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1. COMCIUSIOM A TA 51 BD F t re WOrK crai eun elisa E A E ecco aaledhans codecs eeeas ca 51 REFERENCE Scsi uan aNea anaa aUa na Nanta aaa Nasan au ananas 53 ANNEX USB OSCILLOSCOPES LIST eese enne 54 ANNEX Il CIRCUIT ANALYSIS neue eee eeeene eerie eite nennen nemen erasa nnn nen anna 55 ANNEX lll COMPARING DATA OBTAINED USING COAXIAL CABLE AND EXTERNAL DIVISOR PROBE 2 53i tix sinant arabi aO cu niv 2aE S ce ckRu cuc Due Y Eau ie CU DEAE GE ida 64 ANNEX IV MATLAB CODE cioniiininiani n nic 67 ANNEX V ALTERNATIVE PEAK DETECTION AND HISTOGRAM 70 ANNEX VI DYNAMIC DATA EXCHANGE IN LABVIEW DDE 77 List of Figures Figure 1 1 Basic scheme of Mossbauer effect 3 Figure 1 2 Characteristics of Mossbauer spectra related to nuclear energy levels Hyperfine Splitting includes IS QS and DI 6 ooooooocccccc occcocinanacacanininonanananano no 4 Figure 1 3 Basic scheme of MS instrumentation occcccnncnccccccccncnccnnnnnnananoncnnnnnnnnnnnnnns 4 Figure 1 4 Co Decay Schema e LM ML Deo becas 5 Figure 1 5 Spectrum obtained with a commercial photon height analyzer 6 Figure 1 6 Scheme of preamplifier and amplifier output ccoococccnnnnnnccccccccnnnnccnnnnnnns 7 Figure 1 7 Typical Amplifier Pulses 10 cococonncnnnonncccccncnnnnncnncononccccnncnnnananananos 7 Figure 1 8 Unipolar output with three
2. 1 Vosc EE p Rs 2 28 Vi RCsys 22 Design of a low cost Photon Height Analyzer for a M ssbauer Spectrosco Finally as was explained in the section 2 3 2 the peaks with equal or higher frequencies than the cut frequency will be modified in amplitude as analogous to equation 2 10 p A pes 1 R2C2 w2 Ever ETE x 100 x 100 2 29 2 4 Complete circuit Once we have decided which type of wiring we will use it is the moment to introduce in the circuit analysis the effect due to the amplifiers inductance that has been commented in the previous section The output inductance value is not in the user s manual of the amplifier then the best option to find its value is to measure the Bode diagram of the whole system and compare it with our ideal system Figure 2 12 it means to introduce a known input signal to the amplifier sinusoidal and measure for each frequency how the signal changes Theoretical Bode diagram Ose er ih ber inae indui En bre be inae n bra be mum Y 5r ELO a 2 c o S 15 e E lt 20L EDP Freq cut 257 Coaxial Freq cut 80 m m hiia EAR 10 10 10 10 10 10 10 10 10 10 Frequency Hz Figure 2 12 Theoretical Bode diagram and cut frequency black circle The figure above represents in different colours the qualitative shape of a Bode diagram for a coaxial cable and for an external divisor probe As
3. Dar Amplitude V 0 6 b 0 8 ab r r r r r r 1450 1500 1550 1600 1650 1700 1750 1800 1850 1900 sample number Figure A5 4 In red relative minimums smaller than 65 mV Where the red circle indicates the position of the relative minimums along the curve a feature to observe is that the most part of them are on the right side of the peak This is because the shape used by the amplifier is not symmetrical accordingly the time from the signal to peak is lower than the time from peak to signal as was commented in Chapter 1 sub section 1 1 3 Once it is done the code has to distinguish between which points are absolute minimum the minimums that the code uses to do the histogram and which of them are just relative minimum of its segment To do that the code will compare one value with its previous and following value In consequence the code will 74 Design of a low cost Photon Height Analyzer for a M ssbauer Spectroscopy obtain an absolute minimum when these values are bigger less negative than the value that is analyzed 0 2 Opto Annan E nomm 0 2 0 4 Amplitude V 0 6 0 8 r t t r r r 3200 3300 3400 3500 3600 3700 3800 3900 4000 4100 sample number Figure A5 5 Absolute minimums detected by the code in red The figure A5 5 shows how the code works for the minimums that will contribute to the histogram It is essential to comment that here is possible to remove
4. counts Amplitude V Figure 3 13 Energy window peaks selected histogram Definitively it confirms us that the peak that is situated around 0 75 V This conclusion is clearer when superposes in the same histogram the peaks of the Figure 3 12 with the peaks of the Figure 3 13 and comparing this result with the Figure 3 12 see Figure 3 14 Previous numerical data treatment with MatLab 39 Test to detect the position of the energy window over the peak T T T r r t r r r EI Amp EN EW 700 600 counts 0 0 5 1 1 5 2 2 5 3 3 5 4 4 5 5 Amplitude V Figure 3 14 Comparison between the histograms obtained by the amplifier and the energy window 3 2 7 Conclusions This section is dedicated to emphasise some conclusions obtained during the elaboration of this chapter and also to makes some comment about the set up Along the chapter we have concluded some values that is going to be used by the USB oscilloscope such us sampling frequency 0 5 Msamples s and transfer data velocity 35 KB s It has been also determined some other parameters necessaries for the right work of the code such us the minimum value accepted for a maximum peak detected 50 mV and the threshold values to measure dead time V 0 35 mV to avoid dead time On the theoretical point of view it is essential to comment that this chapter explains the condition imposed over the data for avoiding overlap to obtain the p
5. November 1987 5 Pound R V and Rebka Jr G V Phys Rev Letters 4 337 1960 6 Adapted from Dyar M D Agresti D G Schaefer M W Grant C A And Sklute E C Annu Rev Earth Planet Sci 2006 34 83 2006 7 Dickson P E and Berry F J Principles of M ssbauer spectroscopy Chapter 1 in M ssbauer Spectroscopy Cambridge University Press Cambridge 1986 8 Doppler C Uber das farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels Abhandlungen der k bdhm Gessellschaft der Wissenschaften V Folge Bd 2 S 465 482 1842 9 Compton A H A quantum theory of the Scattering of X rays by Light Elements Phys Rev 21 483 502 1923 10 Cramberra amplifiers catalogue http www canberra com pdf Products Model 2022 SS M3833 pdf 11 Spectroscopy amplifier Model 2022 Operator s Manual 12 Planck M On the Law of Distribution of Energy in the Normal Spectrum Annalen der Physik vol 4 p 553 ff 1901 54 Design of a low cost Photon Height Analyzer for a M ssbauer Spectroscopy Annex l USB OSCILLOSCOPES LIST This is a list with all the different options to choose the USB oscilloscope As it was commented in section 3 1 1 the feature that most affect to the prize is the n number of bits followed by the SR sampling rate Table A1 1 Oscilloscopes list PropScope 25 E 10 250 NINIS PicoScope 1 C
6. Recoilless emission Resonance absorption Figure 1 1 Basic scheme of M ssbauer effect Although the theoretical principle of ME was already known many years before no one was capable to recreate it in the laboratory M ssbauer realized that it was necessary to have the radioactive sample in a solid matrix to be able to have the emission process without recoil As the nuclear energy levels have a very narrow width the energy loss due to recoil of the emitting nucleus was enough to avoid the resonant absorption Therefore the insertion of the radioactive nucleus in a matrix was the only way to obtain the effect The spectroscopic technique based on this effect is called M ssbauer Spectroscopy MS The energy levels of a nucleus in a solid are modified by its environment MS it is hugely sensitive to energy changes 10 eV hence it enables to study three main interactions between the absorbent nucleus and the surrounding nucleus and electrons hyperfine interactions i the electric monopole interaction between the nucleus and its electrons that produces a shift in the nuclear energy levels called isomer shift IS ii the electric quadrupole interaction between the nuclear quadrupole moment and an inhomogeneous electric field that produces a splitting of an energy level called quadrupole splitting QS and iii the magnetic dipole interaction DI between nuclear magnetic dipole moment and a magnetic field that produces a further splitting
