Interferometric Optical Testing for High Resolution Imaging in an
Contents
1. Wolf Principles of Optics 7th Edition Cambridge Uni versity Press 1999 Y R P Sortais et al Phys Rev A 75 013406 2007 A Mazouchi Feasibility of Single Atom Imaging in an Optical Lattice M Sc Thesis University of Toronto 2007 M Greiner amp S F lling Q amp A Optical Lattices Nature 453 736 2008 K D Nelson et al Nature Phys 3 556 2004 D Malacara Optical Shop Testing 3rd Edition Wiley 2007 E P Goodwin amp J C Wyant Field Guide to Interferometric Optical Testing SPIE Press 2006 G Fowles Introduction to Modern Optics 2nd Edition Holt Rinehart and Winston 1975 T Wang Lab Notes 2 Volumes Summer 2008 Aberration Balancing Melles Griot Catalog X 1 27 1 28 2005 PizelFly QE Operating Instructions PCO 2006 M E Hetland Beginning Python Apress 2005 M Takeda et al J Opt Soc Am 72 1 1982 D C Ghiglia et al Two Dimensional Phase Unwrapping Wiley 1998 392. Camera which is a simulated camera that always displays an image of an idealized cold atom cloud e lib_pf dll found in the subdirectory C_interface PixelFly and wraps functions from the camera driver DLL in a way that can be accessed from Python This interface was necessitated mainly by the fact that I could not figure out how to deal with the data type HANDLE from the camera drivers directly in Python e pixelfly_interface py imports the wrapped functions from lib_pf dll and defines Python functions for them e pixelfly_camera py contains the definition of the camera object which is a set of attributes and methods calling on the functions defined in pix 35 elfly_interface py Other program elements reference this camera object so attribute and method names were kept as consistent as possible with the corresponding Pixis camera object definition in pixis_camera py My contribution to PyCamera consists of the last three items which enable the program to control the new PixelFly cameras acquired by the lab The lib_pf dll file was built in a C project located in the PixelFly dev lib_pf directory on the disk included with 9 The compiled DLL file is stored in the PyCamera program folder with the path C_interface PixelFly Both pixelfly_interface py and pixelfly_camera py are stored in the root PyCamera folder PixelFly dev PyCamera A 4 Interferometric Optica
3. is to consider two such peaks separated by a small Aw with the left side peak at wo gt gt Aw Fig 2 5 top This is the well known phenomenon of beating between two frequency 12 20mW 10mW SmW Relative optical power output 403 404 405 406 407 408 409 wavelength Ap nm Figure 2 4 Sharp laser diode emission spectrum at room temperature and var ious power settings There are multiple mode peaks in the spectrum enveloped by a gain profile components 2149 gt t cos A t cos wot cos wo Aw t 2cos with a slow beat frequency Aw enveloping a fast oscillation at 2w9 Aw 2 The beat frequency is Aw instead of Aw 2 because envelope maxima differ in phase only by a It is easy to see that our full treatment is simply an extension of this analysis For five equal amplitude frequency components Fig 2 5 middle the beat pattern becomes more complex but the underlying periodicity remains unchanged In the full treatment we add a Gaussian envelope to these five peaks and again we observe the same underlying periodicity with a slight change in the beat pattern Fig 2 5 bottom In this analysis the individual spectrum peaks were taken to be infinitely narrow meaning that these individual modes have an infinite coherence length Consequently the beat patterns depicted Fig 2 5 also extend to infinity and this extension becomes truncated as we consider the broadening of the discrete spectrum peaks w
4. ms and the lack of automated image analysis capabilities such as Gaussian fitting that are vital to experimental work in the lab Demo Project a sample C project supplied by PCO for controlling the camera From this project and specifically cam_class cpp I learned everything about writing a DLL file in C to interact with the camera driver Pccam dll The Demo Project has a video mode Cont Pic1 under the Control menu which is useful for experiment alignment purposes The exposure time can be set to a precision of 1 us by changing the value of the iExp_video variable defined under CpcCam CpcCam int board This variable is an integer which 34 sets in microseconds the exposure time of each video frame PF Driver this is a test bed I wrote for accessing functions from the Pix eFly camera drivers Functions for one image acquisition cycle are called in sequence with diagnostic text messages output to the command line While no image readout functionality has been implemented the code does include a timing algorithm to determine how long it takes to execute a block of code between the lines test startTimer and test stopTimer This allows the user to measure actual image readout times which combine both the hardware readout time given on p 22 of 11 and the execution time of the code Further details can be found by referring to Book 1 p 173 174 of 9 PyCamera a versatile image proces
5. sophisticated acquisition sequence Absorption imaging to obtain the optical density of atoms in a trap involves taking two images in quick succession In the first image a probe laser beam illuminates the atoms which absorb part of the beam The second image is simply a reference image of the laser beam without any atoms present If the intensity distributions captured by the camera are I and Ip respectively then the optical density OD is defined as R OD In A 1 To 36 PyCamera Absorption imaging Pixis Camera _ asmo Egemen Camere Splenng Exponeetine us 1 agger mode Settee tender od des i tee here i DMN Ble 162246 NoriZoncal A oooocooooom mpubvavDoo g g oS 0 G00 B00 100012001200 Figure A 2 An acquired interferogram is displayed in PyCamera bottom left Intensity distributions in the horizontal and vertical directions are displayed and it is evident that fringe visibility here is excellent Periodic intensity minima are close to zero while the maxima are arranged in a Gaussian envelope which is expected given that the light source is a single mode fibre right Camera tab contains user selections for controlling the camera 37 The reason the images must be taken in quick succession is to reduce unwanted noise effects For example there are spurious fringes resulting from internal reflections within various optical components If t
6. 400 500 600 Figure 3 2 Fourier transform of an interferogram using image_2Dft m show ing the three characteristic peaks corresponding to the three vertical white stripes Note that the spectrum has been shifted to bring the zeroth order peak to the center of the image so the horizontal scale has been shifted such that 300 corresponds to 0 e phase_unwrap m performs 2D phase unwrapping on a given array e compute_rms m compute the standard deviation of data points in a 2D image array and outputs to the command line This calculates the root mean square phase distortions in the obtained phase profile The main analysis script analysis m performs the required tasks in several steps by calling the other defined functions Before it is executed an image array with the name imagel must be loaded into the MATLAB workspace for example by opening one of the MATLAB image data files saved by PyCamera The user may specify additional cropping dimensions for this image to remove noisy edge areas The image is Fourier transformed Fig 3 2 and by looking at plots of the spectrum along individual rows of the image using image_1Dft m the user can isolate the side peak and define its center and width With the side peak defined the analysis script proceeds to calculate the phase profile d x y Due to the properties of the Fourier transform the calcu lated phase will be restricted to the range from r to 7 However the
7. Hardware Triggering The camera can be triggered either by code in the software or by the rising edge of a 5V pulse from an external signal generator Camera signal timing diagrams and further details about external triggering are given on p 21 24 of 11 The camera interacts with the external world via an unusual 26 pin HD DSUB port on the PCI controller card A cable converting this port to a single BNC connector for external hardware triggering was provided by PCO 33 Figure A 1 Conversion from 26 pin HD DSUB to four BNC connectors input external hardware triggering output camera busy CCD exposure and image buffer readout In addition a pair of conversion boxes one for each camera were constructed Fig A 1 to allow access to three additional output signals from the camera which indicate the status of various internal processes A 3 Summary of Camera Programs The programs described in this section with the exception of CamWare which is installed as a Windows program can be found on the disk included with 9 in the directory PixelFly dev Note that because all the programs require the same camera driver file Pccam dll only one can be running at a given time CamWare included with the software disk from PCO Gives easy access to camera functions and contains the useful temperature monitoring window de scribed in 2 5 Its drawbacks include being able to specify exposure time only to a precision of 1
