copyright 2006 By NEST NanoEngineering Science and Technology CHSLT Center for Holographic Studies and Laser micro mechaTronics Mechanical Engineering Department Worcester Polytechnic Institute Worcester MA 01609 2280 Al
4. 137 138 139 140 141 148 149 Fig F 3 View the wrapped phase map or the optical modulation map and save the results to the selected directory End the program using the implemented program stop 150 Se Table Table Table Table Table Table Table Table Table 2 1 2D St 4 1 Ih D2 5 3 ch E 2 LIST OF TABLES Microsensor families Comparison of phase evaluation methods without a spatial carrier Sasaki et al 1986a Dorrio and Fernandez 1998 Dubois 2001 Kreis 2005 Reference excitation amplitude and phase versus illumination duty cycle System connectivity chart Shape measurement comparison between sinusoidal modulation and phase stepping Mean optical phase map drift under phase stepping interferometry at f 2 Hz and sinusoidal modulating interferometry at f 10 Hz and 100 Hz uHexFlex quasi static loading conditions Virtual instruments installed with LabVIEW IMAQ modules Programming control blocks required for operation of the PixeLINK PL 741 monochrome CMOS camera system X11 24 46 50 75 81 89 143 144 AQ X rms a AA Ag AWactual AWideal At E EXY o e a Sos OXY fo fo NOMENCLATURE infinite time average mean optical phase map drift mrad geometric or root mean squared average of data set x reference modulation phase rad spectral output width at half output power Unwrapped recover
5. Gaussian zero mean noise acquired frame number 1 2 3 or 4 time sec minimum settling time of a piezoelectric actuator one to multi dimensional data set data point within data set x spatial coordinates on the imaging array amplitude of sinusoidal phase modulation nm compact disk containing installation files included with this Thesis complementary metal oxide semiconductor optical path length difference mean absolute deviation isotropic modulus of elasticity electrical field strength of a planar illumination wavefront discreet complex amplitude of sequential frames frame 1 2 p isotropic bulk modulus intensity of an illumination source continuous complex amplitude of sequential frames frame 1 2 3 p instantaneous photon flux or unmodulated dc component of an illumination intensity X1V IRQ JA Ks Ke LIGA MEMS Ns Ne NDE NIST OEHM PMI PSI Oxy ROI RMS TMA UI average photon flux or unmodulated dc component of an illumination intensity instantaneous modulated irradiance intensity average modulated irradiance intensity inter quartile range n order Bessel function of the first kind with respect to variable y sine and cosine phase constants respectively acronym for a German fabrication process involving Lithographie Galvanoformung Abformung additional mass coupled to a piezoelectric actuator microelectromechanical systems N bucket phase stepping algorithm summed additi
6. Opt Lett 24 309 311 1999 Dubois A Phase map measurements by interferometry with sinusoidal phase modulation and four integrating buckets JOSA A 18 1972 1979 2001 Dyson J Interferometry as a measuring tool Machinery Publishing Co Brighton Sussex England 1970 Edmund Optics Inc Edmund Optics specification sheet USAF 1951 target Edmund Optics Inc Barrington NY 2006 _98 Electronic Design MEMS raise testing issues from the beginning to the end of the design cycle Electronic Design 2000 Exponent Inc www exponent com 2000 last viewed Apr 15 2006 Furlong C and Pryputniewicz R J Optoelectronic characterization of shape and deformation of MEMS accelerometers used in transportation applications Opt Eng 42 5 1223 1231 2003 Furlong C Microelectromechanical systems introduction and applications ISTFA Boston 2004a Furlong C and Pryputniewicz R J Study and characterization of a MEMS micromiurror device Proc SPIE 5531 54 63 2004b Furlong C Optoelectronic holography for testing electronic packaging and MEMS in Optical Inspection of Microsystems Osten W ed CRC Press NY 2007 Gitterman M Simple treatment of correlated multiplicative and additive noises J Phys A Math amp General 32 27 293 297 1999 Glynn E USAF and microscopy resolution test charts and pixel profiles online last updated 2002 Gorard S
7. accomplished through software control of a National Instruments analog output card National Instruments 2006 controlling a piezoelectric phase modulator Furlong and Pryputniewicz 2004b illumination source Opto Diode 2006 and CMOS camera system PixeLINK 2006 The configured interferometric system with all required external components is schematically presented in Fig 4 1 with signal I O connections indicated in Table 4 1 NI PCI 6713 Imaging 1 system emt Reference Mirror lt gt Fig 4 1 Schematic representation of PMI system described in this Thesis Infinity Thor Labs corrected yr i o E ITC 502 o gt objectives Object A0 Table 4 1 System connectivity chart Input Output 1 Cable Purpose PCI 6713 Piezoelectric phase BNC Reference path modulation Ch 0 modulator PCI 6713 ITC 502 Analog Mod Illumination modulation Ch 1 PCI 6713 PL A741 vision control Ch 2 ITC 502 OD 620L BNC Illumination power supply Analog Mod PL A741 data port FireWIRE Camera trigger control 4 1 Experimental system A Linnik configured interferometer was chosen as the platform for this PMI system Dyson 1970 Greivenkamp and Bruning 1992 Kreis 2005 As shown in Fig 4 2 this configuration is very similar to the Michelson configuration The primary difference between the two systems is the addition of an infinity corrected objective along each arm of the interferometer em Ar
8. miniaturization required a new approach to system design due to the effects of force scaling To ensure that MEMS devices function as designed many are enabled with integrated microstructures for in situ measurements of material properties Liwei et al 1997 Osterberg and Senturia 1997 Sandia 2006 However these microstructures require additional space on the fabrication wafers that could be spent providing additional mechanical complexity or allowing for an increase in the number of devices and hence an improvement in the economics of fabrication and design Consequently noninvasive noncontact techniques are needed to measure the geometric and material property data over the full device For materials characterization scaling laws require a measurement resolution of 0 1 1 nm in MEMS structures Interferometric techniques are needed to achieve this accuracy over a full field of view The invention of phase shifting interferometry PSI was a major breakthrough in the field of homodyne interferometry providing a method to measure the optical phase with unprecedented accuracy Creath 1992 Implemented on almost all types of interferometric imaging systems through use of various algorithms PSI allows extraction of a phase map from several intensity fringe patterns Classic phase shifting interferometry requires integration of 3 or more intensity maps during a linear variation in the optical phase over a 27 phase variation Creath 1988 K
9. 1 of full travel or 1 um Physik Instrumente L P 2005 Creep is a change in displacement with time without corresponding changes m the voltage source due to changes in the remnant polarization changes within the piezoelectric material For rapid to moderate acquisition systems the effect of creep on the resulting phase map errors will be minimal as in practice creep is typically a few percent over an hour Physik Instrumente L P 2005 Phase modulating interferometry minimizes both hysteresis and creep effects relative to phase stepping or phase shifting due to the periodic and continuous motion of the piezoelectric actuator Physik Instrumente L P 2005 To eliminate the effects of overshoot and settling time while minimizing hysteresis a sinusoidal reference excitation signal 1s implemented within this Thesis to the piezoelectric actuator This creates a time dependent instantaneous intensity equation which must be integrated over the acquisition time to determine the recovered interferogram intensity Additionally the application of the sinusoidal modulation signal minimized the jerk experienced by the reference mirror at high frequencies while maintaining a relatively simple form for integration ae 3 2 Use of sinusoidal reference excitation Use of a sinusoidal reference excitation creates a reference phase term of the form dp t ysin o t 3 7 where the spatial dependence terms are dropped for simplicity The value of
10. 1s attributed to a combination of the mean and mean squared errors in both the PMI and PSI systems These errors are related to the phase modulation parameters and appear with a spatial frequency equal to twice the optical frequency as explored in Appendix B and Creath 1988 1992 76 Wrapped phase map generated with sinusoidal modulating interferometry imaging a reference flat at f 100 Hz and d 14 showing points used in calculation of optical phase drift 80 Optical phase drift over time recovered with phase stepping interferometry and sinusoidal phase modulating interferometry operating at f 2 Hz and f 100 Hz respectively with d 14 Under these operating conditions the PSI method exhibits a mean phase drift 7 5 times that demonstrated with PMI correlating with results presented by Kinnstaetter et al 1988 and Sasaki et al 1990b 80 Scanning electron microscopy image of a prototype uHexFlex device courtesy of Shih Chi Chen MIT 2004 82 Layered TMA structure of uHexFlex device viewed through a scanning electron microscope courtesy of Shih Chi Chen MIT 2004 83 Recovered shape of 280 um diameter central stage uwHexFlex 85 Recovered shape of 375 um diameter central stage wHexFlex demonstrating damage to the armature structure 86 Recovered shape of 540 um diameter central stage wHexFlex using phase modulating interferometry with damage indicated to the TMA and armature structures 87 Recovered sha
11. 4 at a spatial frequency of 181 019 line pairs mm or spatial resolution of 2 762 um Similarly a pixel profile taken along to the element lines can be used to determine the field of view of the imaging array For a 4x magnification and use of a 1280 x 1024 imaging array the maximum field of view is found as 2 967 x 2 373 mm or 432 pixels mm 5 2 Measurement resolution and repeatability The sensitivity accuracy and precision of the phase modulating system are characterized with the aid of a 500 A 2 5 gold film NIST traceable gauge specifically designed constructed and certified for OEHM measurements Veeco Metrology Group _64 2002 This characterization is important to determine the reliability and applicability in high resolution measurements as required in MEMS devices Figure 5 3 depicts the chosen gauge Fig 5 3 500A 2 5 goal film NIST traceable gauge used for characterization of optoelectronic holographic methodologies Veeco Metrology Group 2002 Measurements are carried out using a 4x magnification with a CMOS camera containing 1280 x 1024 active pixels at 8 bit digitization with a region of interest indicated in Fig 5 3 Measurements involve 1 performing high resolution phase modulation calibration Hariharan et al 1987 2 optimizing the beam ratio between the reference and objective arms to maximize the fringe contrast 3 adjustment of the interferometric and focal planes to maximize contr
12. Excitation Amplitude Interpolate Correct Excitation opp Mavelength O51 Sie Ecale nm to voltage nm to Voltage ae 2 ER Fig D 22 Event Structure 10 this event calculates the modulation and synchronization parameters for output voltage generation based on current UI settings and data read from the excitation parameter file Default Excel file is excite xls Hood 141 APPENDIX E Operation package installation The code developed in this Thesis requires installation of National Instrument s LabVIEW 7 0 Measurement amp Automation Explorer MAX 4 0 2 Image Acquisition software IMAQ with Vision 6 0 and IMAQ Vision Builder 6 0 or higher The basic LabVIEW package is an open programming environment designed to interface interactive assistants and code generation to multiple hardware devices LabVIEW 7 1 2006 Addition of the Measurement amp Automation Explorer package allows for the control and simulation of National Instruments and compatible devices LabVIEW image acquisition processing saving capabilities are then expanded with the addition of IMAQ with Vision and IMAQ Vision Builder With these modules the additional VIs presented in Table E 1 are made accessible to the LabVIEW run time environment 142 Table E 1 Virtual instruments installed with LabVIEW IMAQ modules Image Acquisition Palette Low Level Palette Vision Vision gt Image Acquisition IMAQ Snap
13. Homodyne systems consider the relative optical phase shift between coherent reference and object beams In a multiple path interferometer the relative phase between the two beams is directly proportional to the wave number k and the shape of the object of interest Z A Michelson type interferometer presented in Fig 2 5 recovers shape proportional to twice the optical path length difference D 15 Point detector Gp Beam splitter Light source Reference mirror Fig 2 5 Michelson interferometer Kreis 2005 The object shape can then be recovered as z Ad Ab _ AA 2 k Ae 4m 2 1 A where 2 is the illumination wavelength Ag is the recovered optical phase and kris the wave number along the optical path Kreis 2005 Typical methods for extraction of the optical phase from acquired interferograms include phase stepping or phase shifting of the reference beam path length The optical phase map magnitude and directionality can then be solved for by acquisition of three or more interferograms with relative phase differences Kreis 2005 Phase stepping interferometry can be separated into temporal and spatial methods In this Thesis all comparisons are made with regards to temporal phase shifting which requires that the phase be stepped with time usually in a uniform manner within the whole field by using a modulator device Creath 1988 Greivenkamp and Bruning 1992 During this process a series of interferograms w
14. IMAQ Grab Setup IMAQ Grab Acquire IMAQ Close IMAQ Configure List IMAQ Configure Buffer IMAQ Start IMAQ Fit ROI IMAQ Get Buffer IMAQ Extract Buffer IMAQ Copy Acquired Buffer IMAQ Image To Array IMAQ Stop IMAQ Status IMAQ Set User LUT Pixel Manipulation Palette Vision gt Vision Utilities Image Management Palette External Display Palette Vision gt Vision Utilities Vision gt Vision Utilities gt External IMAQ Create Display IMAQ Image Bit Depth IMAQ WindDraw IMAQ Get Image Size IMAQ WindClose IMAQ Get Image Info IMAQ WindShow IMAQ WindSize IMAQ WindSetup IMAQ GetPalette Files Palette Vision gt Vision Utilities IMAQ Read File IMAQ Write PNG File IMAQ Write File IMAQ Write TIFF File IMAQ Get File Info IMAQ Write BMP File IMAQ Write JPEG File IMAQ Write JPEG 2000 File IMAQ Read Image and Vision Info IMAQ Write Image and Vision Info Installation of all additional LabVIEW modules is accomplished through automated installers on their respective data CDs 143 In addition two developed code libraries Read Excel Values llb and Dbl2usgned vi must be installed to allow the phase modulating system to read the optimized reference excitation parameters and convert double precision values to unsigned 8 bit precision respectively The latter library is required during the display and saving of processed interferograms due to limitations within the base IMAQ image output libraries
15. In this case the intensity of the recovered fringes 1s modulated by the zero order Bessel function of the first kind Stroboscopic illumination allows for an acquisition time which 1s on the order of the dynamic system motion As the illumination period becomes short relative to the motion of the system of interest the recovered interferogram 1s the same as that recovered with double exposure holographic interferometry and so 1s only modulated by a cosinusoidal term This results in the ideal case for optical phase recovery Kreis 2005 To allow for the capture of both dynamic and static systems the effect of stroboscopic illumination on phase modulating interferometry 1s presented with a focus on a sinusoidal reference excitation 7 3 1 General derivation of phase modulating interferometry with stroboscopic illumination The intensity distribution of a holographic interferogram as recovered by an imaging system is a function of the unmodulated DC component of an illumination intensity z x v the interference fringe contrast V x v and the interference phase distribution x y At one instant of time the full field intensity is of the form I x y glx y 0 7 x y cosl vlt 3 1 or I x y Iglxy Lig xy cosl xy 3 2 where Im x y describes the modulated amplitude of interference fringes Kreis 2005 Extraction of the phase distribution requires the solution of a system of equations due to the multiple unknowns
16. Inc Jnageware Surfacer Metrix Inc Montreal Quebec 2006 Montgomery D Applied statistics and probability for engineers 3rd ed Wiley New York NY 2003 101 National Instruments Specification sheet PCI 6713 National Instruments Inc Austin TX 2006 North Morris M VanDelden J and Wyant J Phase shifting birefringent scatterplate interferometer Appl Opt 41 668 677 2002 Osterberg P M and Senturia S D M TEST a test chip for MEMS material property measurement using electrostatically actuated test structures JMEMS 6 2 107 118 1997 Opto Diode Corporation Photodiode specification sheet OD 620L Opto Diode Corporation www optodiode com last viewed Nov 15 2006 Physik Instrumente L P Designing with piezoelectric transducers nanopositioning fundamentals Physik Instrumente L P Irvine CA 2005 PixeLINK Inc User Manual PixeLINK PL A741 PixeLINK Inc Ottawa ON Canada 2006 Pryputniewicz R J MEMS SUMMiT technology Worcester Polytechnic Institute Mechanical Engineering Department Worcester MA 2005 RadioShack RadioShack Corporation Fort Worth TX 2006 Rai Choudhury P ed MEMS and MOEMS technology and application SPIE Press Bellingham WA 2000 Ruiz P Huntley J Shen Y Coggrave C and Kaufmann G Vibration induced phase errors in high speed phase shifting speckle pattern interferometry Appl Opt 40 13 2117 2125 2001 S
17. Mode 1 Low Integrate N Trigger periods N x FPS shutter speed Mode 4 N Frame Capture Acquire N frames when the trigger signal reaches the camera Hardware Free Running Default Hardware Positive Negative defines which side of the signal pulse to trigger on This parameter should be Positive Sinusoidal Phase Modulation Negative Phase Stepping Delay acquisition for ms Default 0 ms Sets the value of N for the above modes Must be gt 0 for Modes 2 4 Sets the minimum number of reference excitation periods per phase step Default 1 Integration time of the camera at current settings 154 Frame Rate Trigger Frequency 50 00 Hz Cycle Time 20 ms Results Block Save Results Complete Path BC mages sr uctures2 bop Directory Diractery amp C images fei File Name Flle Name structures File Type bro kg Data Acquisition Count Data Geld Zon Count 3 2 Begin Save Sequence OF Maximum possible frame rate at current settings Frequency of the camera trigger signal Period of the camera trigger signal Displays the current save path amp most recently saved file Select the directory to save the acquired images to On the pop up selector be sure to click Select Cur Dir to set the directory properly Base save file name Type of image file bmp jpeg tiff png aipd Number of sequential data sets to automatically save Save the f
18. Revisiting a 90 year old debate the advantages of the mean deviation Manchester UK British Educational Research Association Annual Conference presented 2004 Greivenkamp J E and Bruning J H Phase shifting interferometers in Optical Shop Testing 2 ed Malacara D ed 14 501 598 Wiley NY 1992 _99 Guckel H Randazzo T and Burns D W A simple technique for the determination of mechanical strain in thin films with applications to polysilicon J Appl Phys 57 5 1671 1675 1985 Haasteren A and Frankena H Real time displacement measurement using a multicamera phase stepping speckle interferometer Appl Opt 33 19 4137 4142 1994 Haddad W McNulty I Trebes J and Anderson E Ultrahigh resolution x ray tomography in Nondestructive Evaluation Theory Techniques and Applications Shull P ed Marcel Dekker NY 2002 Hariharan P Oreb B F Eiju T Digital phase shifting interferometry a simple error compensating phase calculation algorithm Appl Opt 26 13 2504 2506 1987 Hsu T R MEMS amp Microsystem Design and Manufacture McGraw Hill NY 2002 Judy J W Microelectromechanical systems MEMS fabrication design and applications Smart Mater Struct 10 1115 1134 2001 Kinnstaetter K Lohmann A Schwider J and Streibl N Accuracy of phase shifting interferometry Appl Opt 27 5082 5089 1988 Ko
19. T T T S S g2600 0 l k ynys sj04 u09 Seg BuuebGuy poquop abeyo jO QUOD Blau e 059 Ge Ce 3 uogeoxg wu ose _ DSt oo eas oss 005 LA BUS AB a 5 Jabu eJawen a Y paa Mey wi x e apow uogeladg jo quo5 ugsav0ld jo guog JUSWN QSUT o aw Buissaz0ud XEW IN 8 Yujaxd Aq pap osd SJA Up paseg slebpoy Wey A0 Jog wesbo1 facts pied OVA P LIWE YUNXIA Zuten UOTeMpow aseyg ePlOsnUIs 10J STONUOJ save Results ings ftware controls Base camera sett Basic so ings Cl Sett Fig 116 CH 00S Sf OS Ser OOF SHE OGE Ste DE SC Oe Sec DR SAT OST Ser OOF St 0S Sc H l l l l l l l l l l l I l l l l I l l l l l L Wl cu paddeuy Pxid P EJ aouanbas anes uag Z yunop uogsmboy ee dwg 3WeN a4 Bumeg E dwq T Aoamd Save Results Red Sy 3 dwo5 SIBAJELIY Spur DuSsaOo ld geg SUlfGad MEG O8T 00T og 00t 08T l oo fp A op op o op D o o fh op E hu l Do c am CE 2521 O0T DUR oOo OO DU O00 tf EE pio and Output voltage controls yu D abueyp queuing UO 005 T DOUT woods 0000 A oooi emm Drun aqogs Image processing settings UU 00ST 4O0 OT 2000b DO U 7H 0000 T oana UOMEOX DUuLSaDDuUL jO gu0D aego DIUO Bag L Ca apow aauasayay SIUaIayay amb ca j uogenpaw DussaOp ld ae a de a5eyg paddeuyy Gap 0 das aseyd Buidda 5 asp ajqeug apo uogeadg Duo Bussa0Jg DU MISS 5 pn aw Gurssacq4 XEWHN 8 4
20. a multiple of 8 amp must be equal for proper image display None Every 2 Pixel Sets the pixels read in addressing mode None Decimate Decimate only displays every N pixel as defined in the pixel addressing value Set the primary excitation modulation frequency Hz related to the camera trigger and stroboscopic illumination frequencies as seen in the block diagram Normal operating range 50 100 Hz Sets the amplitude in Volts of the modulation signal sent to the illumination source The modulation automatically ranges from 0 02 V to 2 00 V The maximum change in illumination current assuming use of Thor Labs ITC 502 Sets the integration period of the camera and the length of the strobe signal as a percent of the reference excitation period Static measurement operation set to 14 Adjusts the relative phase between the illumination and excitation signals Default 0 153 Triggering Trigger On Trigger Mode Triggar Moda Mode 1 Low Integrate gt Trigger Type Trigger Typa Hardware K Trigger Polarity Triggar Polarity Positive F Trigger Delay d 0 00000 Trigger Parameter 0 00000 Excitation Period Count Integration Time 17 2 ms Enables reading of the trigger signal pin by the camera Mode 0 Low Trigger Acquires when the trigger signal reaches the camera for the set shutter speed Acquires while the trigger signal is low must be set for proper operation