7. from end of Es mue P error in no error b expected output Using Match Pattern the While Loop searches for numbers run minimizad in the string If no numbers are found then 1 is returned which ends the while loop data size b standard input b wait until compl Output Numbers Simple Error Handler vi Description of reg expression Match 0 or 1 character Match 0 or1 character Match 1 or more numbers Match 0 or1 character Match 0 or more number Waveform Graph X size prueba prz Figure A6 1 DDE connexion between PropScope and LabView
8. if the peaks in red are placed in energies lower that 14 4 keV the inferior limit of the energy window should be shifted to bigger energies and then we should obtain another data file and fix the led option is it the first iteration switched off in order to analyze if the new position is correct This procedure should be done until we observe all the peaks in red placed in the area around 14 4 keV The corresponding steps should be done if the peaks are located over the 14 4 keV 4 3 Display Elements and user s manual The objectives of the display is to offer a tool easy to manage but with all the information needed 48 Design of a low cost Photon Height Analyzer for a M ssbauer Spectroscopy 4 3 1 LabView s Display elements Figure 4 11 shows the display at the moment when it is open where we can observe the different elements Path File g 1 First Iteration orpeakslst of peaks 2nd Histogram Histogram EB i y dead time om Time of execution s 0 Histog 0 0 m 1 1 D 1 gt BEY Energy keV mew xl keV aw a keV V jo NN x2 key 20 Amplitude keV a Amplitude V b b keV fb do jo 28 keV jo Figure 4 11 LabView display First of all it is necessary to distinguish between controls and indicators controls are in the display in order to introduce any key parameter and indicators are just to show a result Working as a control there are some elements as path file fir
9. that we are not considering and also that the amplifier not only works as an amplifier but it also works as a differentiator We can conclude that there exist four reactive elements that provoke two zeros in the System response one positioned around 50 Hz and the other one around 2 KHz and also two poles one located around 100 Hz single pole and the other one around 200 kHz triple pole As a consequence it is not possible to fix what the real elements of the whole system are in our case just for the amplifier Due to the semi logarithmic scale used in the Bode diagram it is not easy to distinguish between the results obtained for the coaxial cable and the EDP In order to get more information about how our system works it will be worth to observe the Figure 2 14 that express the system response in a linear scale 24 Design of a low cost Photon Height Analyzer for a M ssbauer Spectroscopy System response r r r e o t r EDP Coaxial 4 co o T Amplification a Q Nn o eo o 7 ES o T eo r r r r r r 0 2 0 4 0 6 0 8 1 1 2 1 4 1 6 1 8 2 Frequency Hz x 10 Figure 2 14 System response of the whole system for different wiring type linear scale x axis In Figure 2 14 it is clearer than the cut frequency for coaxial cable around 200 kHz is smaller than the cut frequency for EDP around 300 kHz As a consequence we can confirm that although the unknown passive el
10. 1 2 14 igH1 V Time ps Paused Figure 2 8 square signal f21 5 MHz Amplitude 1 V Figure 2 7 and Figure 2 8 shows how the response of the system is Two features are clearly seen in the figure above i exists a ripple effect in Figure2 7 that is produced by an output inductance in the amplifier which value is not present in the manual This effect will modify the amplitude of the peaks because adds a ripple on the semi Gaussian peak Its effect will be studied at the end of this chapter ii the value of the slope in Figure 2 8 is not big enough to recreate the shape of the signal it will change the shape of the signal To do a quantification of the error in amplitude introduced by the impedance it is necessary to use the transfer function equation 2 8 in the complex frequency domain calculate its module and use it in the relative error equation 1 1 14 R2CZqw x 100 2 x 100 2 10 V V E l OSC rel Vi In figure 2 8 it is obvious that the impedance is not compensated then the system is not able to represent properly the square function The time that requires charging a capacitor to 63 2 of full charge is called time constant represented by the Greek letter 7 figure 2 8 permits to obtain a first approximation of the time constant T 0 06 us 60 ns 2 11 Once the complex frequency domain has been analyzed it is worth also to obtain the transfer function in the time domain It is necessary to u
11. 10MQ A2 36 R C 423 C 20 80 pF osc _ eq m edp osc _ 80 pF _ Coys Ceg o Ed DD etio OPF 10pF A2 37 In consequence the equivalent circuit is Figure A2 5 62 Design of a low cost Photon Height Analyzer for a M ssbauer Spectrosco Figure A2 5 Scheme of equivalent circuit wired with EDP As it was commented at the beginning of the section A2 2 the equivalent system has a bigger input resistance and a smaller capacitance than the case of section A2 1 The purpose is to demonstrate why this circuit is better option the first step is to calculate the equivalent resistance as was done in section A2 1 R lt Reg a Rea _1 p F RReg R 1 1 1 Rsys R Req gt Ros R Rea sys R A2 38 This circuit of figure A2 6 is analogous to the circuit shown in Figure A2 2 although with different parameters In consequence it is going to show just the highlights of the process Rsys Vi Csys Figure A2 6 Equivalent circuit s scheme using coaxial cable Accordingly the transfer function is A2 8 1 1 sCsysR T s A2 39 It is dependent on frequency but in that case as it is in A2 19 the cut frequency is Circuit Analysis 63 EDP 10 fee A2 40 cut T m It is a great improvement because just changing the wire type the system is able to obtain data with a frequency ten times bigger without being modified Finally as was explained in the section A2 1 the peaks with eq
12. 5 d pyl pyl py2 d x2 xd 63 py3 d c xl c x1 d 8 x2 c x2 d 9x3 c x3 d 10 tl cputime 11 b length x 12 vecmax2 b 0 13 posmax2 b 0 14 vecmax b 0 cuv EL 15 posmax b 0 16 uz0 035 17 l 0 005 18 for i 2 1 b 1 19 if z i gt 0 05 amp z 1 z i 1 gt 0 amp z i z i 1 gt 0 vecmax i y i noacmavylil vfi Figure 4 9 MatLab script Case False The first part of the code is focused on calculate the linear equivalence between voltage and energy As it was commented along this section it is necessary to introduce as input two values x and xz chosen during the first running of the program Then with x py and xe pye it is simple to calculate it linear equivalence as Amplitude keV a Amplitude V b 5 1 Finally it is simple to find the solution using x py and xe pyo a PP y py 22 3 5 2 X1 X2 X1 X2 Once we got these values applying the equation 5 1 with the parameters obtained via 5 2 it is possible to convert the peak s amplitude value arrays from voltage units to energy units In order to obtain the case b commented at the beginning of the section 4 2 1 it means the peaks that contribute to the histogram belonging to the second data file a new code was created using the information obtained from the output file which data have passed through the energy window it was explained in subsection 4 2 1 2 Energy window output data The idea of t
13. A5 5 it is possible to see that before every single minimum peak the system has a series of positive values This is the key for avoiding overlap effect The first step is to find one peak and create a variable with the 40 consecutive points from the peak minimum value Then we impose the overlap condition which is to search where is located the value of the ten percent of the peak amplitude value in the variable commented at the beginning of the paragraph The idea is to indentify if this value is positive or negative if the value is negative probably does not exist overlap if the value is positive instead it is sure that exists overlap consequently the program remove the peak overlapped and does not consider it for the energy histogram This part of the code is shown below condition 1 0 2 y Ifinal 1 vecmin2 1 vecmin 1 Y 1 0 yoverlap 1 0 for j 2 1 npc 5 condition j 0 2 y Ifinal j if condition j gt threshold condition2 j threshold else condition2 j condition j end for i 1 1 40 nooverlap i 1 y Ifinal 1 i nooverlap i j y Ifinal j i end Y j find nooverlap j gt condition2 j 1 matchpos j 2x Ifinal j Y j yoverlap j y Ifinal j Y j if yoverlap j 1 vecmin j gt 0 vecmin2 j vecmin j else vecmin2 j 0 end end noovernz nnz vecmin2 z find vecmin2 lt 0 Ifinaltest 1 noovernz for i 1 noovernz vecmin3 i vecmin2 z i Ireal i Ireal z i end It is worth to commen