8. Interferometric Optical Testing for High Resolution Imaging in an Optical Lattice TOUT WANG Department of Physics University of Toronto Supervised by Joseph Thywissen May September 2008 Abstract This report describes an interferometric optical testing project aimed at con tributing to the construction of a high resolution imaging system for resolving individual sites in an optical lattice It begins with a background discussion touching upon the relationship between optical distortions and imaging reso lution the motivation for imaging individual sites in an optical lattice and popular methods of interferometric optical testing This is followed by a de tailed description of the components of the actual experiment with an extra emphasis on the laser diode and the CCD camera Finally the report outlines the Fourier transform method of interferogram analysis and presents a success ful calculation of the wavefront distortions resulting from light passing through various interferometer test objects List of Figures 1 1 1 2 1 3 2 1 2 2 2 3 2 5 2 6 2 7 2 8 2 9 Wavefront Distortions Due to an Optical Window 6 Geometric Representation of Aberrations 7 Interferometer Configurations for Optical Testing 9 Overview of Experiment Components 11 Laser Diode Pin Configuration 0 0 11 Laser Diode Mount 2 00002 ee eee 12 Sharp Laser Diode Emissio
9. ability because a cone of light rays emitted from one geometric point on an object can be brought to focus at another geometric point on the image However due to the wave nature of light and in particular due to diffraction effects no imaging system can take light from one point to another This sets a fundamental resolution limit that depends on the wavelength of light used For a microscope with numerical aperture NA and light at wavelength A the resolution limit R is defined as the minimum separation that can be distinguished and the minimum value of R called the diffraction limit is on the order of a wavelength of light A A thorough analysis of image formation in microscopes can be found in 8 6 3 of 1 But this is still in the case of perfect optical components In practice im perfections in the imaging optics will cause additional aberrations in the form of distortions to the the wavefront emerging from the source Fig 1 1 The full treatment of the diffraction theory of aberrations is included in Chapter 9 of 1 but for our purposes it is sufficient to appreciate that wavefront distor tions directly impact imaging resolution The simplest way to understand this is to return to the geometric picture Fig 1 2 Wavefront distortions in the wavefronts a wv a diffraction o limited source gt window Figure 1 1 Illustration of how the presence of an optical window can introduce distortions to wavefronts emergi
10. actual phase has no such restriction and thus may differ from the calculated phase by multiples of 27 This is the phenomenon of phase wrapping Fig 3 3 To de termine the actual phase profile the wrapped phase must be unwrapped Along a single axis this is simple and the method is described in 13 In the current MATLAB implementation this has been extended to work in two dimensions simply by unwrapping the first column then unwrapping each row to obtain the full 2D unwrapped phase function Once the unwrapped phase function 24 100 200 300 400 500 600 700 800 900 Figure 3 3 Plot of the wrapped phase function calculated from the interfero gram The scale on the right goes from z to r Note the distinct phase jumps marked by sharp transitions between white and black Marked regions correspond to noisy points along the first column that will cause errors to occur in phase unwrapping has been computed useful measures such as the root mean square rms phase distortion can be calculated 1 A Orms N DL Hy p Here is the phase at each point while is the average phase across the entire region of interest and N is the total number of sample points 3 4 Discussion of Results The unwrapping algorithm described in 3 3 will produce errors in the un wrapped phase function when the original wrapped phase is too noisy Fig 3 4 for example when there are actual phase differences of more than 7 be tween adjace
11. al lattice These are elaborated upon below in two sections experiment design and analysis methods I do not expect all these suggestions to be acted upon because on the one hand they might not be intelligent ideas and on the other hand at some point the interferometric optical testing experiment might work sufficiently well that further improvements would not contribute significantly towards the overall high resolution imaging effort The points in each section are organized from my perspective in order of priority Improvements to Experiment Design e A possibly significant source of noise in the current experiment is diffrac tion from dust particles on various optics These produce circular fringe patterns which distort the interferogram see for ecample Fig 2 8 and increase the calculated root mean square phase distortion in the MATLAB analysis Currently the most significant source of these spurious fringes is a dirty neutral density filter placed in front of the CCD camera to atten uate the laser beam It has been carefully cleaned but it seems that some of the damage is permanent Fringes due to scattering from point sources on other optical surfaces can be cleaned up by spatial filtering with a lens and pin hole combination in front of the camera e Improved beam quality will allow phase distortion calculations to be done on a larger interferogram area Currently the interferogram has its noisy edges cropped because phase unwrappin
12. an optical window inserted in one of the arms right The Fizeau interferometer contains all the optics in a single arm and relies on single reflections from the reference and test objects to form the two interfering beams negligible effect on the overall interferogram The main disadvantage of this configuration is that another mirror is required along the optical path beyond the test object If the interferometer is used to test distortions due to a vacuum deflected window see 3 4 of 3 it would not be feasible to place another mirror within the vacuum chamber itself because proper alignment would be difficult to say the least On the other hand the Fizeau interferometer is ideal for vacuum testing because the final element along the optical path is the test object itself The reference beam obtained from a single reflection from the reference object in terferes with another reflected beam from the test object Immediately a major problem becomes apparent each object assuming they are flat produces two reflections from each of its two surfaces This gives four interfering beams not two Experimentally two obvious solutions exist One is to coat the object surfaces so that one of the two surface reflections becomes dominant The other solution is to place the two objects very close together and use a low coherence length light source such that the only two reflections capable of producing in terference are those from the two adjac
13. avefront distortion involves a parameter known as the Strehl ratio see 9 1 of 1 and 3 2 of 3 The Strehl ratio is defined as I Ia Ip In this definition we consider the diffraction pattern of light from an idealized point source after passing through some optical system Jo is defined as the Figure 1 2 Geometrical representation of aberrations in an optical system left Consider a cone of light rays emerging from a point source right Suppose that the presence of an optical window after the point source introduces spherical aberrations into the system meaning that light rays emerging from different points on the window have their apparent foci at different locations along the optical axis when traced back Since this apparent source of light rays is no longer a geometric point the resolution of any image formed from the distorted light rays will obviously suffer peak intensity in the Airy pattern for perfect optical components while Iq is the measured peak intensity for the actual distorted wavefronts As the central spot size of the diffraction pattern increases the resolution limit also increases but the peak intensity must decrease to conserve power Thus if J 1 then the system is at the resolution limit described in Equation 1 1 As the Strehl ratio I decreases from this maximum value of 1 the resolution limit of the optical system increases In the case of small wavefront distortions the Strehl ratio J can