21. a single crystal silicon wafer may exhibit a nonlinear spatial variation in residual stresses on the order of 20 MPa This variation illustrates the need for full field of view testing for accurate characterization of the fabricated Structures Ais 118 417 121 421 142 421 a 136 411 142 432 130 409 107 414 142 428 D e 133 423 ai 147 410 e biin l 127 416 gt 145 409 es ig gt 150 425 142 413 139 424 ge p 137 419 WAAN Residual stress Blaxtal modulus CMPa GPa Fig 2 4 Variation in residual stress and biaxial modulus across a silicon wafer Exponent Inc 2000 Much of this material property and fabrication property variation is due to the particular application of many materials used in MEMS structures Silicon and other materials had been commonly used in the integrated circuit industry for decades However their application as thin film structures results in numerous mechanical properties which must be known for each material where traditionally only electrical characterization was required Judy 2001 As with meso and macroscale structures critical mechanical properties include elastic modules yield strength fracture toughness fatigue resistance corrosion resistance creep behavior and residual stress Similarly the novel capabilities of MEMS devices allow for operation under conditions unknown in the macro world Micromirrors foun
22. at 10 illumination duty cycle Representation of K at 5 illumination duty cycle Representation of K at 5 illumination duty cycle Mask defined by the equivalency of K and Ke d 5 Mask defined by the equivalency of K and Ke d 15 Reference excitation amplitude and phase versus illumination duty cycle _yj 12 16 21 25 35 39 40 4 41 42 42 43 43 45 45 46 Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig 4 1 4 2 4 3 4 4 4 5 4 6 4 7 Dak 22 5 3 5 4 DD 5 6 Phase constant magnitude versus illumination duty cycle The optimal operation range shown is within d 14 to 18 5 and limited to 50 of the maximum magnitude Schematic representation of PMI system described in this Thesis Linnik configured interferometer Wyant 2002 Kreis 2005 PL A741 quantum efficiency curve peak 2 660 nm PixeLINK 2006 OD 620L spectral output showing peak and full width at half modulation points for determination of coherence length le Lle is determined to be 16 8 nm Opto Diode 2006 Voltage dependent displacement of the actuator used for phase modulation during the experimentation conducted within this Thesis Sample front panel of developed LabVIEW interface Sample of developed LabVIEW block diagram Recorded USAF 1951 negative glass target with group 7 outlined for containing the smallest reso
23. convergence and convergence rate was calculated numerically using MatLab 7 3 2006 using a 100x100 point grid and whole number duty cycles 1 2 etc As shown in Figs 3 2 and 3 3 K and K converge to their final values within six iterations of the power series for y 6 rad 0 5 rad and d 10 Iterations 10 Value 0 002 Magnitude 8 CH Iterations 10 Value 0 068 9 10 15 20 of iterations Fig 3 2 Convergence of K and K for y 6 rad 0 5 rad and d 10 20 ART gt LA Iterations 10 Value 5 48e 10 Rate of change CH CH 1 5 10 15 20 of iterations Fig 3 3 Convergence rate of K and K for y 6 rad 0 5 rad and d 10 Similarly convergence is reached for both the sine and cosine constants within 8 iterations of the infinite power series to a convergence rate of le 9 or better based on the maximum change found between subsequent iterations This convergence 1s a result of the rapid amplitude decrease of Bessel functions of the first kind at increasing orders As the Bessel function is a multiplicative factor subsequent iterations of the power series have increasingly small effects on the value of the phase constants Consequently all subsequent calculations are done at a power series limit of 10 to ensure convergence within the range of w and 0 of interest With the acceptable summation limit the behavior of the K and Ke can be investigated relative to the variable
24. increase the insensitivity to variations in phase steps has become a common practice with the acquisition of seven or more interferograms as the larger the data set the more accurately it can be windowed de Groot 1995a Schmit and Creath 1996 Ruiz et al 2001 In terms of performance the four bucket PSI algorithm has been shown to be a significant improvement over the three bucket algorithm with regards to vibration sensitivity at the cost of slightly larger memory requirements and slightly longer ee processing time Surrel 1993 de Groot 1995a Ruiz et al 2001 A five bucket algorithm analyzed by Hariharan et al 1987 has been shown to be minimally sensitive to small phase step errors at the expense of increased processing time and memory requirements While increases in the number of acquired data samples correlates with a decrease in sensitivity to phase step errors the number of data samples is typically limited by processing speed computer memory limitations and the limited phase shift range of piezoelectric transducer actuators Surrel 1993 Deck 2003 Spatial phase shifting interferometry differs from temporal phase shifting interferometry by simultaneously acquiring a set of phase shifted interferograms while preserving the measurement accuracies of temporal phase shifting These interferograms are either captured on multiple imaging devices or on a singular array that 1s later subdivided numerically Koliopou
25. increasing modulation frequency in the phase modulating interferometer due to a decreasing sensitivity to external vibration and modulator errors Sasaki 1990a Dubois 2001 The mean phase drift recovered by the PMI system operating at f 100 Hz correlates with the 10 1 to 11 6 mrad drifts demonstrated in Sasaki et al 1990b and Dubois 2001 at illumination wavelengths of A 760 nm and A 545 nm respectively 5 4 MEMS application The shape of and the time variant loading displacement of the prototype uHexFlex device is presented to demonstrate the applicability of the developed phase modulation system with MEMS characterization The wHexFlex device is being developed under Dr Martin Culpepper by Mr Shih Chi Chen to answer a growing need for low cost six axis millimeter scale positioning system for operation in devices including endoscopic scanners integrated alignment mechanisms in micro optic 91 devices and positioners that are used in SEMs Chen and Culpepper 2006 As shown in Fig 5 11 the wHexFlex consists of a central stage ranging from 280 um to 540 um in diameter in the studied devices attached to the surrounding substrate via an amplification flexure and micro scale thermomechanical actuators TMAs Fig 5 12 These TMAs provide in and out of plane actuator displacements that in combination cause displacement in one to six axes through the creation and control of thermomechanical stresses between stru
26. the design and construction of integrated microstructures and electromechanical systems Hsu 2002 MEMS Industry Group 2006 In development since the late 1960s MEMS has evolved from the integrated circuit industry as an effort to radically miniaturize operation scale over traditional mesoscale devices while increasing performance and reducing product cost Judy 2001 As an enabling technology MEMS revolutionized many industries by allowing development of smart products augmenting the computational ability of microelectronics with the perception and control capabilities of microsensors and microactuators and expanding the space of possible designs and applications MEMS Exchange 2006 According to MEMS Industry Group MEMS and MEMS related applications have rapidly grown 15 to 20 per year over the last decade into an estimated 8 3 billion dollar industry in 2007 as shown in Fig 2 1 with one third of that revenue in pressure and inertial sensors as presented in Fig 2 2 MEMS Industry Group 2006 _6 10 6 6 2 0 USD billions 202 2003 2004 2005 2006 2007 Fig 2 1 Worldwide revenue forecast for MEMS MEMS Industry Group 2006 Merite sg army Opti cat MEMS Other Sensors 22 12 RE MEMS Pressure Zi Sensors 4155 Other Actuators i Inertial Sensors GA Z Fig 2 2 Share of MEMS revenues by device 2007 MEMS Industry Group 2006 From Figs 2 1 and 2 2 it is apparent that MEMS de
27. the materials employed in 0 MEMS designs will allow for a wider acceptance of these systems MEMS Industry Group 2006 2 1 MEMS material property variation MEMS fabrication falls into three main families surface micromachining bulk micromachining and lithographic techniques Hsu 2002 Surface micromachining is based on the deposition and etching of different structural layers Starting with a silicon wafer or other substrate layers are grown and selectively etched by a wet or dry etch involving an acid or ionized gas respectively While surface micromachined components may someday grow to as many layers as is needed modern MEMS devices use up to five structural layers Pryputniewicz 2005 Sandia 2006 Bulk micromachining defines structures by selectively etching inside a substrate creating structures within a substrate Like surface micromachining bulk micromachining can be performed with wet or dry etches As this process involves the selective removal of material the particular etchant used 1s strongly dependant on the fabrication speed and quality requirements Wet isotropic etching provides the same etch rate in all directions while undercutting masking material Wet anisotropic etch rate depends on the crystalline plane orientation within the substrate material Consequently the lateral etch rate can be much larger or smaller than the vertical etch rate and resulting structures have angled walls with the angle being a func
28. y rad 0 rad d y rad 0 rad 12 000 5 166 0 290 6 813 0 083 7 000 0 500 S 0 400 S La 6 500 0 300 E S z 0 200 amp S 6 000 0 100 S e gt 5 0 000 5 500 0 100 d 0 200 d 5 000 0 300 ec ne ES O E E E E E g E O oN TO Gi CO N st O Gi O Cl fb N N N Duty cycle E Amplitude rad z Phase rad Fig 3 12 Reference excitation amplitude and phase versus illumination duty cycle A6 0 250 0 200 Optimal operation range 2 0 150 F ON bk 0 100 0 050 0 000 0 0 5 0 10 0 15 0 20 0 25 0 30 0 Duty Cycle Fig 3 13 Phase constant magnitude versus illumination duty cycle The optimal operation range shown is within d 14 to 18 5 and limited to 50 of the maximum magnitude The plots shown in Figs 3 12 and 3 13 highlight the highly nonlinear relationship between the illumination duty cycle with both the reference excitation amplitude and phase Though not a completely unexpected behavior given the mathematical system being solved this observation indicates that implementation of the sinusoidally modulated system requires care in the selection of the illumination duty cycle as l
29. 1 initializes the camera and voltage output devices and allows the operator to align and focus on their object of interest Figure F 2 begins the phase modulating once the user is satisfied with the optical focus and fringe contrast Lastly Fig F 3 describes how the wrapped phase and or optical modulation maps can be saved with the 4 phase shifted interferograms required to recreate them Textually this flow can be described as by the following l Enabling camera trigger signal and setting the base illumination to create a black unprocessed image feed signal Setting the modulation frequency illumination duty cycle and illumination amplitude modulation for viewing within the raw feed view The image should appear with excellent contrast while maximizing the optical intensity range within the raw feed stream This assumes that the focal and interferometric planes have been set coplanar and the object of interest 1s in focus Once all image settings appear appropriate the wrapped phase and or optical modulation maps can be viewed If the wrapped phase map appears to have a non smooth transition between its extreme values the modulation amplitude can be adjusted m the Operation Controls tab Small adjustments can be made to the modulation amplitude through the 146 spin control However optimization of the sine and cosine constants as outlined in Section 3 above will eliminate this need with a well calibrated linear pi
30. 12 2004 Graphically the system of equations can be solved by 1 the generation of a mask showing the locations of equivalency between K and Ke at a given illumination duty cycle 2 application of that mask to the corresponding map of either constant 3 estimation of the local maxima location with respect to amplitude and phase As shown in Figs 3 10 and 3 11 the masks generated in step 1 demonstrate a stronger dependence on the illumination duty cycle than may be expected given the periodicity presented in Figs 3 4 to 3 9 From Figs 3 10 and 3 11 lines of equivalency between the 44 planes described by K and K are shown at d 5 and 15 These lines indicate regions where the mean error is zero although determination of local maxima is required to optimize wand The complex forms of the 2 dimensional masks are suggestive of an underlying equation which may be applied towards the determination of wand in a closed form solution though that work is beyond the scope of this Thesis Eculvalency map d 6 Esc talian phase e x2 PO a Fig 3 11 Mask defined by the equivalency of K and K d 15 45 After appropriate calculation optimal values of yand can be determined as a function of the illumination duty cycle The values chosen for this Thesis are presented in Table 3 1 as well as in Figs 3 12 and 3 13 Table 3 1 Reference excitation amplitude and phase versus illumination duty cycle d
31. 5 If these stability requirements are met digital holographic methods have been shown to be 4 100 accurate Dorrio and Fernandez 1998 Mann et al 2005 20 White light interferometric techniques rely on the application of a short coherence length white light source instead of the more commonly used laser light sources as demonstrated in Fig 2 6 Wyant 2002 Kreis 2005 Traditionally laser light has been used as its long coherence length simplifies the procedures required for the creation of interference fringes as the interferometer path lengths no longer have to be matched as closely as if a short coherence length white light source is used However laser light interference fringes can appear within any stray reflections possibly resulting 1n incorrect measurements The strict optical path length matching requirements of short coherence white light systems eliminates this concern while providing a powerful measurement tool Wyant 2002 While homodyne phase shifting interferometry has proven extremely powerful and useful in many research and commercial systems possessing a measurement resolution of 4 100 the height difference between two adjacent data points must be less than 2 4 where is the wavelength of the light source Creath 1988 Wyant 2002 Ifthe slope is greater than 4 4 per detector pixel then height ambiguities of multiples of half wavelengths exist However the use of white light makes it possible to connect frin
32. 50 00 300 00 250 00 ii i 200 00 f 150 00 ti d II T UR Wu V 100 00 UU WI Hh thom DAT TK OTI 50 00 ths D 1 MN i RU d EL 0 00 g 0 800 1000 1200 Time s PSI Ag 91 04 mrad PSI f 2 Hz PMI f 100 Hz PMI Ag 12 19 mrad Linear PSI f 2 Hz Linear PMI f 100 Hz Fig 5 10 Optical phase drift over time recovered with phase stepping interferometry and sinusoidal phase modulating interferometry operating at f 2 Hz and f 100 Hz respectively with d 14 Under these operating conditions the PSI method exhibits a mean phase drift 7 5 times that demonstrated with PMI correlating with results presented by Kinnstaetter et al 1988 and Sasaki et al 1990b 90 Table 5 2 Optical phase map drift under phase stepping interferometry at f 2 Hz and sinusoidal modulating interferometry at f 10 Hz and 100 Hz Phase stepping interferometry f 2 Hz Ag 91 0 mrad o 75 6 mrad Phase modulating interferometry f 10 Hz Ag 40 1 mrad o 33 3 mrad Phase modulating interferometry f 100 Hz Ag 12 2 mrad o 8 91 mrad As seen in Fig 5 10 and highlighted in Table 5 2 the observed phase drift is greatest in the phase stepping interferometer over the 20 minute test period and is comparable to results presented in Kinnstaetter et al 1988 As predicted both the mean absolute phase drift and standard deviation decrease in a logarithmic manner with
33. NY 1991 Surrel Y Phase Stepping a new self calibrating algorithm Appl Opt 32 19 3598 3600 1993 103 Surrel Y Design of algorithms for phase measurements by the use of phase stepping Appl Opt 35 1 51 60 1996 Suzuki T Sasaki O Kaneda J Maruyama T Real time two dimensional surface profile measurement in a sinusoidal phase modulating laser diode interferometer Opt Eng 33 8 2754 2759 1994 Takeda M Ina H and Kobayashi S Fourier transform method of fringe pattern analysis for computer based topography and interferometry JOSA 72 1 156 160 1982 Thor Labs Laser diode combination controller user s manual ITC502 Thor Labs Newton NJ 2006 Tonner P and Stanley J Supervoltage Computed Tomography for Large Aerospace Structures in Nondestructive Evaluation Theory Techniques and Applications Shull P ed Marcel Dekker NY 2002 Van Arsdell W W and Brown S B Subcritical crack growth in silicon MEMS JMEMS 8 3 319 327 1999 Veeco Metrology Group Sloan DekTek calibration standards set Veeco Instruments Inc Tucson AZ 2002 Wyant J C Use of an ac heterodyne lateral shear interferometer with real time wavefront correction systems Appl Opt 14 11 2622 2626 1975 Wyant J C White Light Interferometry Proc SPIE 2002 Zhang H ntroduction to MEMS Lecture Notes Institute of Microelectronics im
34. Trigger on Mode Low Integrate Type Hardware Polarity Positive g Fig F 1 Turn on the developed code and ensure that the raw camera feed is ready for processing 148 Set DC Illumination to no output Ensure that the unprocessed feed has a good image quality and maximizes the gray scale range Raw Feed ok Raw Feed off Reference Excitation on Adjust excitation settings Adjust settings Enable Phase modulation Enable Processing Fig F 2 Remove the DC component of the illumination signal and begin modulation output control for image processing 149 Wrapped Phase Optical Modulation Select Save Directory Select File Type Select of sequential data sets to save Stop Program Fig F 3 View the wrapped phase map or the optical modulation map and save the results to the selected directory End the program using the implemented program stop 150 APPENDIX G Detailed description of developed user interface or in the optional stop when an error occurs If the program is ended any other way the camera will not be properly released and so will not run again until LabVIEW is restarted Program Stop Stops the program Only end the program with this button Program Error A Displays that an error has occurred during the current operation Control Block Instrument Control Camera Trigger Begins sending a trigger signal to the camera attached to lt E Cha
35. al sampling intervals can range from 50 to 100 nm Caber 1993 de Groot et al 2002 To obtain the location of the peak fringe contrast and hence the surface height information this irradiance signal is detected using an imaging array The signal 1s sampled at fixed intervals as the sample path is varied The signal is then digitally filtered and rectified by square law detection The peak of the filter output is located and the vertical position corresponding to the peak is noted Interpolation between sample points can be used to increase the resolution of the instrument beyond the sampling interval This type of measurement system produces fast non contact true three dimensional area measurements for both large steps and rough surfaces to D nanometer precision Wyant 2002 With this processing 0 1 nm accuracy levels have been demonstrated Zygo Corporation 2006 2 4 Benefits of phase modulating interferometry While the invention of phase shifting interferometry PSI was a major breakthrough in the field of interferometry by providing a method to measure the optical phase to an unprecedented accuracy this Thesis proposes phase modulating interferometry PMI for the nondestructive evaluation of MEMS devices Creath 1988 Schwider 1990 Originally proposed in Sasaki and Okazaki 1986a 1986b and expanded in Dubois 2001 this method answers some of the limitations inherent in classic homodyne and heterodyne tec
36. al line if the physical system becomes more complex and or the motions more uncertain In the case of pure torsional vibration viewed along the length of a shaft the surface line facing the imaging array will appear as if 1t was a nodal line due to the orthogonal motions of the structure To record cosinusoidally modulated fringes during dynamic measurements a short exposure time relative to the frequency of motion 1s required Stroboscopic illumination is commonly used in meeting this need The interferogram can then be exposed over multiple periods of motion until the total required exposure has been reached To accomplish this with phase modulating interferometry the charge storage period of the imaging array is redefined as a short time span around a particular point in the reference excitation for each image For added simplicity in the derivation it is assumed that these points are in quadrature with respect to the reference excitation period As a result the time dependent intensity is then integrated by Aju pl At 42 I I odt 3 13 7 fpo 3 13 DI At 4 2 where T is the reference modulation period Ar is the acquisition or exposure time of the imaging array and p defines the frame number 1 2 3 or 4 This means that the illumination will occur at the quadrature points of the reference excitation signal As shown in Fig 3 1 there are four interferograms acquired during each modulation period during each strobos