14. Di Writing equation A2 27 in the frequency domain Rosc 1 sRoscCeq Rosc T s Rosc RI 1 sRoscCeq A2 28 1 SRoscCeq 1 SRC RosctR FRC RoscCeq RC A2 29 Then the EDP is compensated it is clear that C must be adjustable because each oscilloscope has different resistance and capacitance Circuit Analysis 61 In the PropScope case the adjustable C is m Sereno Fea A2 30 R 10 Returning to equation A2 28 and assuming A2 29 the transfer function resulting is Rosc ES RosctR 10 T s A2 31 This result as was expected means that this part of the circuit does not affect to the measure data in frequency but data are attenuated by factor 0 1in amplitude as is seen in equation A2 32 where the reverse Laplace transform has been applied R V Vose Vi RosctR 10 A2 32 Using the admittance it is possible to find the values equivalent to the capacitance and resistance In order to work with admittance firs it is necessary to calculate the total impedance 42 30 R R m R R Z Z Z osc ES osc A2 total EEAS Ts 1 SRoscCeq 1 5BRoscCeg 1 SRoscCeg A2 33 R 42 7 T Rosc R c Rosc R Ztotal JE nE A2 34 1 SRoscCeq 1tjwRoscCeq And the admittance is 1 1t jwRoscC 1 R y i oscleg jwCa ese A2 35 Ztotal RosctR Rosc R RosctR Therefore the system acts as an equivalent resistance and an equivalent in parallel with the following values Req Rose R
15. Figure 2 9 Circuits scheme wired with EDP Viis the output signal Ha is the amplifiers output resistance H is the resistance of the RC net C is the adjustable capacitance Ceap is the capacitance of the coaxial cable which forms the EDP Rosc and Cosc are referred to the oscilloscope The EDP includes a coaxial cable with an impedance commented in the previous sub section and a RC front circuit with an adjustable capacitance and a resistance of 10 MQ it offers a higher input resistance and a lower capacity in parallel than the oscilloscope alone Previous numerical data treatment with MatLab 19 The circuit figure 2 9 will be separate in two parts the first study will consist in finding an equivalent circuit of the elements that do not belong to the amplifier To obtain the equivalent circuit working in the complex frequency domain it is necessary to calculate the equivalent impedance of the RC front circuit ge 2 14 14 5RC It is also necessary to calculate the equivalent impedance of two parallel capacitances in parallel with a resistance Z ue 2 15 1 sRoscCeq The equivalent circuit is shown in the figure 2 10 Figure 2 10 Equivalent circuits scheme with impedance At that point as the equivalent circuit is analogue to that one it is possible to adapt the expression found in the sub section 2 6 Although now it is going to be written directly in the complex frequency domain then substituting R by Z
16. MatLab 35 Synchronization between the amplifier s output and the energy window r r r T r Amp 0 9F Ew 7 0 87 0 7 s 0 6 F 8 2 05 E 0 4 0 3 0 2r otr 0 L L y L L I 1972 1974 1976 1978 1980 1982 1984 3t of point Figure 3 8 Example of synchronization between amplifier and energy window output This condition will make easier to detect the peak s position because once it is detected the peak over the energy window output it is just necessary to use its position and find in the amplifier s unipolar output what the amplitude of this point is Figure 3 9 shows the selected peaks by the energy window detected Detected peaks selected by the energy window r r r T T r Amp 0 9F 0 8 Peak 0 7F 0 6 0 5 0 4F Amplitude V 0 3 F 0 2 0 1F 0 1 E Fa Fa Fa L L L i hi 6900 6950 7000 7050 7100 7150 7200 7250 7300 7350 of point Figure 3 9 Detected peaks selected by the energy window 3 2 4 Overlap In order to detect if one peak is overlapped or not it is necessary to remember how the behaviour of the peak is This description can be found at the beginning of the section 3 2 2 The feature that it is going to be used is that the peak will last as maximum 6 us in consequence will take as much two points before the maximum value Therefore the idea to detect overlap is to analyze the previous two points of a
17. different shaping time 12 4 and 1 us 11 from rez dioi Mea SEE ac pcm 8 Figure 2 1 Scheme of the system oocccccccccnocococcccccccccnonnnnnnnnnnnnnnnnnnnnnnnnnnnncnnnnnnnnnnnnnns 10 Figure 2 2 Example of the digital signal ooooocnnnnnnncccncccccnnncconanananancnononincnnnnnnns 11 Figure 2 3 A D Analogue Digital Converter the sampling rate could be seen as how many points it are going to be used to represent the signal 12 Figure 2 4 Shows one of the peaks detected with the USB oscilloscope 13 Figure 2 5 Circuit wired with a coaxial Cable ooococnnnnncccccccccnnccconnnnnanacncnnnnncnnnnnnnns 14 Figure 25 Egquivalent arc ids 15 Figure 2 7 Square signal f 100 kHz Amplitude 1 V seeeessssesss 16 Figure 2 8 square signal f 1 5 MHz Amplitude 1 V sseeessessesssssss 17 Figure 2 9 Circuits scheme wired with EDP Vi is the output signal Ra is the amplifiers output resistance R is the resistance of the RC net C is the adjustable capacitance Ceap is the capacitance of the coaxial cable which forms the EDP Rosc and Cosc are referred to the oscilloscope 18 Figure 2 10 Equivalent circuit s scheme with impedance seseess 19 Figure 2 11 Scheme of equivalent circuit wired with EDP ssssssesssss 21 Figure 2 12 Theoretical Bode diagram and cut frequen
18. it the data packs were acquired correctly but they were not scaled and calibrated see Figure 4 2 and Figure 4 4 700 a 99 100 1100 Figure 4 3 Sawtooth signal generated 2 Figure 4 4 Signal acquired in streaming MHz frequency 1 Vpp mode with LV In order to solve this problem we ask to the company contact and the answer was that in few days we will receive the PropScope software modified and ready to work because it was proprietary software But they do not contact us anymore even they do nat reply the e mails sent As a consequence the final idea was to forget the idea to work with the DDE and to save the data in a file and then work over this data file Figure 4 5 shows the first part of the LV code Through the path file it is possible to call the data file then the program open the file measure the size of the file and finally identify every sample as a number with its format through a while loop and send as an array with four rows data ready to work number of point time channel 1 and channel 2 Finally the program closes the data file LabView program and displa 43 OUTPUT DATA ARRAY EzE 0 9 0 9 En E Description of reg expression Match 0 or 1 character Match 0 or 1 character Match 1 or more numbers Match 0 or 1 character Match 0 or more number Figure 4 5 Data acquisition with LV The next part of the code is dedicated to prepare the x axis
19. maximum and then to look out if at least one of them belongs to the area delimited by 36 Design of a low cost Photon Height Analyzer for a M ssbauer Spectroscopy the condition of dead time will be explained in the following section the condition is shown in Annex IV where can be found the whole code In other words the objective is to analyze if when the peak starts the signal is modified by a previous peak or remains around their regulars values given by the noise level on the signal It is worthy to remark that this condition works both data output either received from amplifier or energy window As a example Figure 3 10 will show a peak overlapped avoided by the condition from the amplifier s output data Peak overlapped no detected T T T Amplitude v low limit up limit y 1 r 1 r r 410 415 420 425 430 435 440 of point Figure 3 10 Peak overlapped no detected Observing the previous two points of the peak located in the point 434 we can see that both are located in the area where the detector cannot identified properly the energy consequently the code avoid the detection of the peak 3 2 5 Dead time One key parameter of the program is to give an idea of how the dead time of the system is in other words to know if the distance between the radioactive source and the sample to analyze is optimum On the one hand if the source is too close to the sample then the detector