14. be related to the root mean square wavefront distortion Arms by Equation 24 in 9 1 of 1 Ixi Ar 1 2 A popular standard for imaging quality is the Marechal criterion which requires I gt 0 8 or correspondingly Adpms lt 4 14 The preceding discussion demonstrates that the root mean square measure of wavefront distortion A ms can be meaningfully related to imaging resolu tion This makes it a superior measure of optical quality compared to peak to valley P V wavefront distortion because an imaging system with higher P V distortions can still be superior to another with lower P V distortions if the larger amplitude distortions are isolated to small regions of the wavefront The section on the Star Test in 6 presents a visual test of optical quality using the Strehl ratio which does not require the calculation of the root mean square phase distortion Arms 1 2 Imaging Single Atoms in an Optical Lattice An optical lattice is formed by interfering pairs of laser beams to create a stand ing wave Since atoms interact with electromagnetic fields through dipole forces an optical lattice is basically a periodic potential for atoms An overview of the motivations behind studying atoms in optical lattices can be found by referring to 4 The attraction of working with optical lattices is that they effectively simulate a simple condensed matter system On the other hand experimental parameters in optical lattices can be controlled m
15. belled by LD PD and G L refers to the laser diode while P refers to the photodiode A means anode grounded while C means cathode grounded 2 2 Laser Diode Spectral Characteristics The laser diode from Sharp is longitudinally multimode with its emission spec trum consisting of closely spaced peaks over a range of about 1 nm and enveloped by a gain profile Fig 2 4 We can estimate the coherence length according to 3 6 of 8 Avt amp 1 where Av is the frequency linewidth and Te is the coherence time From this and assuming a linewidth of 1 nm the coherence length is less than 1 mm This sets a strict limit on the alignment of the optics because if the optical path difference OPD of the interfering beams exceeds this coherence length we will not observe clear interference fringes However further analysis reveals that the question of laser diode coherence requires a more sophisticated answer because the width of the gain profile enveloping the multiple emission peaks is not a good approximation for the linewidth used in the previous calculation which comes from considering the broadening of a single mode line If we instead treat the spectrum more accurately as a series of regularly spaced peaks in frequency with a gain profile that we will assume to be Gaus sian we arrive at different conclusions for laser diode coherence that are exper imentally verified To begin the simplest case
16. diode power with the attenuation filter removed Decisive measurements were taken after a good quality beam was obtained out of a coupled fibre and a large area photodiode was substituted for the power meter The results summarized in Book 1 p 157 of 9 revealed reflectivities that were virtually indistinguishable However the New Focus 5100 mirrors seemed to perform marginally better and coupled with the fact that its high reflectivity plateau is centered around 405 nm rather than bordering on it this mirror was selected as the winner 2 4 Remaining Optical Components Following the optical path depicted in the experiment overview Fig 2 1 light from the 405 nm laser diode is sent through an optical isolator to shield the laser against back reflections from optical components along the beam path To 15 Power mW 0 00 0 05 0 10 0 15 0 20 0 25 0 30 0 35 0 40 0 45 Relative Position inches Figure 2 6 Scan across the power meter active area at constant laser diode power revealed significant variations caused by damage to the attenuation filter Such non uniformity makes it challenging to perform power measurements for mirror reflectivity and other tests improve the laser diode beam shape light is coupled into a single mode optical fibre Beam quality is crucial for interferometry because fluctuations in the intensity profile of two interfering beams should come from phase differences between the beams rather than dis
17. ee bb bob ays 2 6 Early Experiments 0 5 50 e ee eee 3 Interferogram Analysis 3 1 Survey of Popular Approaches ooo aa 3 2 Fourier Transform Method 04 3 3 Implementation in MATLAB 3 4 Discussion of Results oaoa a a 3 5 Possible Errors in Interferogram Analysis 4 Future Directions A PixelFly Camera Notes A 1 Software Installation Issues o oo a A 2 Hardware Triggering oaa a A 3 Summary of Camera Programs aaa a A 4 Interferometric Optical Testing 0 A 5 Imaging of Trapped Atoms 204 Bibliography 21 21 22 23 25 27 30 Acknowledgements I had the pleasure of interacting with each member of the group over the course of the summer Marcius repeatedly provided useful advice in matters of camera programming Dylan and Dave the two graduate students in this half of the lab continuously challenged me with thought provoking questions about what I was doing Although Jason Lindsay and Alma spent most of their day next door I had to call upon each of them at one time or another whether it was about finding a missing optical component or asking how to go about setting up new pieces of the experiment Julie and Michael were my fellow summer students and the rapport between the three of us made lab work more enjoy able Both of them have the privilege of continuing their efforts towards an undergraduate thesis I
18. ent surfaces Unfortunately it was not possible to implement either solution in the project However 2 6 does contain some brief descriptions of experimental attempts at doing interferometry in the Fizeau configuration Chapter 2 Experiment Components This next chapter will provide detailed descriptions of the components of the interferometric optical testing experiment Fig 2 1 These are used to set up an interferometer in the Twyman Green configuration although some attempts at realizing the Fizeau configuration are also mentioned The test wavelength is 405 nm which is on the violet end of the visible spectrum It was chosen to coincide with the planned imaging wavelength in the optical lattice experiment 3 Laser diodes at this wavelength are a fairly recent development so I have included a thorough discussion of issues involved in powering the diode as well as careful considerations of its emission properties which are important towards interferometric optical testing 2 1 Powering a 405 nm Laser Diode The light source for the experiment is a Sharp GH04020A2GE laser diode with emission wavelength around 405 nm and output power of 20 mW This diode sits on a ThorLabs LDM21 laser diode mount which contains a thermo electric cooler TEC to regulate the laser diode temperature The laser diode pin configuration Fig 2 2 is a nonstandard one and is not compatible with the interface sockets on the LDM21 Fig 2 3 regardless of
19. ertically aligned Alternately one could include a simple MATLAB array rotation function in the analysis script to rotate the fringes until they are completely vertical The other source of error is more subtle but can be easily corrected The analysis algorithm in 83 3 requires the user to define the center of the side peak by examining plots of Fourier transforms along rows in the interferogram It is possible that a mistake will occur and the center of the side peak will be defined at w wo we instead of wo with we being the frequency error Following the steps described in 3 2 when the side peak is shifted back it will be displaced by we from the origin and upon Fourier transforming back to recover c x y the result is instead c x y exp iwex c x y The extra factor ezp iwex comes from the relationship between Fourier transformed pairs where a translation of one leads to an imaginary exponential factor in the other Now if we substitute the original expression for c x y we have c 2 y Zole y enplion 2 9 where 1 z y a y wex This clearly implies that an error in defining the side peak will result in a large phase gradient in the x direction 29 Chapter 4 Future Directions There are still many areas in which efforts can be made to improve the current interferometric optical testing method bringing the overall experiment closer to its goal of high resolution imaging of individual sites in an optic