37. an be written as Eq B 9 N agta er ayaye s B 9 for simplicity The removal of the third order approximation term simplifies the form of Eq B 9 although its effect on future calculations must be considered Following the procedure outlined in Dubois 2001 the mean error and mean squared error can be extracted from Eq B 9 While accomplishing this a third order accurate approximation must be maintained for consistency with the previously indicated Taylor series Equations B 10 and B 11 show the resultant mean and mean squared error functions 110 Ska E l 2 2 el aoa n ie lai 2aqay Lu agaj EM B 10 and 2 alc B 11 eil Direct solution of Eqs B 10 and B 11 assumes knowledge of the magnitude of additive error within the recovered signal through the mean and mean squared 7 term To determine the independent contributions of the phase constants and optical phase on the additive error the right hand side of Eq B 5 must first be investigated The right hand side of Eq B 5 can be rewritten as shown in Eq B 12 This allows for calculation of 77 as a function of the optical phase through the linear frame combinations amp and lt and the resultant additive error contributions N and Nc by As dis 1 n tan B 12 1 gt C As before this term can be approximated by a third order series MathCad 2001 and squared to form two dependant equations B 13 and B 14 respecti
38. and recover the carrier frequency signal without aliasing Kreis 2005 However measurement accuracy of both spatial and temporal heterodyne interferometry has been found to be on the same order as temporal phase stepping interferometry though typically requiring greater experimental complexity and processing time Dorrio and Fernandez 1998 Digital holography uses a digital imaging system to record holograms for later numerical reconstruction Kreis 2005 The angle between the object and reference wavefronts must be controlled to produce holograms which are resolvable by a given imaging system Recovery of the object surface requires the numerical reconstruction of the wavefront at the image plane by use of the Fresnel transform Kreis 2005 The image plane or observation plane appears at the coordinates where the real image can be reconstructed At this plane the wavefront reflected from the object of interest converges to a sharp image Shape information can then be extracted from the calculated object wave field Phase shifting digital holography involving the capture of three or more digital holograms with a mutual shift in the reference wave can be used for shape characterization of MEMS Furlong and Pryputniewicz 2003 The primary advantage to the phase shifting approach is the elimination of the DC component and twin image within the reconstructed wave field though at the expense of an increased system stability requirement Kreis 200
39. and Ke of 0 21 and 0 20 respectively at d 14 to zero as the stroboscopic duty cycle approaches zero or 25 As expected from Eqs 3 18 and 3 19 the magnitude of the sine and cosine constants at a given duty cycle is sinusoidally related to the excitation phase Similarly _43 the magnitudes of the phase constants are nonlinearly related to the excitation amplitude due to dependence on Bessel function of the First Kind Additionally as shown in the sine constant term the magnitude decreases more rapidly at lower excitation amplitudes shifting the relative magnitudes of local peaks From these observations it becomes apparent that the calculation of wand should be done independently at each illumination duty cycle of interest The periodic nature of K and K will lead to multiple points of intersection between the surfaces over the 0 27 range resulting in the appearance of many local maxima For simplicity this Thesis solves for a combination of parameters that indicate the location of a local maximum that requires a minimal value of amplitude in the reference excitation This is advantageous at higher reference excitation frequencies with respect to the jerk experienced by the reference mirror as the jerk experienced under sinusoidal modulation will scale by o Due to the complex nature of the sine and cosine constant terms optimal values of wand 0 were solved iteratively rather than in a closed form solution using Mathcad Mathcad r
40. andia National Laboratories www sandia gov last viewed Nov 19 2006 102 Sasaki O and Okazaki H Sinusoidal phase modulating interferometry for surface profile measurement Appl Opt 25 3137 3140 1986a Sasaki O and Okazaki H Analysis of measurement accuracy in sinusoidal phase modulating interferometry Appl Opt 25 3125 3158 1986b Sasaki O Okazaki H and Sakai M Sinusoidal phase modulating interferometer using the integrating bucket method Appl Opt 26 1089 1093 1987 Sasaki O Takahashi K and Suzuki T Sinusoidal phase modulating laser interferometer with a feedback control system to eliminate external disturbance Opt Eng 29 1511 1515 1990a Sasaki O Okamura T and Nakamura T Sinusoidal phase modulating Fizeau interferometer Appl Opt 29 512 515 1990b Schmit J and Creath K Window function influence on phase error in phase shifting algorithms Appl Opt 35 28 5642 5649 1996 Schwider J Advanced evaluation techniques in interferometry in Progress in Optics Wolf E ed Elsevier Science NY 28 271 359 1990 Shull P ed Nondestructive evaluation theory techniques and applications Marcel Dekker Inc NY 2002 Sirohi R S and Kothiyal M P Heterodyne and phase shifting interferometry in Optical Components Systems and Measurement Techniques Sirohi R S and Kothiyal M P eds Marcel Dekker
41. are and software modules indicated in Section 4 2 1 The main body is presented in Fig D 1 and commented to highlight the functionality of major code blocks Case blocks and operational event structures are presented in their default operational state within the completed block diagram LabVIEW case structures are equivalent to the If then statements found in other programming languages Figures D 2 D 6 display alternate forms of each case structure with functional descriptions of each structure Event cases which provide responses to changes on the user interface are shown with functional descriptions in Figs D 7 D 22 The function of individual structures is described with each event case 119 GPO 1 Polarity vs GPO 1 Param 1 00 PO II mie True Display raw image feed False Close window Transform 16 bit 2 D Pa image array to double Gh e D6 Rm r H q i True Save results False Reset save function to off Feedback nodes to pass data between program loops S Feedback reference data to following data loops Iculate Ref values a function Save sequential data set s based on UI settings Case Structures emm a daks KS bere Compute Straight Phase Num Der cb Sine RH gt E Numerator v Fig D 2 Block diagram case structure set 1 Group 1 Calculates the numerator and denominator terms used in the arctangent wrapp
42. asing performance and decreasing the cost of the final product These goals evolved from the success of the IC industry with their bulk fabrication techniques and their incredible economies of scale Judy 2001 Today MEMS has come to represent an entire field of systems in the nanometer to millimeter size excepting IC devices where the smallest characteristic dimension is on the order of a micron Judy 2001 Hsu 2002 Pryputniewicz 2005 Kuppers et al 2006 The scale of these devices from 10 nm to 1 mm is shown in Fig 1 1 relative to other common microscale and mesoscale systems Scales and Dimensions P w 3 N 4 Gn H SN aus Y d a kg Das WEI S gt SC gt gt oe sS CG gt gt Kai 1A Inm lum mm Im MEMS Gesten wafer thin films beams membranes optical lithography integrated circuit limit ooo mmm m m nanotechnology precision machining chemistry molecular biology Fig 1 1 Scale of various microscopic systems with comparison to MEMS Zhang 2004 During the development of early MEMS devices it became apparent that bulk continuum material property data could no longer be applied when working at scales 5 where crystalline structure and thermo mechanical fabrication effects became dominant factors At the microscale these effects create variations in material properties between and within fabrication batches Osterberg and Senturia 1997 Rai Choudhury 2000 Similarly
43. ast at the surface of the gold film 4 removal of carrier fringe pattern from the full field of view 5 adjustment of operation properties within developed control system _65 a wavelength 620 nm b modulation frequency 50 Hz c stroboscopic amplitude 0 25 V d illumination duty cycle 14 e trigger mode Low Integrate f trigger polarity Positive PMI Negative PSI Both phase modulating and phase stepping interferometry techniques were used for shape extraction to demonstrate the correspondence of both methods on the developed system Before experimentation the displacement rate of the phase modulator is verified to be 100 58 nm V Hariharan et al 1987 Determination of the optical phase is similar in each technique The implemented systems require the acquisition of four interferograms at known relative phase values These interferograms seen in Fig 5 4 represent an interferograms acquired at 1 33 radian phase shifts in phase modulating mode and a 7 2 phase shift under phase stepping 66 Ti 0 0 000 rad l 0 0 000 rad l Lo 0 1 333 rad 0 T 2 rad 13 s 0 2 666 rad 0 n rad l4 l 0 4 000 rad 0 37 2 rad a b Fig 5 4 Interferograms acquired with phase modulating interferometry a and with phase stepping interferometry b 67 Extraction of the optical phase requires the arctangent calculation of a sine and cosine term in both techniques Phase modulating int
44. ate an RMS difference of 0 256 nm and similar mean absolute deviations However the significant difference between the standard deviation and mean absolute deviation values indicates the presence of multiple outliers in the data set These outliers may be due to dust particles on the reference flat Table 5 1 Shape measurement comparison between sinusoidal modulation and phase stepping Sinusoidal modulation pping LA Zuel 0 256 nm o 18 262 nm o 18 518 nm D 0 015 nm D 0 018 nm 275 To verify the full field correlation of the two methods a difference map is generated and presented in Fig 5 8 This difference map is found by subtracting the shape information obtained using phase stepping interferometry from that obtained with sinusoidal phase modulating interferometry nm kuch NO 0 1 5 i on F 5 H 0 1 CS a 07 5 07 10 39 0 4 1 74 2 32 1 74 0 5 1 16 1 16 0 58 Location mm 0 00 0 58 Location mm Fig 5 8 Shape difference map between sinusoidal modulation and phase stepping Both measurements performed at the operational frequency of f 10 Hz The sinusoidal variation having amplitude of 0 4 nm and frequency of 3 4 cycles mm is attributed to a combination of the mean and mean squared errors in both the PMI and PSI systems These errors are related to the phase modulation parameters and appear with a spatial frequency equal to twice the optical frequency as explo
45. ated at a frequency above 0 Hz 133 amera control settings Attached camera id numbers Operating camera id number Error flow Cul Wrapped Phase Map Modulation S Fig D 15 Event Structure 5b this event displays the unprocessed camera feed but does not allow for image processing when either the camera trigger signal is not output or the modulation frequency is set to 0 Hz 134 amera control settings Attached camera id numbers Operating camera id number Error flow Deeg Modulation rapped Phase MapJLTE h Wrapped Phase Map Fig D 16 Event Structure 6 this event reads the current value of the Wrapped Phase Map and Modulation buttons from the user interface 135 amera control settings Attached camera id numbers FEATURE FLAG MANUAL Ox00000002 v Operating camera id number ees f Error flow Fig D 17 Event Structure 7 this event sets the gain value of the acquired images based on the currently selected value on the user interface 136 amera control settings FEATURE FLAG MANUAL Attached camera id numbers Operating camera id number Error flow TT E Fig D 18 Event Structure 8a this event stops the current image feed to set the pixel addressing mode and value as explained Appendix F It then re starts the feed stream and re opens any image displays if previously enabled 137 amera control settings FEATURE FLAG MANUAL At
46. ay exist in the data set The standard deviation o is equal to the square root of the variance of the data set The standard deviation measures the spread of a data set from its arithmetic mean value or its overall uncertainty In a large population 75 of all data points will lie within Ze Larger values of standard deviation indicate that a given data may suffer from a high amount of noise or other experimental errors Itis calculated by 5 8 which is necessarily always greater than or equal to zero due to the squared difference term The mean absolute deviation is an alternative to traditional standard deviation calculations As shown in Gorard 2004 the standard deviation typically over estimates the statistical dispersion of a data set due to the use of the squared difference term The mean absolute deviation as given by RES m l 5 9 typically uses the arithmetic mean of a data set and can be shown to be always less than or equal to the standard deviation Gorard 2004 Ifthe arithmetic mean is found to be an inappropriate measure of the central tendency of a data set it can be replaced by the 279 RMS value within the presented equation It has been shown that for an experimental data set with any level of randomness the mean absolute deviation more efficient than the standard deviation for distributions other than perfect normal and is closely related to a number of other useful analytical tech
47. be copied with excite xls to a readable working directory on the host computer Excite xls contains the modulation amplitude and phase information required to operation in a stroboscopic duty cycle range of 0 25 and is only read during operation of the phase modulating interferometer The location of this file must be updated within the code block unless saved to the default location of C Labview Controls on the host system The stroboscopic modulation parameters within the developed code assume the use of the ThorLab s ITC 502 laser diode controller In the event a different laser diode controller is needed the default voltage to current proportion set in the voltage control section of the developed code presented in Fig DI must be adjusted from its default value of 20 mA V to ensure proper operation Similarly Fig D 22 contains the linear displacement rate of the attached piezoelectric device calibrated using an algorithm presented in Hariharan et al 1987 This parameter must be adjusted based on the currently attached piezoelectric actuator where units are specified as nm V With this installation procedure the developed control systems can be run as outlined in Appendices F and G 145 APPENDIX F Standard operation flow chart Presented in Figs F 1 to F 3 1s an operational flowchart for nominal operation of developed software and user interface as described in Appendices C and G Procedurally Fig F
48. ckaging procedures Testing issues must be included in the overall design of the device package in the early phase of development to minimize the final cost of the device Modern testing can be as much as 33 of the overall development cost of a MEMS device MEMS 8 Exchange 2006 Testing can and must occur at multiple stages of MEMS development as illustrated in Fig 2 3 This figure presents a typical MEMS development cycle with testing requirements at each stage of the design process These tests include materials characterization during fabrication and accelerated lifecycle testing to ensure the longevity of the developed components L zeg web Lem reliability bag Fil m prope rtj as a batch consistency Ki aw Independent lab standards Accelerated testing Fol Validation and test shock environment accumulated cycles Marketing Failure prevention maa and redesign Fig 2 3 MEMS development cycle Exponent Inc 2000 A major concern within these testing procedures is the unknown reliability of many MEMS devices due to uncertainty in the long term stability of these devices As a consequence of scaling in micro components and fabrication variability bulk continuum material property data are not applicable to MEMS devices where crystalline structure and thermo mechanical fabrication effects are dominant factors Only greater knowledge of the basic material properties and failure mechanisms of
49. clear what displacement characteristics the device would exhibit due to a lack of prior testing on devices exhibiting this degree of experimental damage The interferometric system was configured for operation as with the static tests under a modulation frequency of 100 Hz The uHexFlex was powered by an HP E361 18 voltage limited to 20 VDC the nominal safe voltage limit for the system Due to the limited resolution of the power supply 6 current amplitudes were investigated as indicated in Table 5 3 while allowing the voltage to rise as needed Table 5 3 uwHexFlex quasi static loading conditions Applied Voltage V Applied Current A 5 7 CA E a 90 Instantaneous shape was recovered at each data point for later analysis with the displacement of the central stage measured relative to the base substrate connected to the active TMA as shown in Fig 5 17 Reference points wi Fig 5 17 Relative displacement points on central stage and substrate connection of active TMA The relative displacement of the central stage was then plotted to determine a displacement voltage relationship As shown in Fig 5 18 the recovered displacements are near linear with respect to applied voltage with a characteristic resolution of 0 75 A mV The nominal displacement behavior of 1 0 A mV is also shown for comparison Chen and Culpepper 2006 90 gt Ge CH gt iN D
50. copic illumination amplitude peak 0 p Amplitude z Object or Reference a 8 Excitation i A Illumination on amp Acquisition oft Set Set 2 Fig 3 1 Quadrature acquisition with stroboscopic illumination Kuppers et al 2006 Through appropriate integration presented in Appendix A based on Eq A 8 the intensity recovered at the recording element becomes 335 I le 1y cos d Jo y 7 o Ir nmp Jom EML oos EI TN m cos 2m0 sin m 27d B14 3 14 Jami SSES 00 2m 1 M sing SI JIT m 0 sinf 2m Es d sin 2m 1 27d for each acquired frame where the stroboscopic illumination duty cycle d is related to both the exposure time and the period of the reference excitation by do 3 15 based on an integration procedure defined in Dubois 2001 This form of the acquired intensity equation is independent of the reference excitation frequency or acquisition period which is advantageous during optimization of the reference excitation amplitude and phase considered in the following Section Extraction of the optical phase requires the solution of a system of no less than 4 equations concerning 4 acquired interferograms The optical phase of the object of interest can be calculated through a linear combination of 4 acquired frames given by Zs 1y h 13 14 sinf Ke y 8 3 16 and 2e Ly tly 13 14 cosl K v 8 3 17 where K w 0 and K w 0 are the sine and cosine phase cons
51. cquired images based on the currently selected value on the user interface Event structure 8a this event stops the current image feed to set the pixel addressing mode and value as explained Appendix F It then re starts the feed stream and re opens any image displays if previously enabled Event structure 8b this event sets the pixel addressing mode and value as explained Appendix F when the camera feed has not been enabled Event structure 9a Event Structure 9a this event stops the current camera feed to alter the region of interest ROI within camera view both in size and location ROI values must be multiples of 8 and width height must be equal for proper display and processing No error checking has been implemented to ensure that the selected ROI is within the imaging array area Event Structure 9b this event alters the region of interest ROT within camera view both in size and location when camera feed is not previously enabled Restrictions from figure D 20 apply Event structure 10 this event calculates the modulation and synchronization parameters for output voltage generation based on current UI settings and data read from the excitation parameter file Default Excel file is excite xls Turn on the developed code and ensure that the raw camera feed is ready for processing Remove the DC component of the illumination signal and begin modulation output control for image processing X 133 134 135 136
52. ctural silicon layers separated by an insulating silicon dioxide layer Chen and Culpepper 2006 Measurement Arm Flexure f hinge 7 AE brn Fig 5 11 Scanning electron microscopy image of a prototype wHexFlex device courtesy of Shih Chi Chen MIT 972 Negative Terminal lt lt S102 layer Si layer Positive Terminal Sam Fim BAGG 26 AUG B4 ee SE e e Fig 5 12 Layered TMA structure of uHexFlex device viewed through a scanning electron microscope courtesy of Shih Chi Chen MIT While these devices are currently in the prototype stage the research objective 1s the creation of on site positioning within enclosed spaces Previous testing has found the uHexFlex to have a nominal displacement resolution of 1 A mV with a standard deviation of 8 nm due to uncertainties in the thermal materials and actuation control Chen and Culpepper 2006 Currently a need exists for full field shape characterization and bidirectional quasi static displacement testing for further characterization and system development 5 4 1 Shape measurement Shape measurement of the wHexFlex device was conducted with both phase modulating and phase stepping interferometry Both the PMI and PSI system have been implemented and characterized on the same Linnik interferometer with controls from the LabVIEW programming environment under functionally identical interfaces Due to 83 the stage of developm
53. d on the DigitalMicromirror Device from Texas Instruments Inc commonly operate in excess of 1 trillion of cycles without failure Douglass 1998 However this total number of accumulated actuation cycles extends far beyond what has been required in macro applications As with ES macroscale devices microscale devices can experience fatigue and wear from contacting surfaces during individual actuation cycles However little information about fatigue or wear 1s available under these conditions for either macro or MEMS devices As a result lifetime predictions are device specific and due to fabrication variations are not always largely validated by statistics Rai Choudhury 2000 2 2 Nondestructive evaluation of MEMS Nondestructive evaluation NDE is used to evaluate prototype designs during product development to provide feedback for process control during manufacturing and to inspect the final product prior to service without affecting the object s future usefulness Shull 2002 The basic principle of NDE 1s finding and measuring physical phenomena that will interact with and be influenced by the test specimen without altering functionality Functionally choosing the proper NDE method from all available techniques requires considering of the following factors 1 understanding the physical property to be inspected 2 understanding the physical properties of the NDE methods 3 understanding the interaction between