20. the oscilloscope s features i 10 bits ii At least 0 5 Msample sec In section 2 3 it was made a theoretical study between wiring our system with a coaxial cable as was before the project or with an external divider probe EDP The theoretical study was clearly favourable to EDP because although both connexions make to work the system as a low pass filter using EDP increases the cut frequency more than 10 times It permits to obtain four times more peaks with the Previous numerical data treatment with MatLab 27 same time sampling see Annex Il It means that although our system is going to work slower than the data acquisition system with its commercial software used before the project we are able to decrease in four time our acquisition time in comparison with the time necessary to obtain the same statistics with a coaxial cable Considering the information obtained thanks to the analysis of the system s response it is possible to conclude that the amplifier not only works as a linear amplifier but also as a differentiator which causes that the whole systems response is a pass band filter Finally it is concluded that the peaks around 14 4 keV which are those necessary for the MS are located around the maximum amplification over the frequency domain 28 Design of a low cost Photon Height Analyzer for a M ssbauer Spectroscopy Chapter 3 PREVIOUS NUMERICAL DATA TREATMENT WITH MATLAB Since the beginning of the project we
21. thought that could be possible to obtain the spectrum of the radioactive sample using the peak that has a near Gaussian shape instead of the peak that is similar to a Dirac s delta We also thought that the information about dead time could be obtained first detecting all the peaks and then impose an overlapping condition to remove the peaks overlapped Finally we realize that the most reliable way of work should be the ones presented in Chapter 3 Then in Annex V will be shown the first work done in order to obtain a histogram with the peaks that have a near Gaussian shape In this chapter it is explained how was the process to create the MatLab code with a wide explanation about its highlights the idea is to focus into the mathematical idea of how to treat this kind of signal First of all it is interesting to say that the platform used to make the first code was MatLab The reason is that LabView LV has as a tool a MatLab script that allows us to insert the previous code almost directly to LV The full code is presented in Annex IV it contains commentaries about the idea behind each important step In Chapter 3 is going to be shown how the data were treated including images to make it more visual allowing the reader to understand what was the author s idea doing each step The first stage of numerical treatment once the oscilloscope was bought and available in the laboratory was to determinate how it works e sampling frequen
22. was calculated in section 2 3 1 and also in section 2 3 2 the theoretical results show that the cut frequency is higher for an EDP than for a coaxial cable In order to measure the real Bode diagram of the system it is necessary to calculate what the working area of the signal is over the frequency domain Previous numerical data treatment with MatLab 23 In previous section 2 2 2 was commented the main feature of a peak Then in order to obtain the two slopes which define us the area of work in the frequency domain it is necessary to find the maximum and the minimum amplitude of a peak without overlap and divide its amplitude by the time duration which could be approximated for the time passed between two points and a half of this time looking table 3 1 we can conclude that for TS of 100 us this time will be 3 us Consequently the range of working frequency it is calculated as follow Amplitude slope 2 30 The following graphic Figure 2 13 shows the real Bode diagram for both wiring types EDP and coaxial over all the frequencies Bode diagram for the whole system T d T Amplification dB or EDP Coaxial s 1 s F 10 10 10 10 10 10 10 Frequency Hz Figure 2 13 Bode diagram for EDP and coaxial cable First of all it is possible to conclude that the system is not a low pass filter as we supposed at the beginning It means that there are some more passives elements
23. will receive a number of photons too big to be able to have a good response in consequence the information of the photons will be overlapped it means that the second photon arrived to the detector will contribute to the histogram with a wrong energy quantity On the other hand if the distance from the source to the sample is too big a fraction of the information could be lost because the photons emitted by the source will not impact on the sample Previous numerical data treatment with MatLab 37 It is easy to understand that the worst option of both is to have the set up explained in the first case where the source is too close to the sample Then for avoiding counting this photons in the histogram with their modified energy the program incorporates an option that could be used when the user decide In order to explain this idea easily it is important to know how is the behaviour of the data when appears an emission peak In order to know which the energy limits are where a photon could be detected with its correct energy it is necessary to look the Figure 3 4 As was commented below that figure it is possible to observe that the upper limit is 35 mV and the lower limit is 0 V Then to obtain the percentage of dead time of the detector it is necessary to use the equation below dead _ mV gt points with V 0 lt points with V E total of points x 100 3 2 3 2 6 Histogram It is known that MatLab contains a fun
24. 0 3000 sample number Figure A5 3 Non emission level up to 0 065 V The size of the segments that divide the signal in smaller parts is a critical parameter of the code it is not difficult to realize that the minimum size of the segments will provoke the maximum time running the code because this part of the code is the one that takes more time to carry out by the system see Table A5 1 Then it is essential to find a medium terminus giving priority to the needs of the project Alternative peak detection and histogram 73 Table A5 1 Time dependence on the execution s time and minimum time separation detected between two consecutive peaks due to the size of the segments using the same data file 4 67 8 395 12 8 30 5 382 28 16 17 3 363 60 Analyzing table A5 1 it is possible to see that the effect on execution time is huge in consequence if not necessary then the best option is to use the medium size And only when it will be essential use a smaller segment s size With the bigger segment s size are lost some peaks that should appear in the histogram Working with MatLab code it has been considered that using 8 points a great fraction of the peaks 96 that must contribute to the code are identified If the whole group of identified peak obtained during the analysis it is not considered the values greater than 65 mV samples due to electronics then the relative minimums calculated is shown below 0 2 b
25. 2 LabView display user s manual In order to use properly the code presented during this chapter it is necessary to carry out three simple steps Once we have acquired a statistically significant data file we set up the display as shows Figure 4 12 Path File CAworkMinalhistoamplfine3 i First Iteration amp 9 orpeakslst of peaks 2nd jo fo Histogram Histogram ES 250 dead time 10 200 Time of execution s jo 20 30 amp a Energy keV E maw xl keV aw a keV V 0 y 30 0 x2 keV 20 Amplitude keV a Amplitude V b b keV 0 Fo jo 8 keV lo Figure 4 12 Initial display set up We should just indicate the data file to work with and indicate if it is the first time that the program runs in order to obtain a histogram pattern and the linear equivalence between voltage and energy Once we execute the program the display obtained is shown in Figure 4 13 50 Design of a low cost Photon Height Analyzer for a M ssbauer Spectroscopy Path File CAwork finalhisto2ampifine3 bt ot First Iteration j z Histogram EzS orpeakslst of peaks 2nd 4531 bo dead time 120 6 Time of execution s 1157 124 CET Histog 0 76347 168 a 1 1 i Energy keV az maw xl keV la a keV V o 9034 lo x2 keV 20 Amplitude keV a Amplitude V b b keV 0 90 16 jo x3 keV Figure 4 13 The figure sh