20. g beams are derived from a single light source and we place an optical component in the path of one of the beams the resulting interference pattern becomes a measure of the wavefront distortions introduced by the component under testing Two good references for interferometric optical testing are 6 and 7 I will not describe the basic concepts that are already clearly explained in these books Instead I will comment on some of the practical issues surrounding the common interfer ometer configurations Fig 1 3 The Twyman Green interferometer is perhaps the most familiar configura tion because it is simply a modified Michelson interferometer The beam with the distorted wavefront is formed by light transmitted through the test object reflected by the end mirror and then transmitted through the test object a sec ond time For a transparent component such as an optical window the final beam intensity is close to the original intensity meaning that spurious interfer ence patterns formed by internal reflections within the test object itself have mirror beam termination H test mirror beam object ET beam H splitter splitter 4 output Pe eee 4 gt output 1 beam beam I test input reference input object beam object beam Figure 1 3 The two most common interferometer configurations for optical testing left The Twyman Green configuration is basically a Michelson inter ferometer with a test object such as
21. g would not succeed otherwise This unfortunately limits the cross sectional area of the optical compo nent that can be analyzed for wavefront distortions The main improve ment to beam quality should come from a better alignment of the beam expansion telescope 30 e Different geometries such as the Mach Zehnder configuration can be at tempted Both of the current geometries the Twyman Green and the Fizeau cannot produce a beam that traverses exactly the same optical path as would be the case for imaging in an actual lattice namely a single transmission through all optical components in the imaging system to the camera The Mach Zehnder is the only common interferometer configuration that can test distortions due to single transmission through an optical component However it is a challenge to align especially given the phenomenon of periodic fringe visibility observed for our light source e Along a similar line of thought to test for distortions in a set up that mimics the actual optical lattice imaging system as closely as possible it might make sense to focus the beam down using a large NA lens and then pass the beam through an optical window shortly after the focus Of course the lens will introduce additional spherical aberrations to the beam but this will be present in both of the interfering beams while the final interferogram will only capture differences between them Also approaches for testing components other than f
22. hase distortions Equation 3 1 can be rewritten as g x y a x y c x y exp iwor c x y exp iwox 3 2 1 c z y zbe yexplio a y If we take the Fourier transform in x of Equation 3 2 we get where the capitalized letters denote the corresponding Fourier transformed func tions Now comes a key assumption suppose that spatial variations of a x y b x y and a y are slow compared to the spatial frequency wo of the underly ing fringes This means that the frequency space widths of A w y and C w y are small compared to w and we see that the plot of Equation 3 3 would consist of three separate peaks Fig 3 1 If we then apply a bandpass filter to isolate C w wo y followed by a shift of wo we recover C w y which can be Fourier transformed back to give c x y If we now apply the logarithm function Inle x y Inl5b 2 iole y which suggests how the phase information can be extracted p z y Im in c a y 3 4 Clearly this outlined method rests crucially on the assumption that spatial variations of a x y b x y and x y are slow compared to wo As a result this method of analysis is inappropriate for interferograms with high levels of 22 A a y C y C y 00 Oo Figure 3 1 Three separate peaks in the Fourier transformed spectrum of an interferogram The two side peaks are symmetrical about the origin and contain information about the phase dis
23. hase profile across the entire region of interest The 600 pixel width corresponds to about 2 3 mm of transverse beam area microscope slide and a thick vacuum window have Arms equal to 0 91 and 0 18 waves respectively The region of interest in all these cases is a square of 600 pixels in length which corresponds to approximately 2 3 mm of the transverse beam area A full record of these tests can be found in Book 2 p 89 101 of 9 It is interesting that the thick vacuum window shows less evidence of wave front distortions compared to the expensive high quality sapphire window On the one hand this could be due to the fact that the sapphire window is ex tremely thin making it much more difficult to produce low distortion surfaces On the other hand the distortion measurements in this report were performed using a collimated beam at normal incidence on the window As mentioned in 1 1 greater distortions due to spherical aberrations in the thick vacuum window would have been observed for an incident beam with a larger NA and these distortions will certainly be relevant to the actual high resolution imaging system Two other pieces were also tested another sapphire window of lower quality and a crude piece of transparent plastic but both plots of the wrapped phase showed significantly more distortions compared to the other test objects and were too noisy to be unwrapped in the given region of interest 3 5 Possible Errors in Interferogra
24. he time between exposures is short enough that the fringes do not shift significantly this depends on the frequency of mechanical vibrations in the system and should be less than 1 ms which is far shorter than typical CCD camera readout times then the compu tation for OD in Equation A 1 will cancel out any intensity variations due to these fringes The previous camera model used to image atoms in this way was the Pixis It had a kinetics mode to get around the limitation of CCD readout time and enable fast double exposures The CCD chip would be divided in the vertical direction into regions of equal height and only one of these regions would actively acquire images The others act as image buffers and after one image is taken the charges are quickly shifted to a buffer region to allow a second exposure to occur This kinetics mode is fast because shifting charges between areas of a single CCD chip can be done much more quickly than charge readout from the entire chip into a memory buffer The PixelFly camera does things a little differently It has an interline CCD architecture meaning that for every line of active imaging pixels there is a corresponding line of masked pixels whose sole task is to be a temporary image buffer The image readout process occurs via first shifting charges from the active to the masked pixels and then reading out to an actual memory buffer As with the Pixis camera charge shifting can occur very quick
25. here are three important pieces of documentation for the camera e PixelFly Operating Instructions 2006 version directly from PCO 11 is more in depth than the 2002 version from Cooke which is included on the CD accompanying the camera e PCO Camware User s Manual which describes the features of the default image processing software from PCO e PixelFly Software Development Kit which contains detailed instructions about how to write code to interface with the camera hardware drivers Camware in particular contains a useful Camera Control window which can display the CCD electronics temperature The PixelFly camera does not contain an active cooling system and is designed to shut down if the CCD temperature exceeds 65 C this is not in the manual but is given in the online FAQ s for the PixelFly VGA the less sensitive version of the QE The camera begins to warm up as soon as it is powered even if it is not acquiring an image and typical temperatures when powered but dormant for extended periods of time are 53 C for the unit with serial number 270 XD 13933 and 48 C for the unit with serial number 270 XD 13934 Significant changes to these steady state temperature levels might indicate the onset of camera hardware failure In addition to the software provided by PCO the camera has also been made to work with various programs written within the lab For example the inter ferogram analysis method described in Chapter 3 requ