54. de developed for the interferometric system with descriptions of individual code sections 29 f 4 2 1 Installation The developed software was written in LabVIEW 7 1 with the NI IMAQ 3 1 IMAQ Vision for LabVIEW and NI Measurement amp Automation Explorer 4 0 2 MAX packages The NI IMAQ IMage AcQuisition package expands the base LabVIEW image acquisition processing saving capabilities NI MAX includes features for configuring and testing input output capabilities as well as storing scaling calibration and channel aliasing information important for achieving short time to first measurement and for maintaining and troubleshooting test systems without additional programming Performance increases with MAX because multiple threads can access the NI DAQmx driver at the same time as long as those threads are executing different NI DAQmx tasks Functionally this allows multiple channels to execute synchronously on multiple channels of the same PCI card LabVIEW 7 1 2006 Direct camera control is accomplished through the camera s FireWire port and TTL signals from the PCI 6713 FireWire control is based on VIs provided by PixeLINK These supplied VIs require the NI IMAQ 3 1 package due to their reliance on high end image processing functions not available in the base LabVIEW 7 1 installation package This Thesis has adapted these VIs for simple parameter modifications within the operating LabVIEW environment It 1s sugg
55. ding substrate of 2 1 um although this is 3x less than that demonstrated by the medium sized uHexFlex device The central stage of this device was found to be flat to within o 10 nm after removal of all tilt effects A difference analysis was conducted to compare the recovered shape maps obtained with the PSI and PMI systems As with the analysis presented in Section 5 2 this involved the subtraction of the shape measurements obtained with PSI from those obtained with PMI The difference map was then found to have an IQR of 0 201 nm o 0 305 nm and D 0 048 nm These results readily compare to the comparative results obtained during prior characterization of these systems further indicating the reliability of the acquired data set 99 5 4 2 Quasi static testing To further demonstrate the applicability of phase modulating interferometry quasi static analysis was conducted on a 375 um central stage uHexFlex device Mr Chen the lead uHexFlex researcher had expressed interest in the use of this system for bi directional measurements as prior testing had been limited to unidirectional studies Chen and Culpepper 2006 Unlike the previously tested devices the uHexFlex device tested suffered thermomechanical damage to five of the six TMA structures until failure of those TMAs However the substrate and device itself remained intact and therefore potentially available for an additional time variant loading experiment However it was un
56. e Du edu cn Peking University Peking China 2004 Zygo Corporation www zygo com last viewed December 2006 104 APPENDIX A Integration of instantaneous intensity function As presented in Section 3 the instantaneous intensity of the optical map can be described by I t Ip t Ly t cosl y sin a t 8 A 1 removing all spatial dependence terms for simplicity The derived equation cannot be directly integrated over the acquisition time of the imaging array due to the nested sine function By first extracting the additive terms through the trigonometric identity cos X Y cos X cos sin X sin Y A 2 the nested sinusoid term can be treated independently Application of Eq A 2 results in a new form of the instantaneous intensity function of the form cos cos y sin t ul I t Ig t Im t f sin sin y sin t 8 A 3 Through this new representation the additive terms can be treated independently According to Abramowitz and Stegun 1970 a sine function nested within either a cosine or sine function can be replaced with an infinite power series index m consisting of Bessel functions of the First Kind multiplied with a cosine or sine term respectively As seen in Eq AA 105 cos X sin Y Jo X 2 S Liz LX cos 2k Y m and A 4 sin X sin Y 2 Voms X sin 2k 1 y A these identities can be applied to Eq A 1 and so create an integratable in
57. e Kreis 2005 Application of a stroboscopic illumination signal converts the Jo fringes into a sinusoidally modulated fringe pattern greatly simplifying extraction of the optical phase map due to the complexity of the Bessel function term The focus of this work is the derivation and implementation of the phase modulating interferometric system that uses both stroboscopic illumination and a reduced exposure period The addition of these physical attributes will allow for use of the PMI system in both dynamic and static studies 26 3 THEORETICAL ANALYSIS OF PHASE MODULATING INTERFEROMETRY Sasaki and Okazaki 1986a and Dubois 2001 have presented the derivation of a phase modulating system using the 4 integrating bucket method and a sinusoidal reference excitation This approach assumes a constant illumination source and requires multiple excitation periods to fully capture the modulation waveform The latter limitation is based on the recording media used due to the finite time required between interferogram acquisition periods This prevents the continuous capture of a single reference excitation waveform particularly at the rapid reference excitation frequencies required for rapid display of the wrapped phase map Additionally this approach 1s limited with regards to dynamic systems as it requires an exposure time which may be long compared to the period of excitation This situation is known as time average holographic interferometry
58. e stepping interferometry under both low and high frequency sinusoidal modulation The qualified system has been applied for both shape measurements and quasi static testing of the uwHexFlex device under a 100 Hz modulation frequency Due to its prototype development stage multiple configurations were available for shape measurements with the medium sized system configured for single axis testing All samples tested had been previously cycled to failure and suffered distortions from their nominal planar configuration Tilt and deformation from the substrate material ranged from 1 7 um on the smaller devices to 7 4 um on the moderately sized systems To verify the reliability of these results the largest uHexFlex device was qualified on both the phase stepping and the phase modulating systems and found to have a IQR of 0 201 nm o 0 305 nm and D 0 048 nm between the two techniques further indicating the reproducibility of the results obtained through phase modulating interferometry Quasi static testing was conducted with a damaged wHexFlex to qualify its out of plane motion relative to the system normal As presented the damaged device provided a linear displacement of 0 75 A mV with a mean experimental deviation of 27 1 nm compared to nominal motion of 1 00 A mV and standard deviation of 8 nm Based on an interview with the developer Mr Chen this difference is within the expected variation of the device under these conditions For future
59. ed optical phase rad actual modulation step during phase stepping ideal modulation step during phase stepping Acquisition time sec optical phase error rad strain component in X Y plane fringe contrast wavelength of illumination source primary diode output wavelength tangent of the optical phase with additive noise contribution mirror excitation phase rad standard deviation of data set x stress component in X Y plane interference phase distribution rad reference phase modulation rad linear combinations of four sequential frames relative phase between illumination and reference modulation reference mirror excitation frequency rad angular frequency of illumination illumination camera exposure duty cycle natural frequency of an unloaded piezoelectric actuator natural frequency of a piezoelectric actuator with additional mass orthogonal coordinates SA MN eff n SS Nj N2 N3 N4 Np P t f min Au Xk x y CD CMOS D E Eo Er Ez 3 ba Ep G I Ly Lo 13 L4 Lp g wave number 27 4 wave vector wave number taken in the z direction optical path length reference arm coherence length of illumination source line length of the USAF 1951 target power series index effective mass of a piezoelectric actuator equal to 1 3 the mass of the ceramic stack general Gaussian zero mean additive noise contribution total number of elements in data set x additive noise on sequential frames
60. ed phase map calculation The case shown in the block diagram calculates the numerator and denominator terms used for calculation of the relative wrapped phase map Group 2 When true displays the middle row or column of the displayed wrapped phase map or optical modulation map 21 4 a False el ek EEN a E rapped Phase Fig D 3 Block diagram case structure set 2 Group 3 Calculates the optical modulation of within the imaged region of interest Normalizes and displays the resulting map with an 8 bit resolution in window number 3 If the modulation is low the display will appear with a low signal to noise ratio If the optical modulation display is set to off window 3 is automatically closed and the modulation is not calculated Group 4 Calculates the wrapped phase map using a n r arctangent calculation within the imaged region of interest Normalizes and displays the resulting map with an 8 bit resolution in window number 2 If the optical modulation is low the display will appear with a low signal to noise ratio If the wrapped phase map display 1s set to off window 2 is automatically closed and the wrapped phase is not calculated 22 ee sy oe lr Soy Se ee ee ee ee ee aaa k a a T in A Deele Save SE Sc E bel TR a bei heir Wek eee CC ee ae ev ew Ze Fig DA Block diagram case structure set 3 Group 5 When true pre calculates terms used in calculati
61. efines the charge storage period of the imaging sensor as one quarter of the reference excitation period Four images are then recorded through integration of the time varying signal during the four quarters of the modulation period T allowing for recovery of optical phase As demonstrated in Dubois 2001 this approach provides a mathematically complex result describing the recovered illumination intensity map During the study of static structures the resultant phase map remains cosinusoidally modulated allowing for sub fringe measurement resolution However in dynamic studies a long exposure time compared to the period of sample motion causes the acquired fringe pattern to become modulated by the zero order Bessel function of the first kind These fringes will have relatively low contrast compared the cosinusoidally BA modulated pattern as the dark centers of the fringes correspond to zeros of the Bessel function Jo while the intensity of the bright fringes degrades with distance from the nodal line in a vibrating structure Physically these changes in fringe contrast result from the motions of the system of interest As with static structures some regions will reflect more light towards the recording media during their motion As a result these regions will appear brightest A nodal line in a plate or other simple structure does not move and so will be providing light during the full acquisition period Other regions may appear as a nod
62. ent multiple sizes of the uHexFlex device were available for study However prior to testing all samples had previously been subjected to thermal loading until failure and were believed to contain distortions outside of their operating parameters For data comparison shape measurements were recorded using both interferometric methods on the 540 um diameter uHexFlex device to maximize the number of pixels imaging the central stage At this size and magnification the central stage could not be imaged with all substrate connections Consequently this device was placed so that the central stage and 2 of the 6 TMAs could be interferometrically imaged As with the system qualifications carried out in Section 5 1 to 5 3 measurements were carried out using a 4x magnification with a CMOS camera containing 1280 x 1024 active pixels at 8 bit digitization with a region of interest All tests were conducted at a 1000 x 1000 pixel ROI centered on the imaging array Measurements taken require 1 performing high resolution phase modulation calibration verifying the displacement rate of 100 58 nm V Hariharan et al 1987 2 optimizing the beam ratio between the reference and objective arms to maximize the fringe contrast 3 adjustment of the interferometric and focal planes to maximize contrast over the entire device 4 removal of any carrier fringes from the substrate 5 adjustment of operation properties within developed control system a wavele
63. erferometry calculates the sine or numerator as Xa 1 1 4 13 Ly 5 2 and the cosine or denominator as Xo L 1 13 14 5 3 as shown in Section 3 where to 74 represent the interferograms acquired at the quadrature points of the sinusoidal modulation signal Similarly phase stepping calculates the sine and cosine terms with Zeil 5 4 and Ze tly 5 5 respectively using a standard four phase step algorithm with relative phase shifts of 7 2 from 0 to 37 2 radians Kreis 2005 An arctangent function is then applied to a ratio of the calculated sine and cosine maps as shown in Fig 5 5 to extract the wrapped optical phase Furlong 2007 As shown the recovered wrapped phase maps are visually indistinguishable through the methods used to obtain each are significantly different To determine the accuracy and repeatability of these data sets they must be processed and quantitatively compared _68 Sine map Cosine map _ 9 a b Fig 5 5 Sine cosine and arctangent maps calculated with phase modulating interferometry a and with phase stepping interferometry b Wrapped phase After gross removal of the object s tilt and all 27 discontinuities within the wrapped phase map the recovered unwrapped data can be scaled by the wavelength of the illumination source to determine the shape of the object of interest The recovered shape information is then imported into Image
64. ested that camera properties be preset using external PixeLINK Capture OEM software for speed and ease of use as the PL A741 will maintain operational settings while it is powered Software and hardware installation procedures are outlined in Appendix E _58 4 2 2 Operation Due to the requirements of the phase modulating interferometer a flow chart was developed to direct the programming work This chart presented in Appendix F demonstrates a standard operational procedure Functionally the developed code must 1 Control the imaging camera gain gamma shutter period etc 2 Display the raw images returned from the camera 3 Generate the magnitude and phase of the reference modulation signal relative to the illumination cycle 4 Synchronize both the reference modulation and the illumination cycles with the camera acquisition period 5 Acquire four interferograms over the reference modulation period 6 Calculate and display the wrapped phase and optical modulation maps based on the presented mathematics 7 Save the acquired interferograms and calculated maps Synchronization of the analog signals requires the frequency and relative phase of each output channel be known To ensure synchronization the signal controlling the reference modulation also serves as the trigger frequency for the system As a result all other output parameters can be fixed relative to the phase and frequency of this modulation signal As such
65. ezo actuator 4 Ifthe resultant phase modulation maps appear appropriate the results can be saved to the directory and file of choice When selecting the save directory press Select Cur Dir to ensure the current directory is properly selected for saving File type can be set as indicated in Appendix F Data Acquisition Count can be adjusted to save multiple sequential data sets for comparison and post processing 5 Ifan error occurs during operation an error dialog will appear Select Stop to end the program safely and attempt to restart code If error persists restart LabVIEW and continue testing If the camera or output card is not properly released by selection of the in program Stop or the in error Stop LabVIEW will incorrectly read the connected hardware disabling camera control or creating a DC offset to the output voltage signals respectively 6 Ifthe interface freezes after a user command wait for 30s 1 minute If function has not been restored force a LabVIEW close and restart program System will restart and operate correctly with forced restart 7 End program through the in program Stop 147 Automatically input parameters from Input Excitation Parameters Initialize Camera 1 Camera memory 2 Modulation parameter file 3 Default settings within LabVIEW block Camera Trigger on i Raw Feed on G G t Adjust settings
66. f developed user interface 151 V Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig 1 1 2 1 PADA 2 2 4 2D 2 6 27 3 1 3 2 3 3 3 4 SE 3 6 ome 3 8 3 9 3 10 3 11 312 LIST OF FIGURES Scale of various microscopic systems with comparison to MEMS Zhang 2004 Worldwide revenue forecast for MEMS MEMS Industry Group 2006 Share of MEMS revenues by device 2007 MEMS Industry Group 2006 MEMS development cycle Exponent Inc 2000 Variation in residual stress and biaxial modulus across a silicon wafer Exponent Inc 2000 Michelson interferometer Kreis 2005 Monochromatic red light versus white light interferograms of a sample with gt 4 step discontinuities demonstrating the ability to connect fringe orders using white light interferometry Wyant 2002 Simulation of the interferometric signal I t and how it is integrated over the four quarters of the modulation period Dubois 2001 Quadrature acquisition with stroboscopic illumination Kuppers et al 2006 Convergence of K and K for y 6 rad 0 5 rad and d 10 Convergence rate of K and K for y 6 rad 0 5 rad and d 10 Representation of K at 15 illumination duty cycle Representation of K at 15 illumination duty cycle Representation of K at 10 illumination duty cycle Representation of K
67. fective natural frequency and with the attachment of masses to the piezoelectric stack The significant overshoot coupled with the settling time may result in an average modulation error of 5 10 during phase stepping Surrel 1993 As phase stepping relies on constant phase steps this modulation error will correspond to a mean error in the recovered optical phase map described by Eq 3 6 Surrel 1993 ea 3 6 2N sin 2 V ideal From Eq 3 6 it is apparent that the mean optical phase map error decreases with larger N bucket algorithms and increases with larger modulation errors For the case of a 5 modulation error the mean phase error becomes 39 25 mrad for N 4 As shown this modulation error may be due to actuator overshoot and settling time however other factors including hysteresis and creep may contribute to an error in the modulation step Physik Instrumente L P 2005 Hysteresis and creep describe positional errors during open loop operation due to crystalline polarization effects and molecular effects within a piezoelectric material The amount of hysteresis increases 30 with increasing voltage applied to the actuator The gap in the voltage displacement curve of a piezoelectric actuator typically begins around 2 and widens to a maximum of 10 to 15 under large signal conditions If for example the drive voltage of a 50 um piezoactuator is changed by 10 the position repeatability 1s on the order of
68. ge orders across this step at similar measurement resolutions Fig 2 6 Monochromatic red light versus white light interferograms of a sample with gt A 4 step discontinuities demonstrating the ability to connect fringe orders using white light interferometry Wyant 2002 i Coherence probe interferometers are used to obtain height measurements on structures exhibiting large steps or rough surfaces With a short coherence length source good contrast fringes will appear only when the two interferometric paths are closely matched Consequently if the path length of either the object or reference arms 1s adjusted the maximum fringe contrast will translate along the instrument sensitivity vector The height variations across the sample can then be determined by looking at the locations at which the fringe contrast is maximized As the translation of the fringe contrast is controlled there are no sign ambiguities in the recovered height map Additionally as the maximum fringe contrast is obtained when the sample is in focus there will be no focus errors during surface measurement Caber 1993 Wyant 2002 The major drawback of measurements with this type of scanning interferometer is that only a single surface height is being measured at a time As a result transient event may be overlooked or misinterpreted Additionally a large number of measurements and calculations are required to accurately determine surface height values where typic
69. ger Type ve pep t Trigger Polarity us H JDBT Trigger Delsch Cp Trigger Parameter L2E1 Fig D 11 Event structure 3a update the current camera trigger settings based on parameters found on the user interface and operate under the new settings Parameters are explained in Appendix F 130 amera control settings i Trigger Update Attached camera id numbers rig Undate gt EE Operating camera id number Error flow GE e BD je rigger Type oe me JE rigger Seet JH et Trigger Delsch 061 Trigger Parameter 051 Fig D 12 Event structure 3b update the current camera trigger settings based on parameters found on the user interface Deactivate reading of the trigger settings for camera operation 131 vv GE Trigger Trigger Mode Trigger Type Trigger Polarity Trigger Delay Trigger Parameter Value Change Camera control settings p Trigger Update A r Bool strict 9 gt Disabled Attached camera id numbers Operating camera id number Fig D 13 Event structure 4 this event enables the Trigger Update button on the interface to set triggering parameters on selected camera system 132 amera control settings Attached camera id numbers Operating camera 1d number w Error flow Raw Feed OTE Hi i nable Processing Fig D 14 Event structure 5a this event begins the display of the unprocessed camera feed if the trigger signal is being gener