26. 22 A AAA Po An 26 CHAPTER 3 PREVIOUS NUMERICAL DATA TREATMENT WITH MATLAB 28 3 1 Characterization of oscilloscope s data acquisition system esses 28 3 1 1 Sampling rate and time scale ssssssssssssseeeenennne enne 29 34 2 Transiter data Veloclty ete rra caged na ose rette ee itd eee ri Ee EET nein 30 Beli Se Glipped sigtial etie i eee eh seii ed sei seo eee Rose Er Macao 30 3 2 MatLab codena eana ara aa AAAA nidnledaldu hei 30 3 231 Roading Gata cett et nte itr athe A EA t dani eet ote 31 3 2 2 Peaks detection over amplifiers output lata oooonnoccccnnnnicinnnococccnncnnnnnncononccnnnnnnnnnnoncnncnnn 32 3 2 3 Peaks detection over the energy window output data sess 33 a O EIU 35 3 225 O A EE 36 ALO USO AM ice 37 32M CONGIUSIONS A A A AA AA RIOR 39 CHAPTER 4 LABVIEW PROGRAM AND DISPLAY e eeeeus 41 4 1 Data ACQUISIUOn ee rec wee ead eec dice A 41 4 2 Data Treatment laa ii 44 4 2 1 Histograim eaa eE a aN dd 44 4 3 Display Elements and user s manual 4 eese nennen nennen nnn nnne nns 47 4 3 1 LabView s Display elements sss nennen nennen nnne nns 48 4 3 2 LabView display user s manual sssssssseeeene nennen nnne enne 49 CHAPTER 5 CONCLUSION AND FUTURE WORK se sesses 51 Babs
27. 73 Table A5 2 Time running comparison between a code with or without the overlap CONAN saeta eae T a A A E ER 76 Introduction A T INTRODUCTION The present work consist in designing and building a low cost analyzer of the photon energy emitted by a radioactive source in order to be able to check easy and automatically where the energy window for selecting the photons needed in a M ssbauer experiment is located Moreover if necessary it will allow to know how its position should be modified and also to obtain information about the dead time of the detector It is important to keep in mind that the equivalent commercial equipment and software cost around 4000 fifteen years ago The total price of our system is 200 the price of the USB digital oscilloscope therefore it is necessary to understand that itis highly complicated to obtain the same features on accuracy or time duration On the one hand in order to determine where the energy window is located and also for getting information about the dead time it is not necessary for the system to be extremely accurate Accepting a small error over precision we will save an important quantity of budget using a system with less bit s number n On the other hand the Photon Height Analyzer is going to be used when the set up is changed because the radioactive source is changed or the distance between detector to sample or sample to source is changed twic
28. MASTER THESIS Design of a low cost Photon Height Analyzer for a Mossbauer spectrometer Luis Fernando Sarmiento Bascones SUPERVISED BY Pere Bruna Escuer Oscar Casas Piedrafita Universitat Politecnica de Catalunya Master in Aerospace Science amp Technology MAY 2012 Design of a low cost Photon Height Analyzer for a Mossbauer spectrometer BY Luis Fernando Sarmiento B scones DIPLOMA THESIS FOR DEGREE Master in Aerospace Science and Technology AT Universitat Polit cnica de Catalunya SUPERVISED BY Pere Bruna Escuer Departament de F sica Aplicada EETAC UPC scar Casas Piedrafita Departament Enginyeria Electr nica EETAC UPC ABSTRACT M ssbauer spectroscopy is a technique that allows investigating with high accuracy the changes in the energy levels of an atomic nucleus due to the surrounding environment The technique consists in measuring the energy dependence of the resonant absorption of M ssbauer gamma rays by nuclei To obtain these gamma rays a radioactive source is needed In the laboratory the isotope Co is used which spontaneously captures an electron to reach a metastable state of Fe which in turns decays in a more stable state ground state by a gamma ray cascade that includes the 14 4 keV M ssbauer gamma ray To work just in this energy range the spectrometer has an energy window which should be centered at 14 4 keV The objective of the present work is to design and build a low
29. a low cost Photon Height Analyzer for a M ssbauer Spectroscopy Figure 2 16 is very interesting there it is possible to appreciate three key features i the EDP amplifies more than the coaxial cable the peaks which important information for the M ssbauer experiment ii the peaks more amplified are the ones who satisfy the conditions energy range imposed by the energy window and finally iii comparing it with Figure 2 15 it is possible to conclude that over the region where appear the three main peaks of the source 6 4 14 4 21 keV the amplifier works approximately linear As was said before the amplifier is working also as a differentiator it means that when the amplifier receives a pulse first of all it derivates the pulse and amplifies it then finally on the negative area is superposed a near Gaussian form it allows to obtain information over the dead time In order to get an example of what differentiator does see Figure 2 17 Vin Vout Figure 2 17 Amplifier Differentiator 2 5 Conclusions As a conclusion of this chapter it is worth to make a simple summary In section 2 2 we discussed about which acquisition system will be our best option evaluating features against cost It was an easy decision because the difference of cost was huge between a DAQ device and the oscilloscope around ten times cheaper Although it means that our system will be slower At the end of the section it was presented the conclusion about
30. a low cost project In consequence it will be impossible to compete with the previous system in terms of time of execution or precision The idea is to buy a low cost acquisition system with its features good enough in order to obtain a good Photon Height Analyzer not to design a system as powerful as the actual The objective of this project is to replace this system by another one cheaper Then the purpose of the project is not only to buy a low cost acquisition system but also to design software that allows to obtain a good photon energy spectrum and also to be able to obtain information of the dead time The first step was to convert an analogue signal into a digital one Therefore the acquisition of the data could be done if it is not considering the actual device mainly with one of these two options a DAQ Data AcQuisition device or a USB Universal Serial Bus digital oscilloscope Previous numerical data treatment with MatLab 11 The relation between cost and performance was clearly favourable for the USB digital oscilloscope That is because the DAQ usually has between 8 16 or 32 channels and they need a huge sampling frequency to obtain the possibility to work in parallel with all of them it implies also a huge transfer data velocity that makes the device more powerful but also increase the price To decide which oscilloscope would be the best option it is important to determine its main specifications fs n and Bandwidth Then
31. aboratory of this master thesis is radioactive Co because Fe has the most advantageous combination of properties for MS 7 The radioactive cobalt isotope undergoes a transition by spontaneous electron capture to reach a metastable state of Fe which in turns decays in a more stable state Principles of M ssbauer Spectroscopy 5 ground state by a gamma ray cascade that includes the 14 4 keV gamma rays that are used in MS see Figure 1 4 It is necessary to place the radioactive source in an electromechanical transducer driven by an appropriate electronic system to obtain by Doppler s effect 8 a slightly wider range of energy to analyze the absorber Without this energy range one could only study pure Fe It is important to remember that the studied system determines the radioactive source needed For example with the 5Co source only systems containing Fe can be studied 270 day Ty 136 keV e capture O keV 57Fe Figure 1 4 Co Decay Scheme It is essential to keep in mind that the objective of the project is to design a system able to measure the energy spectra of the gamma ray cascade in order to be able to select only the photons with 14 4 keV necessary for the ME 1 1 2 Detector There are three different kinds of detectors to work with low energy gamma ray a gas proportional counter energies lower than 40 keV b scintillator energies between 50 100 keV c Solid state detectors Due to the energy of M ssbauer ga