26. hich are a set of functions that describe the interferogram appearance resulting from various types of aberrations such as tilt defocusing and astigmatism More in depth descriptions of these polynomials can be found on p 24 29 of 7 and in Chapter 13 of 6 The coefficients obtained in this fit are an indication of the amount of aberration of each type present in the optical component under test and this can then be transformed into a measure of phase distortion However complicated fringe finding algorithms are required to define the locations of fringe centers in an interferogram order to map the distortions in the fringe pattern The supplementary disk that comes with 6 contains a program which can generate interferograms according to user specified Zernike polynomial coefficients This is also installed in the OpticsTesting Interferogram directory on the disk included with 9 and it is useful for getting a sense of how various distortions affect the appearance of interferograms Unfortunately it cannot do the reverse Another approach is known as phase shifting interferometry PSI It is ex plained in detail on p 32 42 of 7 and Chapter 14 of 6 Ideally it would be possible to compare two interferograms one with the optical test compo nent in place and one with empty interferometer arms and extract the phase distortion information from the changes in intensity at each point of the two corresponding interferograms Practica
27. hich reduces the coherence lengths of the individual emission modes Clearly then coherence length depends more on the linewidths of the individual spectrum peaks than the shape of the overall gain profile meaning that the coherence length of our Sharp laser diode is orders of magnitude greater than the 1 mm estimated at the start of this section This bodes well for using such a light source for interferometry 13 Figure 2 5 Analysis of laser diode coherence in Mathematica Functions com posed of sums of cosines at the indicated frequencies are plotted to examine their behaviours For simplicity the phase of each cosine was set to zero and Aw w 1 400 top Two equal amplitude spectrum peaks showing the clas sic beating phenomenon middle Five equal amplitude peaks bottom Five peaks in a Gaussian envelope Looking at the behaviour of the laser emissions we are studying Fig 2 5 it is also apparent that if two such beams undergo interference with one another the greatest fringe visibility is achieved when the envelope maxima overlap As the OPD between the two interfering beams is changed this overlap will be periodic at the beat frequency Aw and likewise for the fringe visibility This periodicity of the fringe visibility is experimentally observed in 2 6 The phenomenon of periodic fringe visibility suggests another solution to the problem of multiple spurious reflections in a Fizeau interferometer described in 1 3 Assu
28. ires images to be saved in a MATLAB file format and this is done with an image processing program written in Python Additional notes about the PixelFly camera including de tailed instructions for its use in both interferometric optical testing and imaging of trapped atoms are included in Appendix A It is important to be careful not to damage the camera by exposing it to a focused laser beam As a safeguard a negative lens has been placed in front of the camera Fig 2 7 to gently expand any incident beam Also an attenuator in the form of a neutral density filter is present to further protect the CCD chip from overexposure Finally a movable positive lens in front of the camera allows adjustments to the size of the beam at the image plane of the camera 2 6 Early Experiments In this section I will describe some of the earliest experimental work with the Twyman Green interferometer This mainly involved observing interferograms qualitatively for properties such as fringe visibility and distortion A more sophisticated and quantitative analysis method for extracting phase information from these interferograms can be found in Chapter 3 17 neutral density filter positive lens negative lens C mount to SM1 adapter Figure 2 7 A C mount to SM1 adapter is used to change the PixelFly camera thread to that of the ThorLabs lens tubes A neutral density filter and a negative lens are attached to the camera body A
29. isual inspection of the wrapped phase function might be sufficient 32 Appendix A PixelFly Camera Notes In this Appendix I will provide instructions for how the PixelFly camera is to be used in the lab The camera has been programmed and tested for use in both interferometric optical testing and imaging of trapped atoms A 1 Software Installation Issues A number of difficulties were encountered with software installation at the start of the summer The lab s main image processing program is written in Python using a specific version called the Enthought Python Distribution EPD which includes a large collection of scientific computing libraries Many of the library references included in the program code turned out to be obsolete with endless errors arising when the program was executed with the newest version of the EPD The implemented solution was to install exactly the same version of the EPD and its various associated libraries as was used when programming work first began back in 2006 These install files can be found on the disk included with 9 in the directory PythonInstall Another issue that came up was a WindowsError encountered when Python attempted to load the DLL file written in C to interface with the camera driver DLL This can be resolved by installing Microsoft Visual Studio 2005 on the system If the error persists it might also be necessary to recompile the DLL file on the local computer A 2
30. l Testing As mentioned in Appendix A 3 for initial interferometer alignment it is best to use the Demo Project from PCO because it is written in C and can achieve fast frame rates whereas PyCamera can only manage two or three frames per second even when analysis algorithms are disabled Once it is clear that the camera is capturing an interferogram of sufficient quality the user can switch to image acquisition using PyCamera Fig A 2 The camera should be set to single exposure with software triggering Also in the Acquisition tab the Save images box should be checked This will bring up a window for the user to specify the folder and file name under which the images will be saved PyCamera will append both a four digit index and the MATLAB extension mat to the specified path At this point activating the Toggle button will produce a set of MATLAB files corresponding to each image acquired Each file when opened will contain at least two image arrays imagel and image2 The second of these is simply a blank image in the single exposure mode of operation so only imagel needs be imported into the MATLAB workspace Analysis of this imported interferogram image then proceeds as outlined in 3 3 A 5 Imaging of Trapped Atoms The main difference between using the PixelFly camera to image trapped atoms and using it to capture interferograms is the fact that absorption imaging of atoms requires a more
31. lat windows are offered in 6 and 7 e Using a single mode laser source can avoid the issues caused by periodic fringe visibility and possibly open up new possibilities for interferometer configurations However narrow linewidth long coherence length light sources are typically not used for interferometric optical testing because they will introduce more spurious fringes from internal reflections within various optical components e A Geller MRS 5 optical target consisting of high density bar and square patterns was acquired during the course of the summer for testing of imag ing system resolution However the project did not proceed that far but the components are in place to test the change in pattern contrast when illuminated by light which then passes through various optics such as vac uum windows and lenses The PixelFly camera can be used to capture an image of the optical target pattern and this can then be analyzed in MATLAB in much the same way that the interferograms were studied Improvements to Analysis Methods e Currently the calculations for root mean square wavefront distortions in troduced by the optical components under testing do not subtract the underlying phase variations of the empty arm interferometer which is on the order of 4 10 It would be a simple extension of the current analysis algorithm to subtract the two unwrapped phase functions one being that of the test object and the other corresponding to the empt