70. hase stepping interferometric phase modulating methods methods methods interferometry Required gt 3 gt 3 continuous gt 4 interferograms detection static noise dynamic noise requisites In Sasaki and Okazaki 1986a 1986b and Dubois 2001 the developed interferometric systems operate under sinusoidal modulation in four integrating bucket mode as shown in Fig 2 7 Eye interfercaneitie senal t D T 2 3T4 T Time Fig 2 7 Simulation of the interferometric signal Z t and how it is integrated over the four quarters of the modulation period Dubois 2001 According to Fig 2 7 this integration is performed by a two dimensional detector array with a charge storage period equal to one quarter of the period of the sinusoidal phase modulation 7 4 Interferograms are then acquired over sequential quarters to generate a set of four interferograms for data processing This combination of sequential acquisition periods each over one part of the modulation cycle is known as an integrating bucket method Sinusoidal modulation was chosen to minimize errors within the recovered optical phase map by minimizing the jerk experienced by translation of a reference mirror PSI techniques involve 3 or more stepped motions of a reference mirror to solve the underlying interferometric equations Each stepped motion involves the rapid acceleration and deceleration of the attached reference mirror Increasing acquisition speed results i
71. he Data Processing and Image Analysis tabs have not been enabled in the current software build However the underlying functions are present within the block diagram Appendix D and can be implemented in future builds as needed These tabs are designed to provide image feedback specifically concerning contrast and the mean minimum maximum pixel values The graph shown next to the tab controls displays the values of the mid row or mid column within the wrapped phase or modulation maps based on which calculation 1s currently being displayed If both calculations are called simultaneously the chart will alternate between viewing of both processed maps Selection of the mid row column is done through the Operation Mode block as shown in Appendix F 115 pE aseud padden Gd 10 aouanbas anes uag z E uno uogsnbog 13eg BCL O05 SF OS Ser OOF SZE OSE SEE OOF B OGE See 00e SZT OST Set OOF Sf Of Ge U i v l l l l l l l l l l l I l l l l I l l l l l a e dwg swepy 20 Dua pe GI dwg s T Apg ped a1adu0 SAIL aew Bussa Ep SUE AAR ja Voten apop GuISSSuppy jax E auo anea Des D JaXld SIOIDUOH PsoUeApY OOF OE 00 E OS S Oe OST OT 06 C HLH e Porrr beurre br D S T bree bora beara baa baad COTIF ee WM Bug DG DO a li SS an i a ee i ne a a ne ae ee Eat ah a I oof ee UES OOO00 T coocoo oocos o oooo o ooooz o O000 0 a Le S O O T T O O O D O TO O S OS T O D S S D O OS O S S O D T T O S D
72. he mean error is equal to zero for equal values of Ke and K As this condition of equality was enforced to eliminate the contribution of the phase constants during recovery of optical phase the mean squared error is used to provide a secondary indication of the error effects within the developed system As shown in Eq B 19 the mean squared error is minimized when the phase constants Ke and K are maximized These error terms can then be minimized through appropriate selection of the reference excitation amplitude and phase A consequence of this derivation is the realization that any inequality between K and K will result in a non random error appearing as a sinusoidal type pattern at twice the frequency of the optical phase The standard deviation of the additive noise errors can be found as the square root of the mean squared error term Assuming that K and K are equivalent its magnitude is found as Eq B 20 Lei EE B 20 min 21yT K om 113 From Eq B 20 we see that maximization of the magnitude of the phase constants will minimize the standard deviation of any recovered error due to additive noise effects 114 APPENDIX C Front panel of the developed LabVIEW VI for control of the phase modulating interferometer Figures C 1 to C 3 display the various settings and controls available within the developed user interface Each figure displays a different set of usable tabs As mentioned in Appendix F settings under t
73. hen J Statistical power analysis for the behavioral sciences 2nd ed Hillsdale NJ Lawrence Erlbaum Associates 1988 Creath K Phase measurements interferometry techniques in Progress in Optics Wolf E ed Elsevier Science NY 26 349 393 1988 _97 Creath K Phase measurement interferometry beware these errors Proc SPIE 1553 213 220 1992 Deck L Fourier transform phase shifting interferometry Appl Opt 42 13 2354 2365 2003 de Groot P Derivation of algorithms for phase shifting interferometry using the concept of a data sampling window Appl Opt 34 4723 4730 1995a de Groot P Vibration in phase shifting interferometry JOSA 12 2 354 365 1995b de Groot P and Deck L Numerical simulations of vibration in phase shifting interferometry Appl Opt 35 2172 2178 1996 de Groot P de Lega X Kramer J and Turzhitsky M Determination of fringe order in white light interference microscopy Appl Opt 41 22 4571 4578 2002 Dorrio B and Fernandez J Phase evaluation methods in whole field optical measurement techniques Meas Sci Technol 10 R33 R55 1998 Douglass M Lifetime estimates and unique failure mechanisms of the DigitalMicromirror Device DMD Proc IEEE 36173 9 16 1998 Dubois A Boccara A C and Lebec M Real time reflectivity and topography imagery of depth resolved microscopic surfaces
74. hniques while combining strengths of each By continuously modulating an illumination wave front and using a four bucket algorithm shown in Fig 2 8 it has been demonstrated that a time varying interference pattern can be detected and analyzed to a measurement accuracy of 1 0 nm under a 600 nm illumination source This is possible because the amplitude and phase of the modulation signal is chosen to minimize the effects of Gaussian additive noise on the recovered optical phase map As shown in Table 2 2 and discussed in Sasaki and Okazaki 1986a Sasaki et al 1990a 1990b Dubois 2001 and Dorrio and Fernandez 1998 sinusoidal phase modulating interferometry has demonstrated an accuracy level of 0 1 nm which is on par with that obtained with temporal phase modulating interferometry though at the cost of higher processing complexity This increased complexity is offset by an increased immunity to static and dynamic environmental and systematic noise effects Da below the modulation frequency versus both temporal and spatial phase stepping interferometry Sasaki and Okazaki 1986a 1986b Creath 1988 Suzuki et al 1994 de Groot and Deck 1996 Dorrio and Fernandez 1998 Dubois 2001 Kreis 2005 Table 2 2 Comparison of phase evaluation methods without a spatial carrier Sasaki and Okazaki 1986a Suzuki et al 1994 Dorrio and Fernandez 1998 Dubois 2001 Kreis 2005 Temporal Spatial Heterodyne Sinusoidal phase stepping p
75. ices Unlike commonly used PSI methods PMI requires reference excitation amplitude of less than the illumination wavelength However this excitation amplitude is a strongly non linear function of the stroboscopic illumination duty cycle Additionally both the quadrature and integrating bucket methods require a known phase difference between the illumination acquisition period and the reference excitation period Dubois 2001 Sasaki and Okazaki 1986a Additive noise concerns of the PMI system are presented in this Thesis and used in the determination of the reference excitation amplitude and phase _4 Error in the recovered phase map is then proportional to the error in these two parameters The phase modulating system reported in this Thesis was implemented in a Linnik configuration and is controlled with software designed in the LabVIEW graphical programming environment LabVIEW 7 1 2006 The implementation required synchronization of the illumination source with the reference excitation and camera acquisition time Representative Results are presented showing feasibility of the developed PMI technique for high resolution measurements of shape and semi static loading situations of MEMS 2 BACKGROUND MEMS or microelectromechanical systems is an approach to fabrication that uses the materials and processes of microelectronics fabrication to convey the advantages of miniaturization multiple components and microelectronics to
76. ices from MIT s Precision Compliant Systems Laboratory is presented under phase modulating and phase stepping interferometry Shape characterization indicates a central stage displacement of up to 7 6 um With a linear displacement rate of 0 75 A mV under time variant load conditions as compared to a nominal rate of 1 0 A mvV in an undamaged structure Chen and Culpepper 2006 rg ACKNOWLEDGEMENTS First of all I would like to thank my advisor Prof Furlong and Prof Pryputniewicz who provided me with the opportunity to study interferometry and MEMS systems at WPI I would like to thank them and my committee for their assistance and support during my completion of this Thesis research In addition I gratefully acknowledge the support of the Center for Holographic Studies and Laser micro mechaTronics CHSLT in Mechanical Engineering Department for the use of their facilities and equipment in my studies I would also like to acknowledge and thank Prof Martin Culpepper and Mr Shih Chi Chen from the Precision Compliant Systems Laboratory at MIT for the use of their developed uwHexFlex device in my experimental work I would particularly like to thank my family and especially my fianc e Amanda O Toole for their assistance and unending support during my work over the last couple of years Without them I know I couldn t be where I am today 111 TABLE OF CONTENTS Copyright Abstract Acknowledgements Table of content
77. iles Data Processing not enabled Image Analysis not enabled 155
78. in the general equation This system must also be posed in a way that eliminates the phase ambiguity present in the above equations with respect to the phase distribution due to the even periodic nature of the cosine function Traditional phase shifting and phase stepping methods provide a means for extraction of the optical phase and solution of the sign ambiguity This is accomplished through the acquisition of multiple intensity distributions with mutual phase shifts Nonlinear equations of the form shown in Eq 3 3 can then be solved for the optical phase over the full field of view When the reference phase shift R x y between each interferogram is known a minimum of three intensity distributions must be found to solve for g x y x y and g x y Kreis 2005 I x y Ig x y Iu x y cosl lx y ss y 3 3 29 While phase stepping or shifting rely respectively on discreet step or saw tooth variation in the optical phase to provide the known phase term within recovered interferograms phase modulating interferometry uses a known continuously varying phase variation Sasaki and Okazaki 1986a Kreis 2005 In this Thesis the continuously variant signal is accomplished with motions of a piezoelectric actuator attached to the reference mirror Phase modulation is differentiated from phase shifting by eliminating the linear phase variation requirement allowing for the application of a continuous phase modulation funct
79. inear interpolation may not provide an accurate estimation of parameters away from those explicitly calculated This is most apparent between an illumination duty cycle of 13 and 14 due to a discontinuity within that range at d 13 45 Other implementation recommendations become apparent when considering the charted data As found in Appendix B the mean squared additive error is inversely related to the squared magnitude of the sine and cosine constants This condition led to the maximization of the equations describing those values and in part allowed for the _47 creation of the plots described in Figs 3 12 and 3 13 However as shown in Fig 3 13 the optimization of wand 0 leads to a variation in magnitude of K and Ke with respect to the duty cycle d This causes the value of the mean squared additive error to be proportional to the stroboscopic duty cycle used As shown in Fig 3 13 a maximum constant magnitude exists at d 14 Therefore the mean squared additive error will be minimized when operating at this duty cycle Also from Fig 3 13 the optimal operation range is d 14 to 18 where the magnitude of the upper limit 1s half of the maximum It becomes apparent that the stroboscopic duty cycle should not be set between 13 and 14 as a discontinuity exists in the above charts By refining the calculated values within this range a step discontinuity appears at d 13 45 Consequently while interpolation appears to provide a reaso
80. ion With this implementation the overshoot and settling experienced by piezoelectric actuators during discontinuous motion can be reduced or eliminated As shown in documentation from Physik Instrumente L P 2005 piezoelectric actuators undergoing discontinuous motions experience an instantaneous displacement overshoot of 10 15 under low displacement steps The actuator then requires a finite settling time to attain 1ts nominal displacement As shown in Eq 3 4 the minimum settling time 1s related to the natural frequency of the actuator and attached components When operating below 10 of the resonant frequency the minimum settling time is given by Physik Instrumente L P 2005 fmin a 3 4 The additional mass of the reference mirror and surrounding structure alters the natural frequency of the unloaded actuator fo While the resonant frequency of the unloaded actuator is normally given by a manufacturer the loaded natural frequency fo can be found by 20 m fo Jo een 3 5 Meff where M is the additional mass coupled to the piezoelectric actuator and my is the effective mass of a piezoelectric actuator equal to 1 3 the mass of the ceramic stack Physik Instrumente L P 2005 For a piezoelectric actuator with a resonant frequency of 2 kHz and negligible loaded masses the minimum settling time will be approximately 0 5 ms This settling time will be greatly increased at modulation frequencies approaching the ef
81. ious VIs during application development it is possible to perform the required tasks Bitter et al 2000 LabVIEW 7 1 2006 At the heart of LabVIEW is structured dataflow diagramming It is in fact a much richer computational model than the control flow of popular text based languages because it is inherently parallel while C C and BASIC are not As traditional languages must rely on library calls operating system functions to achieve parallelism the compiler can not ensure shared sections of code are properly protected within the operating system making it difficult to build parallel programs These problems do not exist in LabVIEW as the compiler does not have to parse the diagram because it 1s already 56 parsed LabVIEW 7 1 2006 A small sample of the code written for the interferometric system is presented in Fig 4 7 Illuminaion Properties Sen value Fig 4 7 Sample of developed LabVIEW block diagram According to Fig 4 7 each icon represents a particular task or value where the blue and orange wires are used to connect these icons and so define the program flow In this case the integration time of the camera can be traced to find its dependence on the reference excitation frequency the stroboscopic illumination duty cycle and a term called the excitation period count which defines the number of stroboscopic pulses included in each acquisition period Appendix D shows the full block diagram co
82. is contact may have a significant influence on the recovered data An X ray system may be used in 2 D or 3 D as a way to measure the shape and hence deformations of the object of interest The major disadvantages to this technique are the high cost danger and potential for imaging artifacts to make analysis difficult Positively X ray computed tomography has been applied to objects from 5 um to 2 m which is on the scale of MEMS devices Haddad et al 1994 Tonner and Stanley 2002 Similarly various optical techniques exist which allow for shape measurements of the system of interest As with X ray computed SEN tomography this shape information is then used to determine the deformations of the system of interest and hence the strains resulting from an applied stress However unlike X ray methods optical techniques have demonstrated subnanometer shape measurement resolution 2 3 Interferometric options Interferometry uses changes in an optical wavefront to measure how an object behaves under loading Where many techniques exist to record these changes each have different strengths and weaknesses when used in a NDE application Modern techniques include and are not limited to the following categories homodyne interferometry spatial and temporal heterodyne interferometry digital holographic interferometry and white light interferometry Dyson 1970 Sirohi and Kothiyal 1991 Greivenkamp and Bruning 1992 Wyant 2002 Kreis 2005
83. isplacement um gt ho Actual behavior 0 75 A mV 5 0 6 0 7 0 8 0 9 0 10 0 11 0 12 0 13 0 14 0 15 0 Voltage V Fig 5 18 Displacement of the damaged uHexFlex device versus applied voltage as determined through the system developed in this Thesis 0 As seen in Fig 5 18 the actual displacement of the uHexFlex device is 25 below nominal and mean deviation from the trend line of 27 1 nm Given the construction of the uHexFlex device it is expected that some of these deviations from ideal are due to unmeasured in plane displacements of the central stage According to materials published in Chen and Culpepper 2006 when only the one half of a TMA device is functional the central stage will undergo both in plane and out of plane motions The combination of these motions are used to determine the full displacement vector of the central stage and hence its nominal displacement characteristics _9 6 CONCLUSIONS AND FUTURE WORK This Thesis has demonstrated the feasibility of phase modulating interferometry as an alternative to phase stepping and phase shifting interferometric techniques through comparison of measurement resolution and environmental stability under multiple operating conditions It has also included the characterization of shape and displacement for a MEMS device 1 2 3 4 5 The objectives of this work were the derivation of stroboscopically illumina
84. ith a certain phase increment between them is obtained Once these phase shifted patterns have been combined using a 16 phase shifting algorithm we can obtain the phase values modulo 2r for all of the full field of view points simultaneously This method can provide as accuracy level of up to A 1000 if the ambient conditions and experimental setup are well controlled Creath 1988 1992 Haasteren and Frankena 1994 Dorrio and Fernandez 1998 However due to the need to obtain different separate patterns in time temporal phase stepping methods cannot be applied to dynamic processes without the application of a stroboscopic illumination source or implementation of an acquisition system that is rapid relative to the dynamic processes being studied as standard methods assume that the background intensity contrast and phase be stationary over the interferogram acquisition period Creath 1988 Kreis 2005 The number of interferograms acquired depends on the particular phase extraction algorithm employed where larger numbers are used to reduce sensitivity to systematic noise and environmental effects Surrel 1993 de Groot and Deck 1996 Ruiz et al 2001 Historically temporal phase shifting algorithms were restricted to combinations of three or four interferograms where modern algorithms have been demonstrated with linear combinations of up to seven interferograms Hariharan et al 1987 de Groot 1995a Surrel 1996 Using windowing to
85. itude of the additive noise signal is assumed to be much weaker than the recorded signal while equally contributing to all frames in a given set as shown in Eq B 3 In p lt lt Je B 3 These additive noise assumptions have been validated by Luth 1989 for high signal to noise ratio images acquired through standard CMOS or CCD array systems The addition of additive noise n will cause the instantaneous intensity equation to take the form shown in Eq B 4 for an arbitrary relative phase as I x y Ip x y Lng x y cosld x y bala y n B 4 Following the derivation procedure presented in Section 3 a tangent function Eq B 5 can be recovered containing the optical phase and a phase error term as K 2 tanl ea A C C B 5 109 N and N shown in Eqs B 6 and B 7 respectively represent the error present within the linear frame combinations of and 3 and take the form N n n n n4 B 6 and No n n Any Fna B 7 This tangent function shall be represented by 7 for simplicity in future reference The error term must be extracted from within the tangent calculation to determine its magnitude and full field behavior To accomplish this the tangent term 1s approximated with a third order Taylor series with respect to e derived through MathCad 2001 shown as Eq B 8 Equation B 8 1s of the form tan tan 1 tan e tan g 1 tangy eo ole e B 8 which c
86. l rights reserved Ki ABSTRACT This Thesis proposes phase modulating interferometry as an alternative to phase stepping and phase shifting interferometry for use in the shape and displacement characterization of microelectromechanical systems MEMS Creath 1988 de Groot 1995a Furlong and Pryputniewicz 2003 A phase modulating interferometer is developed theoretically with the use of a stroboscopic illumination source and implemented on a Linnik configured interferometer using a software control package developed in the LabVIEW programming environment Optimization of the amplitude and phase of the sinusoidal modulation source is accomplished through the investigation and minimization of errors created by additive noise effects on the recovered optical phase A spatial resolution of 2 762 um over a 2 97 x 2 37 mm field of view has been demonstrated with 4x magnification objectives within the developed interferometer The measurement resolution lays within the design tolerance of a 500A 2 5 thick NIST traceable gold film and within 0 2 nm of data acquired under low modulation frequency phase stepping interferometry on the same physical system The environmental stability of the phase modulating interferometer is contrasted to the phase stepping interferometer exhibiting a mean wrapped phase drift of Ag 40 1 mrad versus Ag 91 mrad under similar modulation frequencies Shape and displacement characterization of failed uHexFlex dev