32. and Zeg by Zo obtaining directly TE Y 2 16 Z2 Z1 Substituting the expressions 2 14 and 2 15 in the previous equation the transfer function of the system is found T s e 2 17 1 sRoscCeq OSE 1 sRC The condition that satisfies the EDP when it is compensated is 20 Design of a low cost Photon Height Analyzer for a M ssbauer Spectroscopy RoscCeq RC 2 18 It justifies that C must be adjustable because each oscilloscope has different resistance and capacitance In the PropScope case the compensated value for C is _ Roscleq _ Ceq C Tetas LIU 10 pF 2 19 Returning to 2 17 and assuming 2 18 the transfer function is ese es 2 20 RosctR 10 I This result as was expected means that this part of the circuit does not affect to the measure data in frequency In amplitude data are attenuated by factor 10 Applying the inverse of the Laplace transform to the expression 2 20 the transfer function in the time domain is obtained R Vi Vse Vi RosctR 10 2 21 This factor is corrected by the oscilloscope s software because exists an option to setup the probes Using the admittance it is possible to find the values equivalent to the capacitance and resistance Then to work with admittance first it is necessary to calculate the total impedance Rosc R Ztotal Z4 Z2 bid 2 22 And the admittance is 1 1 Rosc im Ztotal B Rosc R TdWEsg RosctR 2 23 The
33. as explained which where the goals of the master thesis the main one is to create a code that makes the histogram of the emitted Previous numerical data treatment with MatLab 31 peak s amplitude Photon Height Analyzer and to get information about the dead time of the detector The complete code is shown in Annex IV in this section the code will be explained step by step focusing on the main ideas that allow analyzing the signal properly 3 2 1 Reading data This section is divided in two sub sections because is going to be worth to understand the signal obtained through two different outputs On one hand a long data file will be acquired from the amplifier s unipolar output in order to obtain the total spectrum of the radioactive sample On the other hand a data file shorter than the previous will be acquired from the energy window output in order to obtain the peaks that accomplish the condition imposed on the energy by the filter In Figure 3 2 it is shown as a example the signal s shape using directly the output data of the amplifier obtained from the oscilloscope with the goal to observe that the PropScope acquire data packs of 1024 sample length and then the next pack starts again at zero point PS F T 38 32 a E S IU r r r r r 0 200 400 600 800 1000 1200 sample vector Figure 3 2 Shows that position vector goes between 0 and 1023 As a consequence it is needed to spread out t
34. as finished at those moments we had not taken the decision of which USB oscilloscope to buy yet In consequence the first approach to the data was to create a MatLab code which recreates the signal observed in an analogue oscilloscope The oscilloscope signal s recreation could allow starting to check the MatLab code with a kind of simulated real data Once the oscilloscope was bought and it was in the laboratory the following stage was to determinate how it works i e sampling frequency fs data transfers clipped effect etc explained in Chapter 3 A3 1 Signal simulation Once the signal was observed one of the most plausible options was to use the form of the Planck s Law 12 because its shape was asymmetrical and similar to the near Gaussian curve used in the amplifier The parameters which determine the shape where modified randomly because the objective was to recreate all kind of peaks figure A5 1 shows the simulation obtained It is possible to see that there are peaks with different amplitudes widths and some of them are overlapped as the original signal Alternative peak detection and histogram 71 Recreation of the signal observed in the analogue oscilloscope T T c T T T T T T 0 8r 0 6F Amplitude V 0 4 0 2 0 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 Time us Figure A5 1 Recreation of the signal observed in the analogue oscilloscope Just at the time that the recrea
35. ax2 i y i posmax2 i x i else vecmax2 i 0 posmax2 1 0 68 Design of a low cost Photon Height Analyzer for a M ssbauer Spectroscopy end end nnzvecmax nnz vecmax rvm find vecmax gt u lrvm length rvm nnzvecmax2 nnz vecmax2 rvm2 find vecmax2 gt u lrvm2 length rvm2 index 1rvm 1rvm2 for i 1 1 index if i lt lrvm newamp i vecmax rvm i newpos i posmax rvm i else newamp 1 vecmax2 rvm2 i lrvm newpos 1 posmax2 rvm2 i lrvm end end dtpercentage nnzxdt b 100 amplitude 0 0 05 5 5 hist newamp amplitude figure plot x y b newpos newamp ro Code created to detect all the peaks that fulfil the energy window condition without peaks overlapped clear all a load dani txt b length a 1 a T 1 Bs x a ter 135 la 4 i b 16 z a 1 b 16 bbb hee vecmax2 b posmax2 b vecmax b posmax b u 0 035 1 0 005 for i 2 1 bbb 1 if z 1 gt 0 05 amp z i vecmax i y i posmax i x i vecmax2 i y i posmax2 i x i z i 1 gt 0 amp z 1 z 1 1 gt 0 else vecmax posmax vecmax2 posmax2 end end for i 23 1 b 3 if vecmax i vecmax posmax nanah m UNE ll X K i MatLab Code y i 2 lt u amp y 1 2 gt 1 end rvm find vecmax gt u lrvm length rvm nnzvecmax2 nnz vecmax2 rvm2 find vecmax2 gt u lrvm2 length
36. cnnnnnnns 64 Figure A3 3 Laboratory data histogram spectrum seeesssssesss 65 Figure A5 1 Recreation of the signal observed in the analogue oscilloscope 71 Figure A5 2 Signal without values greater than 65 mV excepting peaks 71 Figure A5 3 Non emission level up to 0 065 V 72 Figure A5 4 In red relative minimums smaller than 65 MV 73 Figure A5 5 Absolute minimums detected by the code in red 74 Figure A5 6 Amplitude histogram 0 03 V bars width sessssssssssss 76 Figure A5 7 Amplitude histogram 0 05 V bars width 76 Figure A6 1 DDE connexion between PropScope and LabView 77 List of tables Table 2 1 Resolution offered depending on the number of bits 12 Table 2 2 Frequency working range of the signal using At 3s 24 Table 2 3 Frequency range for peaks around 14 4 keV ssseesusssss 25 Table 3 1 Dependence of the time acquired in a vector against SR TS 29 Table A1 1 Oscilloscopes Sacate cesos 54 Table A3 1 Ratio between points analyzed and minimum detected 66 Table A5 1 Time dependence on the execution s time and minimum time separation detected between two consecutive peaks due to the size of the segments using the same data lead
37. cost analyzer of the photon energy emitted by the radioactive source in order to be able to check easier and automatically where the energy window is located and if necessary to know how its position should be modified The steps necessary to perform this work are the following a Characterization of the main properties of the emission s peaks time duration and amplitude that are going to be analyzed These features are needed to know the characteristics of the data acquisition system i e sampling rate bit number and price b Signal analysis in order to differentiate properly all the emission peaks from peaks due to noise or overlap c Creation of software to automate all the steps to do and prepare a graphical user interface easy to understand Finally the performance of the designed system will be evaluated and compared with analogous commercial equipment ACKNOWLEDGEMENTS would like to thank my Master Thesis director Pere Bruna Escuer for all the guidance and support during the master thesis and his great support during the ending of the project Furthemore would also like to thank my Master Thesis supervisor scar Casas Piedrafita for all the discussion about the electronics of the data measurement system would like to thank Daniel Crespo for his generous effort during the ending of the project The working atmosphere in the office has been excellent for the execution of the project as well as the suggestions and discuss