32. lly however this does not work because of the unavoidable non uniformities in the source beam of light PSI solves this problem by shifting the phase of one of the two interfering beams by known amounts using for example piezoelectric crystals A minimum of three such in terferograms are taken and these can be analyzed to extract information about the phase This proposal is obviously complicated by the need for piezoelectric crystals to generate well defined shifts A simpler method exists for extracting the phase profile of light passing through the optical testing component using 21 only a single interferogram This is known as the Fourier transform method of interferogram analysis 3 2 Fourier Transform Method The Fourier transform method of interferogram analysis is a remarkable method of extracting phase information that does not involve either fringe finding or phase shifting The basic theory presented here closely imitates the approach of the original paper 13 The method is also explained on p 43 of 7 and in 14 14 5 of 6 A 2D interferogram consisting of phase distortions on top of straight fringes in the horizontal direction can be described by g x y a x y W x y coslwox zx y 3 1 where a x y represents the background and b a y takes into account non uniformities in the interfering beams The spatial frequency of the fringes is determined by wo while x y is the term corresponding to the added p
33. ly while charge readout to a memory buffer consumes most of the image acquisition time To take two images in quick succession the first exposure occurs and while the charges from this first image are in the buffer pixels being read out the active pixels are exposed again for the second image A key limitation is the fact that the exposure time of the second image cannot be independently specified it must be equal to the time it takes to read out the first image Thus actual exposure times must be determined externally through the timing of probe laser beam pulses Further description of this special mode of operation can be found by referring to p 23 of 11 In the PyCamera interface Fig A 2 setting up the camera to take two shots with either type of trigger signal and Dual Trigger 0 will enable this fast double exposure mode of image acquisition With hardware triggering and Dual Trigger 1 the PixelF ly camera can also take two slow single exposures defined by two external trigger pulses The purpose of this slower double exposure mode of operation is to enable absorption imaging tests of a magneto optical trap in which atom dissipation times are long enough that no real advantage is gained by taking fast double exposures Performing two single exposures on the other hand allows much greater control over the timing of each individual image 38 Bibliography N DD oO A 10 11 12 13 14 M Born amp E
34. m Analysis There are two obvious possible errors that can occur in using the interferogram analysis algorithm described in 3 3 First of all Equation 3 1 assumes that the underlying straight fringes are in the x direction If the interferometer is misaligned and the fringes are tilted it is clear that the calculated phase function 27 4 L 1 l L 0 100 200 300 400 500 600 Figure 3 7 Plot of data points along the center row 300 in the wrapped phase function Fig 3 5 The horizontal scale is the pixel number while the vertical scale is the phase A width of 600 pixels corresponds to approximately 2 3 mm in the transverse beam area A clear phase jump between 7 and 7 is observed between pixels 500 and 600 0 100 200 300 400 500 600 Figure 3 8 Plot of data points along the center row 300 in the unwrapped phase function Fig 3 6 The horizontal scale is the pixel number while the vertical scale is the phase A width of 600 pixels corresponds to approximately 2 3 mm in the transverse beam area 28 100 200 300 400 500 600 Figure 3 9 The effect of errors in defining the side peak is demonstrated in comparison to the original wrapped phase function Fig 3 5 Note that this wrapped phase function shows a significant gradient in the x direction will have a large gradient in the y direction It seemed to be sufficient during this project to simply make sure visually that the fringes are v
35. m also grateful to Alan for the occasions when he took the time to explain to me how one should do electronics work properly Final thanks go to Joseph for challenging me with this project teaching me numerous experimental skills that will no doubt serve me well as a graduate student and allowing me to turn part of his lab into an optical testing experiment This work was funded by the Natural Sciences and Engineering Research Council of Canada NSERC Introduction I had several goals for my final summer prior to starting graduate school I wanted of course to have as much fun as possible before the inevitable pressures of studying for a Ph D I thought it might also be a good idea to keep my mind sharp by doing an interesting research project and so I tried with obvious success to get a position in the Ultra Cold Atoms Lab led by Joseph Thywissen Finally I decided that it would be to my advantage if I could get some practice with computer programming over the summer months because it had been a while since I had thought seriously about programming problems and these skills will no doubt be vital to doing physics research In the end it turned out to be a minor miracle that I was able to accomplish all these goals with the work described in this report because at first glance they would appear to be mutually exclusive The remainder of this report presents my two main contributions to the experimental efforts in the lab First as the
36. ming that the internal reflections within each individual optical com ponent interfere with low fringe visibility due to a non ideal OPD the separation between the two objects can be adjusted to maximize interference fringe visi bility between reflections from the surfaces of interest However experimental measurements described in 2 6 showed that the spurious internal reflections produced fringes that were already highly visible meaning that this proposed solution would not work 2 3 Dielectric Mirrors Before I describe the remaining optics in greater detail it is worth mentioning the decision involved in the choice of mirrors for the experiment Three dielectric coated candidates were considered ThorLabs E01 E02 and New Focus 5100 From the theoretical reflectivity plots Book 1 p 110 112 of 9 and also the online catalogs the high reflectivity plateau shifts to higher wavelengths as the angle of incidence goes to 0 Since 405 nm is already at the short wavelength end of the E02 coating range the decision was made to acquire only the ThorLabs E01 and the New Focus 5100 mirrors for testing The actual measurements of mirror reflectivities unearthed further compli cations due to non uniformities across the active area of the power meter in the lab Fig 2 6 This is a consequence of damage to the attenuation filter on the power meter and for comparison see Book 1 p 146 149 of 9 where measure ments were taken at low laser
37. n Spectrum 13 Coherence Considerations 000 000004 14 Power Meter Non uniformity 0 16 Beam Shaping Optics Prior to the CCD Camera 18 Demonstration of Varying Fringe Visibility 19 Mounting Optical Components for Testing 19 Fourier Spectrum of the Transformed Interferogram 23 Fourier Transform of an Interferogram in MATLAB 24 Plot of the Wrapped Phase Function 25 Error in Phase Unwrapping 200 26 Wrapped Phase Function in a Smaller Region of Interest 26 Successful Unwrapping of a Phase Function 27 Plot of a Single Row in the Wrapped Phase Function 28 Plot of a Single Row in the Unwrapped Phase Function 28 Effect of Errors in Defining the Side Peak 02 29 PixelFly Camera Interface Box 00 34 PyCamera User Interface 0 2 0 0 000 37 Contents Acknowledgements Introduction 1 Background 1 1 Effect of Wavefront Distortions 0 0 1 2 Imaging Single Atoms in an Optical Lattice 02 1 3 Interferometric Testing Methods 2 Experiment Components 2 1 Powering a 405 nm Laser Diode 002 2 2 Laser Diode Spectral Characteristics 2 3 Dielectric Mirrors a wa ee be ee Be eek Pe ee A 2 4 Remaining Optical Components 0 2 53 CGD Camera murre Soe Oe ddd 4G RE d