87. le of 14 As previously the displacement rate of the phase modulator is verified with a five bucket PSI algorithm presented in Hariharan et al 1987 and found to be 100 58 nm V A reference flat containing five carrier fringes and exhibiting 4 4 flatness is observed for these trials Additionally the interferometer is enclosed to minimize the effects of air turbulence on the results Interferogram sets are acquired once every 10s over a 20 minute window where each interferogram has an exposure time of 10 ms Instantaneous phase is calculated by extracting the value of the wrapped phase map at the points highlighted in Fig 5 9 and calculating the mean The phase drift is then taken as the change in this mean between sequential interferogram sets When the absolute change in this mean value is plotted over the 20 minute interval with the minimum set to zero the mean phase drift becomes the DC offset of the data Phase drift observed during operation of the phase stepping interferometer and the phase modulating interferometer operating at f 2 Hz and f 100 Hz respectively is presented in Fig 5 10 20 Absolute phase drift mrad Wrapped phase extraction points Fig 5 9 Wrapped phase map generated with sinusoidal modulating interferometry imaging a reference flat at f 100 Hz and d 14 showing points used in calculation of optical phase drift 3
88. liopoulos C Simultaneous phase shift interferometer Proc SPIE 1531 119 127 1992 Krauss O Micro Machining Colorado Engineer Magazine cem colorado edu 2002 Kreis T Handbook of holographic interferometry Wiley VCH Weinheim Germany 2005 100 Kuppers J Gouverneur I Rodgers M Wenger J and Furlong C Dynamic characterization of AFM probes by laser Doppler vibrometry and stroboscopic holographic methodologies Proc SPIE 6293 57 68 2006 Kwon O Shough D and Willians R Stroboscopic phase shifting interferometry Opt Lett 12 855 857 1987 LabVIEW 7 1 National Instruments Inc Austin TX 2006 Liwei L Pisano A P and Howe T R A micro strain gauge with mechanical amplifier JMEMS 6 4 313 321 1997 Luth W Isolation of Moving Objects in Digital Image Sequences Academy of Sciences of the GDR Dresden Germany 1989 Mann C Lingfeng Y Chun Min L and Myung K High resolution quantitative phase contrast microscopy by digital holography Opt Exp 13 22 8693 8698 2005 Mathcad r 12 Mathsoft Engineering amp Education Inc Needham MA 2004 MatLab 7 3 The Mathworks Natick MA 2006 MEMS Industry Group Industry in transition 2006 MEMS forecast an The MEMS Industry Group In Stat www memsindustrygroup com 2006 MEMS and Nanotechnology Exchange www mems exchange org last viewed Nov 19 2006 Metrix
89. los 1992 Dorrio and Fernandez 1998 4D Technology Inc 2006 A spatial separation of the interferograms can be achieved with rotational polarizing components diffraction gratings or computer generated diffractive optical elements Dorrio and Fernandez 1998 North Morris et al 2002 4D Technology Inc 2006 In this method errors due to environmental instabilities are avoided with the simultaneous acquisition of the patterns However other types of errors appear due to variations in the different camera systems used or within different parts of the same imaging array Koliopoulos 1992 Consequently additional data processing is needed to match the measurement accuracy of temporal phase stepping therefore real time evaluation methods are obtained at the cost of measurement accuracy Kwon et al 1987 19 By contrast temporal heterodyning uses the interference of two optical waves of different frequencies which produces an intensity oscillating at a beat frequency equal to the frequency difference Sirohi and Kothiyal 1991 These systems split the reference and object beams by use of an acousto optic modulator A Zeman splitter may be used to separate the beam within the laser head through use of powerful magnets Chapman 2002 Another technique involves the use of a dual mode laser with beat frequency of 1 GHz or above Alternatively acousto optic modulators can be used to shift the beam path between multiple output angles c
90. lution of the phase modulating system was tested to provide experimental verification of the presented mathematics as well as of the developed control system The spatial resolution and field of view were tested noninterferometrically with a negative 1951 USAF glass target by Edmund Optics Edmund Optics Inc 2006 Measurement resolution and accuracy was determined through measurement of a 500A 2 5 thick gold film National Institute of Standards and Technology NIST traceable gauge Veeco Metrology Group 2002 Lastly shape and displacement testing of a series of uHexFlex devices from the Precision Compliant Systems Laboratory at MIT was conducted demonstrating the applicability of the phase modulating system in MEMS applications All shape and displacement measurements were verified with a phase stepping algorithm also implemented through the LabVIEW environment on the same system With a developed interface functionally identical to the phase modulating controls the use of phase stepping allows for rapid measurement comparisons Shape measurement results correlate to within 0 2 nm between the two interferometric techniques 5 1 Spatial resolution The 1951 USAF shows several groups of test target elements which conform to Military Standard 150A Each group consists of six elements which are progressively smaller by 62 2 5mm a gt Group Element 1 6 i 3 1 where is the line length in millimeters for a given g
91. lvable element set Edmund Optics Inc 2006 Spline fit intensity profile of pixels extracted along horizontally oriented bars in Group 7 of the USAF 1951 negative glass target 500A 2 5 goal film NIST traceable gauge used for characterization of optoelectronic holographic methodologies Veeco Metrology Group 2002 Interferograms acquired with phase modulating interferometry a and with phase stepping interferometry b Sine cosine and arctangent maps calculated with phase modulating interferometry a and with phase stepping interferometry b Deviations from planarity as determined by difference analysis using phase modulating interferometry operating at f 100 Hz d 14 indicated a nominal film thickness of 503 7 under PMI PSI methods indicated a nominal film thickness of 501 A 7A Furlong 2007 Vli 47 49 50 51 52 53 56 57 63 64 65 67 69 70 Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig 5 7 5 8 5 9 5 10 5 11 512 SE 5 14 5 15 5 16 5 17 Shape of reference flat recovered with sinusoidal modulation operating at f 10 Hz and demonstrating a surface flatness of AA 75 Shape difference map 0 between sinusoidal modulation and phase stepping Both measurements performed at the operational frequency of f 10 Hz The sinusoidal variation having amplitude of 0 4 nm and frequency of 3 4 cycles mm
92. ms the code is written in a block diagram format similar to a flow chart design allowing for rapid debugging and program augmentation LabVIEW 7 1 2006 A LabVIEW program will inherently have two components the front panel and the block diagram The front panel is simply the user interface UI It is automatically generated during block diagram programming though the final version is fully customizable as with comparable graphical programming languages A subsection of the developed UI is presented in Fig 4 6 A more complete view of the developed front panel is presented in Appendix C 55 Camera Control Voltage Control Triggering Basic Controls Shutter be S 0 00986 0 00004 D 20000 o 49000 D on o Sonn L 00000 Gain oe 0 00 0 00 O 19 20 Gamma a SE 0 10 0 50 1 00 1 50 2 00 EES zm 3 50 4 00 Advanced Controls ROI Pinel Addressing Value None el Pixel Addressing Mode DECIMATION e E E 232 a Fig 4 6 Sample front panel of developed LabVIEW interface The block diagram side of a LabVIEW program contains the developed code as written for this Thesis While code can be imported from standard C C MatLab etc most programs are inserted by way of the LabVIEW VI system These VIs or virtual instruments are pre parsed pre compiled code blocks which can be used to accomplish tasks much like commands in standard programming languages By wiring corresponding terminals of var
93. n greater operational jerk creating nonlinearities in the reference modulation A 10 modulation miscalibration error correlates with an error in the recovered optical phase map of 0 20 radians in a 4 frame algorithm or 20nm under a 620nm illumination source Creath 1992 Surrel 1993 An increase in the number of acquired interferograms will reduce the phase error to 0 0796 radians at the expense of DS increased processing requirements Surrel 1993 The sinusoidal modulation of the PMI system minimizes the jerk of the reference arm demonstrating a theoretical phase measurement accuracy of less than 0 5 0 8 nm under a 600 nm illumination source Sasaki and Okazaki 1986b Experimentally these errors have been found to be from 0 5 1 0 nm when operating under a 200 Hz modulation signal Sasaki and Okazaki 1986a 1990a Dubois 1999 2001 While the previously presented four bucket method has been proven for the analysis of static structures the currently defined system has not been demonstrated with dynamic studies Due to the relatively long acquisition period the observable intensity field becomes modulated by the square of the zero order Bessel functions of the first kind Jo Y In harmonic vibration studies the fringes become contours of equal vibration amplitudes at the spatial vibration nodes Additionally fringe contrast decreases with increasing fringe order with the maximal contrast existing at the nodes of the vibration mod
94. nable estimation of the excitation magnitude and phase values within the operational range it cannot be applied from d 13 to 14 though the magnitude of the sine and cosine constants is high in this region Figure 3 13 provides operational limits to the sinusoidal phase modulation system Between d 0 to 5 the magnitude of the phase constants is ul of peak This indicates that while operation is possible under ideal conditions any small errors will be accentuated due to the inverse relationship between mean squared error and phase constants magnitude shown in Appendix B Operation at these low illumination duty cycles requires alternative combinations of excitation amplitude and phase parameters that may provide a higher phase constant magnitude However this limitation may be dealt with by increasing the reference excitation frequency until the acquisition time at the higher duty cycle 1s that required experimentally _48 4 IMPLEMENTATION Realization of a phase modulating interferometer requires a controllable imaging system with a stroboscopic illumination source coupled to an optical path length modulation system The derived technique assumes synchronization between the optical path length modulation and the stroboscopic illumination period Similarly the optical path length modulation amplitude and relative phase must be set to minimize errors in the recovered optical phase map due to additive noise effects This synchronization is
95. ng results in periodically missing frames preventing display of the correct optical phase map As a result the base code was adapted so that frames would be acquired as needed and recovered as a 2 D array rather than as a coherent image While this approach prevents the loss of image data it limits the speed of the system and requires a square region of interest to correctly display the originally acquired frame Due to a non standard indexing used in the PixeLINK camera system all other region of interests will not display correctly in the currently developed software package Functionally this approach also requires the camera trigger signal to 60 be the first thing turned on when operating the system Otherwise the system will lock up as it waits for the camera to provide a frame to the processing code Additionally the developed program is not configured for true real time display of the unwrapped phase map The current display is at a rate of several frames per second This limitation is primarily due to the need to generate a sinusoidal waveform within the developed code This creation process requires a significant portion of the processing time and so greatly slows the overall program speed Processing time may be reduced in further developments through external creation of the sinusoidal signal or the addition of other LabVIEW packages for further optimization 4612 5 REPRESENTATIVE RESULTS The measurement and spatial reso
96. ngth 620 nm 84 b modulation frequency 100 Hz PMI 2 Hz PSI c stroboscopic amplitude 1 25 V d illumination duty cycle 10 e trigger mode Low Integrate f trigger polarity Positive PMI Negative PSI As shown in Figs 5 13 and 5 14 the small and medium sized wHexFlex devices exhibit a severe tilt and displacement relative to their surrounding substrate The smaller device exhibits a 1 1 um positive displacement of its 280 um diameter central stage from the surrounding substrate Width mm 0 5 Length mm Fig 5 13 Recovered shape of 280 um diameter central stage uHexFlex 85 0 25 0 5 E an c 0 75 gt 0 25 0 50 0 75 1 00 Length mm Fig 5 14 Recovered shape of 375 um diameter central stage uHexFlex demonstrating damage to the armature structure As with the smaller device the medium sized wHexFlex device exhibits a displacement with respect to the surrounding substrate In this larger device this displacement is found to be 7 4 um with respect to the 375 um central stage It is believed that this larger displacement is partially due to the broken area indicated in Fig 5 14 Within this area little to no structure was observed indicating that it had broken away from the connected armature perhaps during testing causing this device to fail It should be noted that the measurement arms used in other displacement characterizations radiating from the central stage exhibi
97. niques Gorard 2004 Both the standard deviation and mean absolute deviation are presented here to demonstrate the low level of data error in the acquired measurements while providing a secondary point of reference between the data sets The inter quartile range serves as an additional comparison tool measures the spread of the middle 50 of the data when sorted from smallest to largest As with the standard deviation the smaller the IRQ value the tighter the data set The IRQ is used as a way to remove the effects of outliers on a data set during analysis This is most appropriately used when it is known that some degree of randomness exists in a data set independent of the measurable results A common application of the IRQ is the removal of the outer 25 of the data set for linear correlation calculations Cohen 1988 Correlation between the acquired data sets is calculated with the Pearson product moment correlation coefficient This method investigates linear relationships between two or more data sets by calculation of an R value ranging from 0 to 1 with larger values indicating a stronger the linear relationship This coefficient is calculated from Cohen 1998 5 10 73 where a and b are data sets of size m x n and as previously X indicates the arithmetic mean of a particular data set x These statistical measures are used to describe the shape data presented here obtained with sinusoidal phase modulating interferome
98. nnel 2 of the NI PCI 6713 card Must be enabled before any other settings are adjusted whether or not it will be required for the particular mode of operation Raw Fee Displays the raw feed from the attached camera system Oo This will only display correctly when the system is set to a square ROI SE _ Sends the illumination modulation signal through Channel LC Ri 1 of the NI PCI 6713 card oa _ Sends the reference excitation modulation signal through Gel Channel 0 of the NI PCI 6713 card Wavelength 500 220 NW _ Set to the primary wavelength of the illumination source 450 Ps SS for scaling the excitation modulation amplitude wo 6m Processing Control Enable Phase Stepping Begins stepping the relative phase between the Cen illumination and excitation modulations for optical e phase extraction 151 Phase Step 270 deg Enable Processing Wrapped Phase Map C Ki Modulation e Reference Mode B Acquire Reference Operation Mode Tweak Ref Mirror Excitation 0 25 w 0 25 ks Z 8 0 5 0 757 Fa a w Plot Line Line Selector Row S column Settings block Camera Control Shutter HAMM WA WA GoT WS LAM Displays the current relative phase between the illumination and excitation cycles Allows for image processing to occur Displays the wrapped phase map if Enable Processing is on Displays the optical modulation map if Enable Processing is on Enable double exposu
99. o 100 Hz and has been demonstrated in the hundreds of Hertz range Sasak1 et al 1990b Dorrio and Fernandez 1998 5 3 Environmental stability It is believed that a four bucket phase modulating interferometer will exhibit greater phase stability than a four bucket phase stepping interferometer implemented on the same device and that this stability will increase with modulation frequency As mentioned in Section 3 1 the accuracy of temporal phase stepping interferometry is related to phase modulator errors appearing from hysteresis and overshoot of piezoelectric actuators random vibrations during constant phase step periods and high frequency distortions of the modulator Creath 1988 Kinnstaetter et Ey i al 1988 Surrel 1993 de Groot et al 1996 Dorrio and Fernandez 1999 Dubois 2001 Ruiz et al 2001 However increasing the number of interferograms acquired for phase calculations will decrease the sensitivity of the PSI system to low frequency effects at the cost of increased computing power and processing time Creath 1988 Surrel 1993 de Groot 1995b Ruiz et al 2001 With traditional PSI algorithms it has been shown that the use of a seven bucket algorithm 1s several orders of magnitude less sensitive to external low frequency noise and vibration than a three bucket algorithm while a four bucket algorithm provides a 2x to 3x improvement over the three bucket algorithm at the cost of minimally larger memory req
100. on of the numerator and denominator for determination of the relative optical phase and modulation maps Group 6 Grabs the next available frame from the onboard buffer of the operating PixeLink camera for calculation purposes Group 7 Transfers the calculated wrapped phase or optical modulation map for creation of a saved output file Group 8 During a sequential save operation automatically increments the save file name to prevent overwriting 123 have raw d images amp either wrapped phase or modulation image EN Kee CN al P Co EE EE i omplete Path ulti File Type 4 AE SA GA E GA Sel ET ee ECH m E iez E CH E EA Te SAC SA SA Te Set SA EA LIES GA Fig D 5 Block diagram case structure set 4 Group 9 Saves the four acquired images needed for calculation of the wrapped phase map and optical modulation map with the calculated wrapped phase or modulation map Group 10 Displays the unprocessed feed from the attached camera system 124 a tow aa Fase Pee Fig D 6 Block diagram case structure set 5 Group 11 Once the save operation is completed reset the file count to 1 for future sequential save operations Group 12 Calculates the relative phase between the stroboscopic illumination signal and the modulation signals at the current phase step and returns this value for signal generation 25 Event Structures Cases 0
101. oped by Hariharan et al 1987 The linearity of the displacement curve is demonstrated m Fig 4 5 where the voltage dependent displacement is correlated to a linear fit with a R 0 99 to ao 10 5 nm or 1 70 at 620 nm I 4 E E D E D ET D E ee ee ee ee ee ee ee a Se E E e ee ee ee ee Displacement nm Displacement nm 100 58 Voltage Vi R 0 9902 Applied Voltage V Fig 4 5 Voltage dependent displacement of the actuator used for phase modulation during the experimentation conducted within this Thesis This high degree of linearity in the displacement curve presented in Fig 4 5 indicates that no additional calibrations are required to ensure a linear displacement of the actuator as ES this 1 modulation error will correspond to a maximum error in the recovered phase map of 0 65 nm at 2 620 nm under PSI operation which is within the published experimental uncertainty of both systems Sasaki and Okazaki 1986a Creath 1988 Sasaki et al 1990a Surrel 1993 This can be assumed for the lifecycle of the actuator as piezoelectric actuators have demonstrated a lifespan in excess of 10 cycles with minimal changes 1n their displacement characteristics when operating under low to moderate displacements under controlled environmental conditions Physik Instrumente L P 2005 However the magnitude of the displacement rate should be verified as above before each experiment with this actuator system to correct f
102. or any drift experienced due to any changes in the environment or fixturing Control and modulation signals are generated by the National Instruments PCI 6713 card controlled through the LabVIEW programming environment This card provides 12 bit arbitrary waveform generation at 1 MS s between a maximum range of 10 V at frequencies on up to 8 channels LabVIEW 7 1 2006 Individual channels are automatically synchronized with a relative output phase of 0 rad based on an internally created trigger signal Additional control is available through the National Instrument Measurement amp Automation Explorer MAX configuration utility for debugging and testing purposes 4 2 Software development The LabVIEW programming environment was chosen to meet the control needs of the phase modulating interferometer due to its ease of use and ability to interface _54 with both FireWire systems and the National Instruments PC control cards LabVIEW 7 1 2006 LabVIEW is a graphical development environment for creating flexible and scalable design control and test applications rapidly and at minimal cost from National Instruments With LabVIEW software development becomes four to 10 times faster than in other programming languages because of its specific design for engineers and scientists National Instruments 2006 Additionally it automatically multitasks and multithreads tasks to optimize processing time Unlike text based progra
103. pe measurement results obtained by imaging of a reference flat under a f 10 Hz modulation cycle This is determined by taking two measurements subtracting them and looking at their root mean square RMS difference standard deviation absolute mean deviation inter quartile range and linear correlation of the difference maps Cohen 1988 Creath 1988 Montgomery 2003 Gorard 2004 This difference should be less than 4 100 for comparison of well calibrated systems and less than 4 300 under low modulation conditions Sasaki and Okazaki 1986a Sasaki et al 1990a Creath 1988 The quadratic mean or RMS value may be used as it 1s less sensitive to outliers though will always be greater than or equal to the arithmetic mean given by CX The RMS can be calculated by H E Zum GE H m where x is the data set of interest k indicates a particular value from the data set and n the total number of values present in data set x The RMS is directly related to the standard deviation o of a given data set by XY X 40 5 7 Ste The shape measurement data acquired from both techniques has been adjusted so that its arithmetic mean will be equal to zero forcing the RMS value to be equal to the standard deviation of the data set This mean is most useful when investigating data which contains both positive and negative components as with a difference analysis as the arithmetic mean may be equal to zero though a large scatter m