38. cquire the data from the digital oscilloscope The decision was pretty simple the best option possible was to create a dynamic data exchange DDE between the LV and the digital oscilloscope which should allow us to acquire data point by point or also acquire packs of 1024 samples see Annex IV The digital oscilloscope accepts this way of work the manufacturer ensures us that was possible to establish a DDE between PropScope and LV In order to check the LabView clock maximum sampling frequency of 1 MHz we tried to acquire data point by point lt is possible to observe the results comparing Figures 4 1 and 4 2 where are shown the generated square signal Figure 4 1 and acquired with LV figure 4 2 It is so clear that working at this sampling rate the digital oscilloscope is not able to rebuild properly the signal generated in conclusion LV does not work fast enough Consequently we decide to work in streaming mode this solutions seems very fair because we choose the sampling frequency in order to do not cut the peaks during the 1024 points pack Then for our purpose it is a good option to acquire packs of 1024 samples even although the packs are not consecutive 42 Design of a low cost Photon Height Analyzer for a M ssbauer Spectroscopy Amplitude V 2 CH1 V Time us Figure 4 1 signal generated 2 MHz Figure 4 2 Square signal acquired point by frequency 1 Vpp point with LV The problem appeared when we tried to use
39. ction that creates by itself a histogram Consequently in this subsection the different histograms of interest will be shown Following the order of this chapter the first histogram to comment is the one which contains all the peaks received from the amplifier s data output Figure 3 11 Amplifier output histogram including overlapped peaks t T T r T T T 900 counts 0 0 5 1 1 5 2 2 5 3 3 5 4 4 5 5 3t of points Figure 3 11 Amplifier output histogram including overlapped peaks Observing figure above it is not too clear where are located the three peaks required It is supposed that around 0 35 V exists one 6 4 keV around 0 7 V maybe exists the second one 14 4 keV but the third one is really complicated to find it In order to obtain a clearer histogram the Figure 3 12 will remove all the peaks overlapped 38 Design of a low cost Photon Height Analyzer for a M ssbauer Spectroscopy Amplifier output histogram without overlapped peaks T T T T T T T 700 counts 0 0 5 1 1 5 2 25 3 3 5 4 4 5 5 Amplitude V Figure 3 12 Previous histogram without overlapped peaks Figure above confirms us that the first two peaks are really the peaks that we chose and it is possible to identify the third peak passed 1 V In order to confirm our supposition about the position of the peaks it is going to be shown in Figure 3 13 the peaks selected by the energy window output Energy window histogram 35 T T
40. cy fs data transfers clipped effect etc The final step was to acquire data and starts to create the code in order to start obtaining the first amplitude s histogram and information about the dead time 3 1 Characterization of oscilloscope s data acquisition system With the oscilloscope s software installed on the computer the first step was to analyze how it works for instance i which sampling frequency fs is used and how it changes when the time scale TS is changed ii how the oscilloscope transfers data into the computer iii how the oscilloscope works when the signal is clipped Previous numerical data treatment with MatLab 29 3 1 1 Sampling rate and time scale The USB Propscope oscilloscope has a fs up to 25 Msamples s although all digital low cost oscilloscopes samples the input data at fixed rates depending on its time scale The cost to be working in a low cost project is that the analogue to digital convertor is not as good as could be The consequences are that the analogue to digital convertor is not as fast as we wished then the internal memory of the oscilloscope is not as big as would be wished and consequently the transfer data velocity is also very limited Fortunately this project pretend to create an application that will be used once in few months when is necessary to check the position of the amplifier energy window that is the reason why the project is going to be very useful although it has
41. cy black circle 22 Figure 2 13 Bode diagram for EDP and coaxial cable sssssesssss 23 Figure 2 14 System response of the whole system for different wiring type linear Scale X axIs A AN 24 Figure 2 15 Bode diagram over region of interest eeeeseseussss 25 Figure 2 16 Bode diagram in the region determined by the energy window 25 Figure 2 17 Amplifier Differentiator ooonnnnnccncccccnnnnccccnnnnononncnnnnncnnnnnnnnnnnncnnnnncnnnnnnnns 26 Figure 3 1 The width of this peak is around 40 points it means 80 US 30 Figure 3 2 Shows that position vector goes between 0 and 1023 31 Figure 3 3 An example some packs of 1024 points of the previous position vector spread Outoa ma e OL D D 32 Figure 3 4 Signal without values greater than 50 mV excepting peaks 32 Figure 3 5 Amplifier s output data with all the peaks detected 33 Figure 3 6 Energy window output data cccooooccccccccccccccccnononancnononnncnnnnnnnnnnnnnnnnnnnnnnnnnnns 34 Figure 3 7 Energy window output data zoomed occcccccnncccccccccccccccnnnnnannanncnonnncnnnnnnnns 34 Figure 3 8 Example of synchronization between amplifier and energy window output Nana 35 Figure 3 9 Detected peaks selected by the energy window 35 Figure 3 10 Peak overlapped no detected oo
42. d be 0 5 Msample sec in order to have 35 points to represent the curve Example of a peak shape T T T Amplitude V L L r r r L L 3780 3800 3820 3840 3860 3880 3900 of point Figure 2 4 Shows one of the peaks detected with the USB oscilloscope It is clear that the f could be improved but in consequence the transfer data velocity would be increased it implies that the cost would increase considerably 2 2 3 Oscilloscope requirements summary With the study done above section 2 2 1 and 2 2 2 it is possible to conclude that the future oscilloscope should has at least 0 5 Msample sec as a sampling frequency and ten bit s number If it is possible to find an instrument that improves these requirements and also keeps the cost then it is going to be possible to obtain more accurate data The final decision was to buy a low cost USB Oscilloscope called PropScope it has a sampling rate up to 25 Msample s bit s number of 10 20 MHz of bandwidth 35 Kb s of data velocity transfer and also includes a function generator and two external divisor probes The complete list of oscilloscopes considered is detailed in annex I 2 3 Errors introduced by effects of non ideal system Ideally the circuit could be seen as an amplifier that is connected to the oscilloscope which is the element responsible to acquire the signal But as was explained in section 1 1 an ideal system never exists 14 Design of a l
43. d in the laboratory consists in three basics elements Figure 2 1 i amplifier ii wire type iii Data Acquisition System DAS The amplifier send the signal through its output impedance composed of a resistance 100 Q and an output inductance with a non specified value in the manual The actual wire connexion is a 1 meter length coaxial cable that introduces an impedance in form of capacitance 80 pF each meter length 10 Design of a low cost Photon Height Analyzer for a M ssbauer Spectrosco And the acquisition system device that has an input impedance formed by a resistance in parallel with a capacitance Zour 2 u E DAS Amplifier Figure 2 1 Scheme of the system Once the data acquisition system has been decided then the unique possible modification in the scheme is to change the type of wire between the amplifier and the DAS 2 2 Data Acquisition System The actual data acquisition system used in the laboratory is called MCDLAP it is an ADC Analogue to digital signal converter with a multichannel data processor The card not only provides the user with a high resolution Pulse Height Analyzing ADC but also with a complete Multichannel data processor The ADC is a 16 kchannel with 14 bits resolution and 100 MHz clock rate The card is particularly designed for use in x ray spectroscopy Its price is 4000 The features of this system are so powerful that it is necessary to keep in mind that we will work in