38. n the interferometer left A microscope slide was taped to a mirror mount middle Sapphire windows of suitable size can be inserted in a ThorLabs LMR05 lens mount right A vacuum window in its flange is held in a large lens mount 19 lent to that of a Fizeau interferometer These are recorded in Book 2 p 21 22 27 33 36 and 39 of 9 While the aim was to observe interference between one reflected beam from each of the two optical components a test object and a reference object experimentally the reflections from the two surfaces of each individual object already produced strong interference fringes This problem which was anticipated in 1 3 made it impossible to use this interferometer configuration to extract any sort of information about the wavefront distortions due to the test object While a working Fizeau interferometer is crucial to measurements of vac uum window distortions under a pressure differential the decision was made to continue onwards to devising interferogram analysis methods using the more successful Twyman Green configuration with the knowledge that such methods would also be applicable to the Fizeau interferometer as well once the experi mental obstacles of this configuration are overcome 20 Chapter 3 Interferogram Analysis 3 1 Survey of Popular Approaches There are a number of approaches to the problem of interferogram analysis One is to fit the obtained interferogram to Zernike polynomials w
39. ng from a diffraction limited point source When traced back the apparent source of these distorted wavefronts is no longer a diffraction limited point form of for example spherical aberrations will increase the apparent size of the source from a geometrical point to some finite spot Interestingly in the case of spherical aberrations there is a circle of least confusion which is the minimum such spot size along the optical axis see p 238 of 1 The location of this circle of least confusion is off focus meaning that if an imaging system contains spherical aberrations its resolving ability may be improved by going slightly out of focus this has been experimentally applied in the imaging of a single atom in an optical dipole trap 2 It is obvious how this simple geometric understanding of the effect of aberra tions on imaging resolution can be extended when considering the wave proper ties of light If perfect wavefronts from a diffraction limited point are distorted Fig 1 1 the geometric light rays which represent the direction of propagation of the distorted wavefront no longer trace back to an apparent source that is a diffraction limited spot Our resolution limit R will then increase which means that the resolution of the imaging system has become worse Thus far the explanation of how wavefront distortions affect imaging res olution has been an intuitive one A quantitative measure of the dependence of resolution on w
40. nt sample points The current solution is to simply restrict the region of interest to a smaller less noisy area Other highly complicated phase unwrapping algorithms exist to properly unwrap phase functions in the presence of such noise 14 After decreasing the region of interest and repeating the analysis from the beginning the unwrapped phase profile becomes a smooth function Fig 3 5 3 8 The sample that has been tested in this case is a high quality sapphire window SCD2889 02A and the calculated Ad is 0 27 waves Note that the underlying phase distortions in the empty arm interferometer due to imperfec tions in the optics gives a base A rms of about 0 15 waves For comparison a 25 100 200 300 400 500 600 f 700 100 200 300 400 500 600 700 800 300 Figure 3 4 Example of errors in phase unwrapping The unwrapped phase function contains several distinct discontinuities in the vertical direction that are the result of excessive noise at points along the first column of the wrapped phase Fig 3 3 100 200 300 400 500 600 100 200 300 400 500 600 Figure 3 5 Plot of wrapped phase function Fig 3 3 in a smaller region of interest The noisy points along the first column of the previous plot are no longer present 26 200 300 400 600 e 100 200 300 400 500 600 Figure 3 6 Successful unwrapping of the previous phase function Fig 3 5 resulting in a smoothly varying p
41. separate movable positive lens can be positioned to determine the beam diameter at the image plane of the camera One of the first measurements was to test whether fringe visibility behaves as described in 2 2 In Book 1 p 160 of 9 the recorded results show that fringe visibility is indeed periodic reaching consecutive maxima as the interferometer end mirror was translated by 1 5 mm which corresponds to an OPD of 3 0 mm Some brief calculations outlined shortly thereafter on p 185 gives an estimate of the wavelength separation between modes as A 0 05 nm the general approach is to assume that the envelope period is the same as in the two frequency beating case From the Sharp laser diode output spectrum at 20 mW Fig 2 4 top we can estimate that there are about 12 peaks over a 0 6 nm range by counting peaks and measuring their range relative to the given scale This gives a mode separation of about 0 055 nm which compares very favourably to the previous computed value Experimental efforts also demonstrated qualitatively the predicted variations in fringe visibility with OPD For example the fringe visibility changes depend ing on whether the interferometer arms are empty Fig 2 8 For a window of thickness d and index of refraction n the OPD introduced after each pass is n 1 d which can be much larger than a wavelength take for instance d 1mm and n 1 5 This means that using our Sharp laser diode as the light so
42. sing tool written in Python by Gael Varo quaux and updated by Marcius Extavour I learned Python by reading 12 which is available online through the University of Toronto Libraries The main disadvantage of Python its inefficiency tasks that can be performed effortlessly in C cause noticeable delays in Python On the other hand because it is such a high level language it is excellent for programming graphical user interfaces Those who first encounter PyCamera might be confused by various snippets of code The program uses a library called TraitsUI which allows the programmer to focus on designing attributes and methods of each object while TraitsUI automatically generates the appropriate user interface Also references to a kinetics mode correspond to a Pixis camera feature that the PixelFly does not have See Appendix A 5 for more details about this Important parts of PyCamera are as follows e pycamera py the core of the PyCamera program This file is executed to run PyCamera An alternate pycamera_fast py is a stripped down version of pycamera py with no analysis capabilities This decreases the time it takes to go through an image acquisition sequence although the program is still limited to about two or three frames per second e experiment py in this file the line from import as Camera de termines which camera class the program will import The options are the PixelFly or Pixis cameras or a Mock
43. title suggests I made progress towards high resolution of imaging of individual atoms in an optical lattice by constructing an interferometer to test wavefront distortions in the imaging system optical components In addition to this I was also responsible for pro gramming the two new CCD cameras in the lab to work with existing image processing software One of these cameras is in place on the atom trapping side of things ready for imaging both the contents of our magneto optical trap and also colder atoms down the road The other camera is serving dutifully on the interferometer optics table where it captures interferograms for computer anal ysis The project culminated in a successful proof of concept analysis of optical window interferograms producing both a phase profile plot and a measure of the root mean square wavefront distortion introduced by the windows Chapter 1 Background In this chapter I will present the basic background information necessary to understand the aim of the project interferometric optical testing for high res olution imaging in an optical lattice Topics include how wavefront distortions affect the resolution of an imaging system the motivation for site resolved imag ing in an optical lattice and key concepts in using interferometers to test the quality of optical components 1 1 Effect of Wavefront Distortions In the idealized geometric model of optics perfect imaging systems have infinite resolving