104. pe of 540 um diameter central stage wHexFlex using phase stepping interferometry 88 Relative displacement points on central stage and substrate connection of active TMA 90 Vill Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig 5 18 CA C2 C 3 DI D 2 D 3 DA D 5 D 6 D 7 D 8 D 9 D 10 D 12 D 13 Displacement of the damaged uwHexFlex device versus applied voltage as determined through the system developed in this Thesis Settings 1 Basic software controls Base camera settings Save Results Settings 2 Image processing settings Output voltage controls Save Results Settings 3 Operation Plot mode Camera triggering controls Save Results Block diagram of developed LabVIEW system Block diagram case structure set 1 Block diagram case structure set 2 Block diagram case structure set 3 Block diagram case structure set 4 Block diagram case structure set 5 Default event when there has been no changes on the user interface continue program with all prior settings Event structure la when the gamma has been adjusted Stop the camera feed while adjusting the camera gamma value and restart the camera feed Event structure 1b when the gamma has been adjusted adjusting the camera gamma value when the camera is not providing an image feed Event structure 2 if the shutter exposure time has been adju
105. put at 300 mA with a primary wavelength of 617 nm The camera is highly sensitive to this wavelength as seen in Fig 4 3 demonstrating a quantum efficiency of 93 The coherence length was calculated as 16 8 um based on Eq 4 1 and the published spectral output curve shown in Fig 4 4 e F I Ii g o F W en AA 15 nm He Ee AL ye o vot i7tT HA oot ST DI alt Let IN S cf KN 570 580 590 600 610 620 630 640 650 WAVELENGTH mm Fig 4 4 OD 620L spectral output showing peak and full width at half modulation points for determination of coherence length le le is determined to be 16 8 nm Opto Diode 2006 where An is the peak output wavelength of the Opto Diode LED 617 nm and A2 is the full width at half modulation 15 nm as shown in Fig 4 4 A Thor Labs ITC502 200mA 16W bench top laser diode controller was used for illumination control due to an output noise level of lt 1 5uA and setting resolution of 52 10uA output noise and low temperature drift while providing analog modulation in constant current mode at a maximum frequency of 500kHz Output current is modulated with an input voltage signal at 20 mA V 5 Thor Labs 2006 The piezo actuator used in this Thesis was previously modified from a commercially available piezoelectric device from RadioShack RadioShack 2006 The voltage to displacement ratio was found to be 100 58 nm V through application of the five phase shifting algorithm devel
106. ray detector Beam splitter Light source Reference mirror ji a Infinity corrected objectives HEY Object Fig 4 2 Linnik configured interferometer Wyant 2002 Kreis 2005 5 0 These objectives allow for adjustment of the system magnification power while providing a relatively simple means for maintaining the same unmodulated optical path length in each arm An advantage to this configuration is the wide variety of allowable illumination sources both long and short coherence For this work a PixeLINK PL A741 1 3 megapixel monochrome camera is used as the imaging system due to its high performance and FireWire control capabilities PixeLINK 2006 As presented in Fig 4 3 the PL A471 has peak quantum efficiency at 660 nm meaning that an illumination source at this wavelength will require a lower output power to generate the same acquired intensity value Therefore the control system will generate the lowest stroboscopic modulation amplitude at this wavelength decreasing the response time and overshoot of the illumination source Thor Labs 2006 Opto Diode 2006 Spectral Response AW 0 400 700 900 1000 Wavelength nm Fig 4 3 PL A741 quantum efficiency curve peak 2 660 nm PixeLINK 2006 5 Consequently a high output LED from Opto Diode was chosen as the stroboscopic illumination source due to the multiple illumination wavelengths available The chosen OD 620L has 23 mW of power out
107. re mode Acquire the reference image set Normally set to 0 allows for a small change in the reference mirror excitation amplitude Plots the midline of the wrapped phase or modulation map on the line graph displayed This plot will alternate between the two maps if both are displayed Determines 1f the midline shown 1s along the row or the column of the wrapped phase or modulation image Controls the shutter acquisition time of the camera when in free run mode in ms Not used otherwise 152 Gamma Gamma a bare RR RE RERER LR RERE RL RR ER ERE RR ERE SERRE RIL EE SE Waser 10 LEI Zu ZB SU an 4o Region of Interest D d a T FL K gt ki e 9 a Pixel Addressing Value None J Pixel Addressing Mode DECIMATION e Voltage Control Frequency Frequency 2 0 000 5 200k 10 30k 15 00k 20 0k S Amplitude qat sawm D 150 ZO Current Change 10 mA Duty Cycle Duty Cyce GER wos eu anu oo Bau uy Phase Phasa a e Sg pny A A0 o Co Adjusts the signal amplitude of the camera system at the expense of increasing the noise level by a similar amount default 0 Affects the brightness of mid level tones in an image by output input Sets the region of interest ROI of the camera view Distance from the left edge of the CMOS Distance from the top edge of the CMOS Width of display window Height of display window Width and Height values will default to
108. reating a misalignment between the object and reference beams However this approach increases the level of physical complexity within the interferometric system while introducing a secondary frequency shift into the reference beam requiring an additional photo detector to determine the shifted beat signal after modulation Regardless of how the beat frequency is created these systems measure the returned optical phase by timing the arrival of zero crossings on the sinusoidal illumination signal Chapman 2002 Spatial heterodyning relies on the addition of a carrier frequency on the interference pattern This technique alternatively known as a Fourier transform method was proposed as an alternative to traditional homodyne and heterodyne techniques Takeda et al 1982 A spatial carrier frequency may be generated interferometrically though the addition of a tilt to the reference mirror in a homodyne system or through the use of a holographic grating Modern applications include projection of a computer generated fringe pattern allowing for the determination of optical phase through a single interferogram while solving for the sign ambiguity problem This technique relies on the projection or creation of a carrier fringe pattern higher than the spatial variations present 10 within the recovered optical phase This condition limits the measurement resolution of a spatial heterodyne system to the ability of the holographic system to both project
109. red in Appendix B and Creath 1988 1992 From Fig 5 8 we see that the difference between the shape maps has a full range of 1 nm with an inter quartile range of 0 220 nm As shown the difference map appears to have a sinusoidal pattern equal to twice the four fringe carrier frequency This variation is expected based on the effects of additive noise on the recovered shape As presented in this Thesis in Appendix B the mean squared error is proportional to twice _76 the optical frequency Similarly errors in phase stepping interferometry have been shown to be similarly proportional to twice the optical frequency Creath 1988 Surrel 1993 As the difference map is not normally distributed standard deviation is no longer an appropriate measure of the distribution however the mean absolute deviation D can be found to be 0 134 nm By calculating the correlation coefficient between the two data maps the degree of randomness between the acquired shape measurements can be found Using the Pearson product moment correlation coefficient the two shape measurements are found to correlate to 0 9856 and to 0 9956 with removal of data external to the IRQ This extremely high coefficient demonstrates the equivalency of the shape measurement results between the two interferometric methods at this low modulation frequency As shown through testing of the optical gauge the reproducibility of these results applies under modulation frequencies up t
110. reis 2005 Later phase stepping interferometry was developed where the intensity integration occurs at discreet phase steps These techniques provide an RMS accuracy of 4 100 ina Be well calibrated system Creath 1988 As the acquisition speed increases the phase error level increases due to increasing phase shift miscalibration error At high frequency the reference excitation waveform becomes distorted due to jerk and other inertial effects on the reference mirror Increasing the number of recorded interferograms reduces the degradation in the recovered phase shift error at the expense of increasing processing time de Groot 1995a This Thesis implements phase modulating interferometry PMI as an alternative technique to minimize the impact of rapid acquisition speeds on the recovered phase map while providing measurement resolution on the order of 1 nm or better When initially proposed by Sasaki and Okazaki 1986a phase modulating interferometry combined 4 bucket integration with a sinusoidal reference excitation providing continuous reference motion with a waveform that will remain undistorted at high excitation frequencies A variant of this initial work has been developed that operated in quadrature under stroboscopic illumination These variations allow for both the rapid acquisition of interferograms and the use of stop illumination techniques for the capture of rapid motions vital in dynamic and in situ measurements of MEMS dev
111. rement of larger shape variations in both the implemented and other interferometric systems Bet 5 development of a portable control system for use with additional imaging systems and phase modulators The above tasks seek to increase the portability and functionality of the phase modulating interferometer system for use in rapid static and modal MEMS characterization Op 7 REFERENCES AD Technology Inc www 4dtechnology com last viewed Sept 7 2006 Abramowitz M and Stegun I A Handbook of mathematical functions with formulas graphs and mathematical tables National Bureau of Standards Dover Publications Washington D C 1970 Agilent Technologies Inc Fundamentals of signal analysis Application note 243 Agilent Technologies Inc 1999 ATIS telecom glossary 2000 ATIS Committee T1A1 prep www atis org te2k American National Standards Institute Inc 2000 last viewed Sept 7 2006 Bitter R Mohiuddin T and Nawrocki M LabVIEW advanced programming technique CRC Press NY 2000 Boresi A P and Sidebottom O M Advanced mechanics of materials Wiley NY 1985 Caber P Interferometric profiler for rough surfaces Appl Opt 32 19 3438 3441 1993 Chapman M Heterodyne and homodyne interferometry Renishaw Group www renishaw com 2002 Chen S and Culpepper M Design of a six axis micro scale nanopositioned uHexFlex Prec Eng 30 314 324 2006 Co
112. roup and element Glynn 2002 The elements within a group are numbered from to 6 and group numbers progress from 0 9 The first element of even numbered groups is at the lower right with the remaining five elements 2 through 6 at the left as shown in Fig 5 1 LI 4 II RI al III M3 EEN Sm 2 IS e d oe cam HH IIl 6 5 II 4 sma pae eem IH Brech fe Fig 5 1 Recorded USAF 1951 negative glass target with group 7 outlined for containing the smallest resolvable element set Edmund Optics Inc 2006 As shown the negative glass target allows for the lines within each group to appear dark relative to the reflective surface surrounding each element set Due to the age of the standard no standardized quantitative metric exists to determine the ultimate spatial resolution recoverable from the target With the advent of modern imaging arrays it has become common practice to extract a line profile along the least resolvable elements 63 given by the dotted line in Fig 5 1 and determine the ultimate spatial resolution at the element containing individually resolvable lines at a contrast level of 10 based on a spline data fit as shown in Fig 5 2 E _ E os CETTE TY D 4 Fig 5 2 Spline fit intensity profile of pixels extracted along horizontally oriented bars in Group 7 of the USAF 1951 negative glass target Through this procedure the limiting element set is found to be group 7 element
113. s List of figures List of tables Nomenclature Objective l 2 Introduction Background 2 1 MEMS material property variation 2 2 Nondestructive evaluation of MEMS 2 3 Interferometric options 2 4 Benefits of phase modulating interferometry Theoretical analysis of phase modulating interferometry General derivation of phase modulating interferometry with stroboscopic illumination 3 2 Use of sinusoidal reference excitation 3 3 Determination of reference excitation amplitude and phase Implementation 4 1 Experimental system 4 2 Software development 4 2 1 Installation 4 2 2 Operation Representative Results 5 1 Spatial resolution 5 2 Measurement resolution and repeatability 5 3 Environmental stability 5 4 MEMS application _iv ll lll IN vi xil xili 10 13 15 23 Zt 28 32 38 49 50 54 58 59 62 62 64 77 81 5 4 1 Shape measurement 83 5 4 2 Quasi static testing 89 6 Conclusions and future work 92 7 References 97 Appendix A Integration of instantaneous intensity function 105 Appendix B Additive noise effects on phase modulating interferometry 109 Appendix C Front panel of the developed LabVIEW VI for control of the phase modulating interferometer 115 Appendix D Block diagram of the developed LabVIEW VI for control of the phase modulating interferometer 119 Appendix E Operation package installation 142 Appendix F Standard operation flow chart 146 Appendix G Detailed description o
114. s in each equation According to the derived equations K and Ke are periodic with respect to the reference excitation amplitude and phase values However they are also dependent on the duty cycle of the stroboscopic A0 illumination source Figures 3 4 to 3 9 display periodicity of these constants between 0 and 2x radians in both amplitude and phase Multiple stroboscopic duty cycles are presented to illustrate its effects on the calculated phase constant maps Sine constant d 15 a os ki L Les o ad a Excitation amplitude rad Fig 3 4 Representation of K at 15 illumination duty cycle Cosine constant d 15 Magnitude Excitation amplitude rad Fig 3 5 Representation of K at 15 illumination duty cycle A1 Sine constant d 10 wm Ka ZE e eu Wi Ba Excitation amplitude rad Fig 3 6 Representation of K at 10 illumination duty cycle Cosine constant d 10 Magnitude Excitation amplitude rad Fig 3 7 Representation of Ke at 10 illumination duty cycle A7 Sine constant d 5 wm Ka ben 7 LES eu Wi i Fig 3 8 Representation of K at 5 illumination duty cycle Cosine constant d 5 Magnitude Fig 3 9 Representation of K at 5 illumination duty cycle From Figs 3 4 to 3 9 and Eqs 3 18 and 3 19 it is shown that amplitude of the sine and cosine constants is varies sinusoidally from an absolute maximum of K
115. s required the development of two software packages to meet the objectives indicated above The first package operates the phase modulating interferometer under stroboscopic illumination while the second implements a phase stepping algorithm again under stroboscopic illumination The resultant packages are functionally identical for the operator to minimize transition between the two systems Both systems operate at several frames per second during calculation of the wrapped optical phase where the frame rate is limited by the generation time of the output voltage signals to ensure the generation of a high quality low distortion modulation function With the developed control system the Linnik configured interferometer demonstrates a spatial resolution of 2 762 um over a 2 967 x 2 373 mm field of view using a 1280 x 1024 CMOS array camera and 4x magnification objectives The measurement resolution of the phase modulating interferometer has been qualified on a NIST traceable 500 A 2 5 thick gold film structure Through the use of a difference analysis relative to a flat plane the recorded data cloud indicates a film thickness of 503 A 7 A which lies within the design tolerance of the investigated sample when operating at a reference modulation frequency of 100 Hz Similar results are obtainable through the use of phase stepping techniques Furlong 2007 The reproducibility of the shape 93 measurement data has been shown in comparison to phas
116. stantaneous intensity function as seen in Eq A 5 I t ell Ly t coslg oly 2y Ven Van v eosam or ot m A 5 21 inl 7 Ms DEED To determine the intensity recovered by the imaging array the resultant time variant equation must be integrated over the acquisition period of the imaging array Fora stroboscopically illuminated system the acquisition period is defined as a percentage of the modulation cycle The integration length Az is then the period of the modulation signal multiplied by the illumination duty cycle d To determine the location of this acquisition window in time the center is defined to be at the quadrature points of the sinusoidal modulation signal where p defines the frame number 1 2 3 or 4 S gel SH A 6 Consequently the limits of integration for the time variant function are 106 pl At 4 2 l I It dt Al p In A 7 EE 4 2 The first two terms within the time variant intensity function will be integrated to the average background and modulation intensities recovered over the acquisition period However integration with respect to time requires that the power series converges and is continuous over for a constant value of time As both the sinusoidal and Bessel functions are continuous their multiplication will provide a continuous function for any value of time Consequently both additive terms can be integrated with respect to time For simplification the instantaneo
117. sted send the new value to the camera system This setting is not read when the camera is operating in Low Integrate trigger mode Event structure 3a update the current camera trigger settings based on parameters found on the user interface and operate under the new settings Parameters are explained in Appendix F Event structure 3b update the current camera trigger settings based on parameters found on the user interface Deactivate reading of the trigger settings for camera operation Event structure 4 this event enables the Trigger Update button on the interface to set triggering parameters on selected camera system X 9 116 117 118 120 121 22 123 124 125 126 127 128 129 130 131 132 Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig D 14 D 16 D 19 D 20 D 21 D 22 FI Le Event structure 5a this event begins the display of the unprocessed camera feed if the trigger signal is being generated at a frequency above 0 Hz Event structure 5b this event displays the unprocessed camera feed but does not allow for image processing when ether the camera trigger signal is not output or the modulation frequency is set to 0 Hz Event structure 6 this event reads the current value of the Wrapped Phase Map and Modulation buttons from the user interface Event structure 7 this event sets the gain value of the a
118. t non uniform shapes Chen and Culpepper 2006 This non uniformity is believed due to residual stresses during the fabrication of these components As these arms are non functional no planar tolerances were enforced during prior qualification However this up to 6 um curvature may be used in future work investigating the residual stresses within these uHexFlex devices DI Figures 5 15 and 5 16 depict the recovered shape of the largest uHexFlex device containing a central stage of 540 um in diameter using phase modulating and phase stepping techniques respectively As with the smaller devices this sample had previously undergone testing to failure Unlike the prior examples failure in this device involved breakage of both a flexure arm and multiple TMA structures as indicated in Fig 5 15 However this device exhibited less distortion otherwise than the other two devices compared to the nominally planar structure Width mm 0 25 0 50 0 75 1 00 1 25 Lan 1 75 2 00 wm Length mm Fig 5 15 Recovered shape of 540 um diameter central stage uHexFlex using phase modulating interferometry with damage indicated to the TMA and armature structures 87 0 25 0 50 0 75 1 25 Width mm 0 25 0 50 0 75 1 00 1 25 Lan 1 75 2 00 m Length mm Fig 5 16 Recovered shape of 540 um diameter central stage uHexFlex using phase stepping interferometry As before a displacement exists between the central stage and surroun
119. tached camera id numbers Operating camera id number Error flow Fig D 19 Event Structure 8b this event sets the pixel addressing mode and value as explained Appendix F when the camera feed has not been enabled 138 amera control settings oxoo000002 A ttached Camera id numbers FEATURE ROI Y a ad Operating camera id number E E Error flow Min allowed ROI fa Fig D 20 Event Structure 9a this event stops the current camera feed to alter the region of interest ROI within camera view both in size and location ROI values must be multiples of 8 and width height must be equal for proper display and processing No error checking has been implemented to ensure that the selected ROI is within the imaging array area 139 a 9 ROT value Change amera control settings 00000002 7 Attached camera id numbers FEATURE ROI 7 ROI e Operating camera id number Error flow Min allowed ROI fa Fig D 21 Event Structure 9b this event alters the ROI within camera view both in size and location when camera feed is not previously enabled Restrictions from figure D 20 apply 140 Wavelength Tweak Ref Mirror Excitation Value Change Set Camera amp Illumination Properties Set Se er step value amera control settings gt See Attached camera id numbers 1000 gt gt _ gt tegration Time Operating camera id number poet Blum Phase rror flow Set Reference Mirror