44. tortions described by the interferogram distortions but for our tests of high quality optical components with only small levels of distortions expected the Fourier transform method of interferogram analysis is a straightforward and accurate way of obtaining the phase profile of light passing through our test object 3 3 Implementation in MATLAB A suite of functions were written in MATLAB to analyze interferograms accord ing to the method described in 3 2 These can be found on the disk included with 9 in the MATLAB_Code directory The following summarizes the contents of the files e analysis m main analysis script Requires an image array named im agel to be loaded into the MATLAB workspace e image_display m displays a scaled version of image array with a speci fied colour map e array_crop m crops an image array in a rectangular window based on input parameters e image_1Dft m performs a Fourier transform in the x direction on a sin gle specified row in an array User can choose to display only a particular interval of the entire Fourier spectrum e image_2Dft m performs a Fourier transform in the y direction on the entire 2D array e image _getphase m takes a Fourier transformed interferogram image ar ray and performs the operations specified in 3 2 to obtain phase function Requires the user to define the center and width of the side peak 23 200 300 400 500 600 100 200 300
45. tortions from the light source itself Due to the power meter problems described in 2 3 it was a challenge to carefully determine the fibre coupling efficiency The best current estimate from the careful measurements documented in Book 2 p 58 60 of 9 is around 50 The beam emerging from the optical fibre goes through a 4x beam expansion telescope taking the beam diameter from about 2 mm to 8 mm to provide sufficient beam area for optics testing The lenses in the telescope are chosen to minimize spherical aberrations 10 The incoming light is divided along two paths by a plate beam splitter to form the two interfering beams The plate beam splitter has a coated front surface and a wedged back surface which avoids the internal reflection problems present in cube beam splitters It is also more stable than pellicle beam splitters which are sensitive to vibrations and inappropriate for use in an interferometer One end mirror in the interferometer in the Twyman Green configuration is mounted on a translating stage in order to allow for fine adjustments of the OPD between the two interfering beams Such adjustments are necessary to obtain an OPD that maximizes the fringe visibility according to the analysis in 2 2 The interfering beams are directed towards a CCD camera which records the interferogram for analysis 16 2 5 CCD Camera Shortly before the start of the summer the lab acquired a pair of PixelFly QE cameras from PCO T
46. uch more easily than their counterparts in condensed matter systems This makes the optical lattice a promising test bed for proposed solutions to the big questions in condensed matter physics for example high temperature superconductivity Conversely they can also provide clear experimental clues that point the way towards ex plaining these same theoretical problems One of the big goals in the field is to be able to resolve single sites in an optical lattice with period less than 1 wm This distance scale is important because interactions between atoms in neighbouring sites get stronger as the lattice dimensions decrease and these interactions are at the core of interest ing condensed matter phenomena that experiments with optical lattices aim to produce and probe However at these lattice separations the goal of resolv ing individual sites is made especially challenging because the distance scales in question are right at the diffraction limit for visible light described in 81 1 So far the smallest lattice separation that has been resolved is around 5 um 5 and efforts to push on towards sub um lattice resolution require imaging systems with extraordinarily low levels of distortions 1 3 Interferometric Testing Methods The fundamental principle behind interferometric optical testing is that when two light beams are interfered with one another the resultant intensity profile is an indication of their relative phase If the two interferin
47. urce the interferometer arm lengths must be adjusted with each new test object in order to maximize fringe visibility Some of the objects that were tested include microscope slides sapphire windows and thick vacuum windows Fig 2 9 In particular see Book 2 p 15 and 37 of 9 for detailed specifications of the various sapphire windows acquired from Meller Optics The windows with part numbers A00E30471007 and SCD2889 02A were of a suitable size for the ThorLabs LMR05 lens mount and these were tested both in these early experiments and later ones involving Fourier transform analysis Further details of the early tests can be found in Book 2 of 9 Attempts were also made to produce interferograms using reflections from the surfaces of the optical components under testing in a configuration equiva 18 Figure 2 8 Comparison of fringe visibilities when a microscope slide is inserted into part of the beam corresponding to the left side of each interferogram left End mirror adjustments made to maximize the fringe visibility of the empty arm half of the interferogram showing clear straight fringes right Interferometer arm length now adjusted to maximize the fringe visibility of the microscope slide half of the interferogram microscope slide attached sapphire window in vacuum window and flange with masking tape ThorLabs LMRO5 in large 3 lens mount Figure 2 9 Various methods for mounting optical components for testing i
48. what settings are chosen for the toggle switches The implemented solution involves inserting the laser diode such that pins 1 2 and 3 are in the sockets labelled by LD G and PD respectively The toggle switches are set as shown in the second illustration from the top with laser diode L cathode C and photodiode P anode A both grounded Finally a special 9 pin DSUB connector with PD and G pins switched pins 2 and 3 respectively is connected between the laser diode mount and the current controller This produces a pin wiring that matches the required configuration Further details can be found in Book 1 p 125 126 130 134 of 9 10 5 3 Figure 2 1 Overview of experiment components 1 Laser diode and mount 2 optical isolator 3 dielectric mirrors 4 fibre coupling 5 beam expan sion telescope 6 plate beam splitter 7 interferometer arm end mirror on a translating stage 8 CCD camera Optical components undergoing testing are inserted between the beam splitter and one of the end mirrors Terminal Connection Laser diode Emission point Figure 2 2 Sharp GH04020A2GE laser diode pin configuration The laser diode package does not contain a monitoring photodiode so the laser diode itself is connected across pins 1 and 3 11 os A c c A t P t Pp k oD an Figure 2 3 ThorLabs LDM21 laser diode mount Toggle switches can change the polarities of the diode pin sockets la
49. y arm interfer ometer and determine whether this gives a more accurate reduced value for root mean square wavefront distortions 31 e More sophisticated analysis techniques such as fitting the interferogram to Zernike polynomials might give more information about the test ob ject For example a program called AtmosFringe can fit the interfero gram to determine aberration coefficients and then compute useful quan tities such as the point spread function PSF and the modulation trans fer function MTF of the optical system under testing A demo version which can only analyze several example interferograms is installed in the OpticsTesting AtmosFringe directory on the disk included with 9 A more limited freeware program called FringeXP has also been installed in the OpticsTesting FringeXP directory It would be nice to try ana lyzing the captured interferograms using this program and compare the results with the Fourier transform analysis in MATLAB Finally a pow erful but of course expensive program called IntelliWave exists but I do not know very much about it beyond its name e It would be nice to implement a more sophisticated phase unwrapping algorithm that is less sensitive to noise However this would likely be time consuming and efforts might be better spent on improving the beam quality to reduce phase unwrapping problems as described above For in terferograms showing significant wavefront distortions a v
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