120. tants respectively These terms are solely functions of the reference mirror motion assuming at a constant illumination duty cycle Mathematically they are given as 36 en Samat nfm Yeo sin 2m Ae Al ge Ps 2m 1 3 18 2 JomulY m Ei ac in 2m 17 d sin 2m 1 2 d I and K y 6 Z a Zanlt cos 2md sin 2mz d hu ge 3 19 Ria cos 2m6 sin 2mz d m 1 m To remove the sign ambiguity a ratio of X and c is used to extract the optical phase through the use of an arctangent calculation as K v 0 unlg SZ 3 20 While Eq 3 17 will provide the optical phase of an object for any known reference excitation amplitude and phase these properties can be optimized to minimize the effects of additive noise on the recovered results improving both accuracy and measurement repeatability Additive noise has the same power everywhere in the frequency domain This arises for example from the fast dynamics along various degrees of freedom within a system from the non zero temperature of a system thermal noise or from electronic read time bias Gitterman 1999 This Thesis assumes a zero mean Gaussian noise distribution as confirmed experimentally Luth 1989 The contribution of this noise on the acquired intensity distribution is given by a new term n and causes the instantaneous intensity term to take the form AT I x y Ip x y Lig x y cosld x y bala y n 3 21 Following the abo
121. ted phase modulating interferometry for use in MEMS characterization the subsequent development of and implementation of a software package for this technique the determination of both the spatial and measurement resolutions of the realized system the application of phase modulating interferometry for characterization of an actual MEMS components and the verification of those results through the use of a traditional phase stepping interferometer The phase modulating interferometry presented in this work serves as an expansion to the techniques presented by Sasaki and Okazaki 1986a 1987 and Dubois 2001 through the incorporation of stroboscopic illumination for dynamic testing This inclusion requires the optimization of the phase modulating parameters both in amplitude and phase relative to the duty cycle of the illumination signal The derived highly non linear relationship between these parameters coupled with the synchronization needs 02 between the modulation illumination and acquisition cycles requires the development of a complex control system with highly accurate calibration of the modulation source This calibration is accomplished through procedures presented in Hariharan et al 1987 The LabVIEW programming environment was chosen for the software development due to its parallel processing capabilities and flexibility in the control of both an imaging system and multi channel output cards This Thesis ha
122. the method and the test sample 4 understanding the potential and limitations of the technology 5 understanding of surrounding economic environmental and other factors 13 Before using any NDE method there must be some knowledge of the properties of interest In MEMS an investigator may be interested in the modulus of elasticity of an object of interest This requires information on how modulus of elasticity may be calculated or how it may affect the system of interest whether through dynamic or static effects This knowledge works to drive NDE method choice If the structure of interest is a laminated plate with homogenous and isotropic material properties modulus of elasticity may be determined through investigation of the stress strain relationships within that structure assuming an application of general plate theory the Kirchhoff hypothesis and planar stress These assumptions allow for calculation of the modulus of elasticity bulk modulus and Poisson s ratio within that object assuming knowledge of the applied stresses and resultant strains Boresi and Sidebottom 1985 Guckel et al 1985 Many NDE methods may be used to extract the stress and or strain information needed for these calculations Larger samples may use an ultrasonic technique for determination of these elastic constants by investigating wave propagation through the sample though typically this requires contact by a transducer receiver In a small system th
123. the user interface only allows direct control of the phase or frequency parameter of this signal excepting a parameter known as excitation period count While the amplitude of the stroboscopic illumination signal 1s independently 59 controllable its frequency can only be adjusted by modification of the excitation period count This parameter allows for the acquisition time to occur over multiple reference excitation periods The result is a linear averaging in the resultant interferogram at a particular phase on the reference modulation signal which serves to reduce transient effects both environmental and systematic Agilent Technologies Inc 1999 Additionally when there is poor reflectivity from an object of interest this parameter provides a means of increasing the number of photons absorbed by the CMOS array without adjustment of the reference modulation signal frequency Appendix G provides a detailed description of additional user interface parameters as displayed in Appendix C Limitations in the developed code will be further discussed in the Future Work Section of this Thesis however several operational issues must be noted Of primary concern is the square region of interest requirement in the developed software As the base PixeLINK VIs and OEM control are optimized for viewing by the user they do not capture nor display a continuous stream of images from the A741 camera system Directly tapping this video feed for processi
124. tion of the crystal orientation of the substrate Dry etching involves the removal of material by gaseous etchants though requires the periodic deposition of an etching protective material to minimize the side 10 wall angle in an etched cavity Rai Choudhury 2000 Hsu 2002 Krauss 2002 Furlong 2004a Lithographic techniques include the LIGA molding process LIGA a German process 1s an acronym for X ray lithography Lithographie electroplating Galvanoformung and molding Abformung Developed in the 1980s LIGA was one of the first major techniques to allow for manufacturing of high aspect ratio structures with lateral dimensions below one micron and thicknesses up to 500um Hsu 2002 Furlong 2004a This technique allows for the creation of 3 D microstructures defined by 2 D lithographic patterns The height to width ratio capability is relevant to the manufacturing of miniature components that can withstand high pressure and temperature and can transfer useful forces or torques Sandia 2006 Variation in the structure and material properties of MEMS devices exists between fabrication sites and within fabrication batches Consequently the material properties of acommon MEMS material deposited by one manufacturer can vary substantially from that deposited by another Further variation is present between and within wafer batches during production runs Exponent Inc 2000 As seen in Fig 2 4 a silicon nitride film applied across
125. try and that with phase stepping interferometry For comparison testing is conducted at a 4x magnification under a modulation frequency of 10 Hz and stroboscopic duty cycle of 14 A 2 32 x 2 32 mm region of interest is imaged of a reference flat demonstrating a flatness of lt 4 Four carrier fringes are introduced over this region to ensure a high contrast ratio and hence high data quality As measurements are taken full field the contrast ratio 1s calculated as y Lmax min l 5 11 Imax min with application of a low pass filter to the raw interferograms to reduce the effects of random noise where Jing and Imin are the maximum and minimum interferogram intensity values respectively From this equation the contrast is then found to be 87 33 indicating an excellent fringe contrast and consequently high data quality Kreis 2005 The tilt corrected shape shown in Fig 5 7 demonstrates the overall flatness of the reference flat as recovered with sinusoidal modulation _74 um 0 05 0 00 0 05 0 10 1 16 2 32 Location mm nen LA 1 16 0 00 DES Location mm Fig 5 7 Shape of reference flat recovered with sinusoidal modulation operating at f 10 Hz and demonstrating a surface flatness of 4 4 For comparison the arithmetic mean of the shape maps recovered with sinusoidal modulation and phase stepping is set to zero As shown in Table 5 1 the low modulation frequency shape measurements demonstr
126. uirements de Groot 1995b Surrel 1996 Alternatively four bucket sinusoidal phase modulating interferometry has been shown to be almost insensitive to external perturbations such as mechanical vibrations at low frequency compared with the modulation frequency Sasaki et al 1990b In part this decreased sensitivity is due to a reduction 1n hysteresis experienced by a phase modulator during sinusoidal displacement Physik Instrumente L P 2005 Additionally individual interferograms are acquired over multiple modulation periods at constant phase locations on the sinusoidal modulation signal The result is a linear averaging within each resultant interferogram that leads to a low frequency filtering which serves to reduce transient effects both environmental and systematic on the recovered optical phase map Sasaki et al 1990a Agilent Technologies Inc 1999 Physik Instrumente L P 2005 Consequently it is expected that at lower modulation frequencies the sensitivity of the PMI system to external vibrations will approach that of a phase stepping interferometer operating under similar conditions Sasaki et al 1990a 29 To experimentally verify the stability of the developed phase modulating interferometer the mean wrapped phase drift is observed for f 10 Hz and 100 Hz and compared to results obtained with a four bucket phase stepping interferometer operating at f 2 Hz All experiments are conducted under a stroboscopic duty cyc
127. ullaxld Ag Set SJA U0 E slebpoy YEW 4q Ee Eg Pleo OVA 9 ewe YUI SXIg SUISN UOTJE NpoW seyd eplosnuls 10 sjoru0 Fig C 2 Settings 2 117 ket aseyd padden SCS 005 Str OG Secr OOF SLE OSE See DE Sc ID Sec WR S T OST Set OOF S ID Se H l l l l l I l I l 5 pn aw Buissaz0dg Bvd EJ souanbas aves uibag H NOD uogsnboy 14eg dug Sswepy a Duape E ug e T Aan b Wed 21207 ss puy aew Buissso014 eq synsay BABS SU D ZH o0 O SW SPAD Aguanbasy 26511 Su D T JEH ag awy WoOQeIGS UT yunga ponad Lopez SJOU PoIleApy ppppp p CG oo000 O SUE U Apg 55u E aAgebapy Aquejog J256 Sea uwung 3344 UUUTH 3344 yo ad 65u 7 ry sa66u moq 0 apop ug apoy a55 Jeu SIODu0OH MES Bunau jo quoy aDpIDA jo Qu0D eJaweT HUT egen MOY E d Es CC l crj A Cep pajeg aun 7 oooerg E en c SUIT 10 xa g M UODELDXZ JOU Ja Man apo Uogevedg DDUO DuUESaO0Old jo quoD zuawngsu XEW IN Yuljexd AQ PaplAqud ia up paseq SlafDpo HEN A0 zeara or DIE ova AN BIOUWIE JUH Xd surs UONE poN ospU d EPlosnuls IO S10 1 U0 D trols Save Results iggering con n Plot mode Camera tr 10 Operat Fig C 3 Settings 3 118 APPENDIX D Block diagram of the developed LabVIEW VI for control of the phase modulating interferometer The following is the developed LabVIEW block diagram code for implementation of the phase modulating interferometer using the hardw
128. us modulated intensity is assumed constant over time to remove its time dependence within the integral This can be assumed 1f the coherence length of the illumination source is large relative to the modulation amplitude resulting in a spatially constant fringe contrast This assumption can be validated after calculation of modulation amplitude Integration is carried out by hand and verified through MathCAD 2004 The resultant recovered intensity map is then found to be 107 Ip 1p 1y cos Joly 00 a Jom T But 2m m cos 2m sin m 27d 2m sin A 8 i Jom Ee e 2m 1 m m 0 sinf 2m E d sin 2m 1 27d Equation A 8 is similar in form to the results produced in Dubois 2001 with differences in the power series due to the addition of the stroboscopic illumination source While these differences increase the mathematical complexity of the acquired interferogram extraction of optical phase can be accomplished as shown in Section 3 by linear combinations of a set of four acquired frames 108 APPENDIX B Additive noise effects on phase modulating interferometry To determine the optimal reference excitation amplitude y and phase the influence of additive noise on the calculation of the optical phase was studied As with Dubois 2001 this Thesis assumes a zero mean Gaussian noise represented by np 0 B 1 and oi if i j en ae ES applied to each of the four frames where the magn
129. ve derivation the recovered optical phase will suffer an error and take the following form as shown in Appendix B Kee Dee lye tan g FREE A C C 3 22 where N and N Eqs B 5 and Bo Appendix B represent the error contribution within each acquired interferogram assuming a high signal to noise ratio These error parameters are of the same form as the linear interferogram combinations 3 and X As demonstrated in Eqs B 18 B 19 and B 20 the mean mean squared and standard deviation of the recovered error can be minimized when the phase constants are equivalent and their magnitudes are maximized These two conditions can be used towards optimization of the reference excitation amplitude and phase parameters 3 3 Determination of reference excitation amplitude and phase As demonstrated in Appendix B the mean and mean squared error functions indicate that the sine and cosine constants K and K respectively must be maximized and equivalent to minimize the additive noise effects on the recovered optical phase ATIS 2006 However the optimization of these parameters is non trivial due to the periodic nature of both functions and the infinite Bessel function summation in each equation The convergence characteristics of these infinite power series must be investigated to provide a functional limit to the power series terms for calculations 29 Convergence is tested over w 0 to 27 and 0 2r to at d 1 to 25 The
130. ve noise contribution nondestructive evaluation National Institute of Standards and Technology optoelectronic holographic methods phase modulating interferometry phase shifting interferometry stiffness matrix XY component Pearson product moment correlation coefficient region of interest within a full field of the imaging array root mean square reference modulation period sec thermomechanical actuator user interface interference fringe contrast or the magnitude of the complex quantity whose phase describes the position of the constructive and destructive interference regions relative to a reference arbitrary constants recovered shape nm XV OBJECTIVE The objective of this Thesis is the review and implementation of a wavefront sensing technology as an alternative to traditional phase stepping or phase shifting methodologies It is expected that this will allow for a reliable measurement resolution of 1 nm or better allowing for nondestructive shape and displacement characterization of MEMS devices This Thesis will compare results obtained under multiple modulation frequencies to those obtained with low frequency phase shifting interferometry to demonstrate the quality of the developed system under high modulation frequencies 1 INTRODUCTION Microelectromechanical systems MEMS have evolved from the integrated circuit IC industry as an effort to radically miniaturize the scale of electromechanical systems while incre
131. vely 2 n tan is EE Ne B 13 dis Ze Ze and N NY Ne NY ui tan g 1425 1 225643 e B 14 s A Zu Ze III An infinite time average can be applied to these error equations allowing for the calculation of the respective mean and mean squared functions The infinite time average is based on the assumed additive noise behavior and so results in the statistical properties seen in Eq B 15 In Eq B 15 it is shown that the mean noise amplitude is zero due to the assumed zero mean behavior of the Gaussian additive noise Similarly the mean combination of the two additive noise constants 1s non zero only when the constants have the same amplitude N 0 N 0 and B 15 N N 40 NN der With the properties determined in Eq B 15 the infinite time average of Eqs B 13 and B 14 can then be written as shown in Eqs B 16 and B 17 2 7 tan i SI B 16 C and 77 tan EEN e B 17 Ls Ze Combining equations B 16 and B 17 with B 10 and B 11 and simplifying we can find that the mean error and mean squared error are inversely related to the magnitude of the sine and cosine constants while being directly related to the obtained optical phase Therefore it 1s possible to represent the mean and mean squared error in Eqs B 18 and B 19 as 12 on l l ee B 18 e 8Iy T P dl Se Ge and Se 2 2 2 O T sin cos ea ee ee ep B 19 Mee Geng oe From Eq BIS we find that t
132. vices are found ubiquitously throughout the modern world Applications stemming from the groups presented in Fig 2 2 include inertial navigation systems integrated optomechanical components for image display embedded sensors and actuators for condition maintenance shown in Table 2 1 and much more Furlong 2004a Be Table 2 1 Microsensor families Position Pressure Inertial Magnetometers Radio frequency Electrochemical Field effect transistors Molecular specific Cell based Much of this industry growth is focused on the development of micro sensors with higher spatial resolutions and temporal bandwidth than their macroscale counterparts while requiring less operating power Judy 2001 Typically it can take 10 yrs and millions of dollars to develop a new sensor or a MEMS platform Over the years most of the development money has been spent on pressure sensors and accelerometers and as such these two areas are the furthest developed MEMS technology Electronic Design 2000 MEMS Industry Group 2006 However little standardization exists within industry in all but the simplest designs though organizations such as the American Society of Mechanical Engineers and the Institute of Electrical and Electronics Engineers have begun developing standards for adoption as industry norms With increasing commercialization there has been a greater push towards the acceptance of these standards particularly in MEMS testing and pa
133. w is related to the amplitude of the sinusoidal phase modulation z by An ee ae 3 8 where the wavelength of illumination Kreis 2005 The reference phase excitation is then also a function of the angular frequency of excitation oi and the relative phase between the excitation and illumination cycles amp Consequently the sinusoidal reference excitation Eq 3 7 has units of radians and therefore can be incorporated into the continuous interferometric intensity distribution With the addition of this excitation the resultant intensity distribution is of the form I t Ip t 1y t coslo y sin a t OI 3 9 To determine the intensity recovered at the imaging system the intensity equation must be integrated over the acquisition period Both the trigonometric identity shown as Eq 3 10 cos X Y cos X cos sin X sin Y 3 10 and the Bessel function identities Abramowitz and Stegun 1970 in Eq 3 11 Ee cos X sin Y Jo X 2 op LX cos 2k Y k and 3 11 sin X sin SE x sin 2k 1 Y are needed to rewrite Eq 3 9 into integrable form The time variant intensity 1s now given by I t p t Im t cos g Joly 21 m Ven gt Vox y cos 2k a t d 3 12 vlt sil 5 Jaga w sin 2k Io t d As discussed previously a four integrating bucket method was proposed to define the acquisition period for static structures Sasaki and Okazaki 1986a Dubois 2001 This technique d
134. ware Surfacer to perform a difference analysis that evaluates the difference between a calculated plane and the measured shape information Metrix Inc 2006 Calculation of film thickness is accomplished by 69 extracting the difference value at multiple locations on both the substrate and gold film These points shown in Fig 5 6 serve to eliminate any small tilt on the object of interest as well as the effects of aberrant peaks or valleys within the recovered shape information Fig 5 6 Deviations from planarity as determined by difference analysis using phase modulating interferometry operating at f 100 Hz d 14 indicated a nominal film thickness of 503 A 7 A under PMI PSI methods indicated a nominal film thickness of 501 A 7A Furlong 2007 The recovered shape information indicates a nominal film thickness of 503 A 7 A under a sinusoidal phase modulation at f 100 Hz and d 14 Similarly phase stepping interferometry indicates a nominal film thickness of 501 A 7 A at f 2 Hz and 20 d 14 These results are comparable to those indicated by Furlong 2007 with phase stepping interferometry and lie within the specified tolerance of the gauge device To demonstrate the reproducibility of the results obtained with phase modulating interferometry over a range of modulation frequencies a low frequency test is conducted using both phase stepping and phase modulating interferometry through a statistical comparison of sha
135. works this Thesis research could be further extended with the following list of tasks _94 1 2 3 4 determination of a closed form solution which describes the equivalency between the phase constant equations This closed form solution would allow for a global optimization of the phase modulating parameters without the use of the power series limits set in this Thesis and the required iterative solver Removal of the iterative solver will allow for calculation of the modulation parameters automatically under arbitrary stroboscopic illumination duty cycles without the need for interpolation as currently implemented in the software control package reduction in the software processing time through the use of an external signal generator As developed approximately 90 of the program cycle time is used in calculation of the analog voltage output signals Consequently the control of an external voltage output device will immediately increase the operational speed of the developed coding leading to higher processed frame rates further error qualification of the developed system particularly focused on comparisons to phase stepping interferometry Itis expected that this work will quantitatively highlight the improvements of phase modulating interferometry over phase stepping interferometry in dynamic motion studies and in its relative immunity to environmental disturbances the addition of multiple illumination sources for measu

Download Pdf Manuals

Related Search

Related Contents

Mode d`emploi à destination des parents  VGN-CR420E/P  Maxi Rotators - User Manual  ICY BOX IB-2216StS  Bandelettes réactives aux fuites de sang    Cummins Fire Pump USER'S GUIDE  LaCie PCI-Express/2 x SATA II  

Copyright © All rights reserved. Failed to retrieve file