44. d the final cost As an example a 12 bits oscilloscope is almost five times more expensive than the equivalent 10 bits oscilloscope See annex l 2 2 2 Analysis of sampling rate The sampling rate is the other key parameter because it will determine how the shape of the signal will be rebuilded A higher sampling rate implies a better reconstruction of the peak s shape Figure 2 3 and in consequence the photon s energy spectrum will be more accurate Voltage Digital Samples Analog Signal Figure 2 3 A D Analogue Digital Converter the sampling rate could be seen as how many points it are going to be used to represent the signal It is obvious that the best sampling rate would be ideal but the cost of the device increases quickly when increasing the sampling rate To be able to decide which sampling rate should be good for the project it is necessary to know how the shape of the signal to analyze is and also which is the less intense peak detected The complete peak could be properly represented as a kind of delta positive as maximum will have 3 points peak and then a near Gaussian peak explained in Chapter 1 and we should decide how many points are needed to represent it The peak chosen see Figure 2 4 in the signal to work with had a voltage amplitude of 2 75 V approximately and a duration of 70 us With this data the minimum Previous numerical data treatment with MatLab 13 sampling rate accepted shoul
45. e c newamp j d q 76 4 lata Graphic jou 71 dip oa nzxdt b 100 f d p ja 4 D i d work histogramdata d Description of reg expression Match 0 or 1 character Histogram Match 0 or1 character EB Figure 4 8 Final histogram code False case If we have a look over the bottom left part of the code we can see how it opens the previous saved file histogramdata txt and gets all the values in order to accomplish two functions a create the histogram pattern with the new x axis in energy units b to be able to add to this array the new peaks obtained in the second data file These actions are done by the MatLab script First the code finds the linear equivalent between energy and voltage Figure 4 9 Then using the information of the energy window data output detect the peaks that fulfil the energy window condition Finally both vector the ones with the previous maximum and the ones with the previous plus the new peaks converts their voltage values in energy ones 46 Design of a low cost Photon Height Analyzer for a M ssbauer Spectroscopy In order to calculate the case a it is needed x x and the energy of those levels see Figure 1 5 called in the script as py py2 and pys po p 1 pyl 6 4 2 py2 14 4 3 py3 21 4 c pyl py2 d x2
46. e expression for calculate the cut s frequency is oe e A2 19 cut DR Cay It means that for frequency equal o higher to the cut s frequency the data will be modified as using equation A2 8 Vi V E l OSC rel Vi x 100 een x 100 A2 20 The voltage measured in the oscilloscope can be expressed as the input voltage multiplied by the transfer function Vosc ITGw Vi A2 21 It is necessary to calculate the module of the transfer function because it is a complex number with both parts real and complex The transfer function equation A2 8 has its complex element in the denominator in consequence it is going to be multiplied in the numerator and in the divisor also by its conjugate complex Then will be possible to separate the real part form the complex one as it is shown in the equation below 42 8 l T 2 i 0800 A2 22 1 jRCw 1 jRCw Then at this point it is possible to separate the real part and the complex ones 1 s RCw 1 R2C2w2 J 1 R2C2w2 T jw A2 23 Circuit Analysis 59 Therefore the module of the function transfer is R C w 1 R C w 1 R2C2w 1 R2C2w2 2 1 R2C2w2 2 TG w A2 24 And finally IrGw A2 25 Going back to equation A2 20 equation below shows how a low pass filter works and then depending on the frequency the signal has a different attenuation vi a zz TR MIE TES UT x 100 EST 100 A2 23 Erei 7 t A2 2 C
47. e or three times a year consequently the large time duration of data acquisition can be accepted because this also will decrease the final price of the project using a system with a slower analogue to digital converter Outline The idea of this chapter is to yield an overview of the project indicating the purpose of the project and their motivation It also will provide to the reader the organization of the project and the methods used Chapter 1 contains a basic overview about the M ssbauer Spectroscopy in order to fix the physics context of the project In Chapter 2 is explained how it is the measuring system and it is also included a study about the architecture of the system and errors It will permit us to fix the features needed for our acquisition data system DAS and decide that the best option to wire our system is using an external divisor probe EDP Before the data treatment it is necessary first of all to understand the possible errors in the measure In addition it allows to obtain a deep knowledge about how works every instrument of the set up 2 Design of a low cost Photon Height Analyzer for a M ssbauer Spectroscopy Chapter 3 is dedicated mainly to proportionate the features of our chosen DAS as sampling frequency or data transfer velocity it also contains an explanation in depth of the MatLab code created for the first data treatment where it is confirmed that the data obtained and the DAS proportionate greats re
48. e signal there exists to different behaviours i when there is not emission the signal remain around zero with a minimum value of 0 V and a maximum value of 50 mV very well determinate see Figure 3 4 ii when there is a peak to detect the values are over this 50 mV As the objective is to determine the peaks due to emission process the region i allows determining properly the minimum value accepted to consider a peak as a maximum Using a for loop and applying the condition expressed in equation 3 1 y i 0 05 amp yi y i 1 0 y i y i 1 50 3 1 The only step to perform later on is to remove over the position and amplitude vectors and the positions with zero value that do not accomplish the condition Then all the peaks will be detected without removing the overlapped ones see Figure 3 5 Amplifier s output data all peaks detected T T T T 45 3 5 25 Amplitude V 1 5 0 5F 0 5 r r r r r r 1800 1900 2000 2100 2200 2300 2400 of points Figure 3 5 Amplifiers output data with all the peaks detected 3 2 3 Peaks detection over the energy window output data In Figure 3 6 it is possible to observe that the function of energy windows is to discriminate the peaks distinguishing the peaks received from the amplifier unipolar output that are inside of the energy window value from the peaks that are not When the discriminator receives a peak with its energy inside the values p
49. eaks that pass through the energy window and some tips to understand properly how the MatLab code works As a corollary it is considered important to comment that every new set up done on the system the user should check that the USB oscilloscope acquire correctly the data Because we found in some cases that the oscilloscope was not able to give the desire data accuracy for the measure of the dead time When this happens it is necessary to increase the amplification over the input signal LabView program and display 41 Chapter 4 LABVIEW PROGRAM AND DISPLAY In this chapter the creation of the LabView software is explained commenting all the difficulties appeared during its evolution from the beginning until the end it will also explain all the options that the display offers and how to use it The LV software is divided in three parts 1 data acquisition 2 data treatment and 3 display they will be explained in three different sections The first section explains how LV acquires the data from the USB oscilloscope and their previous treatment The second section analyze the main data treatment it means to go a step further to understand the changes over the MatLab code and how will be displayed the final histogram Finally the third section will show the final display and will explain some tips to use it correctly 4 1 Data Acquisition The first decision to take at the beginning of the code is to decide how we should a
50. ecessary to work in the complex frequency domain Hence it is necessary to convert the value of each equivalent element by their impedances In this case it is just necessary to convert the value of the capacitance because the resistance does not have any affect in the frequency domain 16 Design of a low cost Photon Height Analyzer for a M ssbauer Spectroscopy 2 7 eq SCeq Where s jw and j is the complex number Expressing equation 2 6 in the complex frequency domain T s 2 8 1 sRCeg Equation above shows the dependence in frequency of the circuit s transfer function in the complex frequency domain s The function has a zero in the denominator that expresses the cut frequency of the circuit Then the circuit works as a low pass filter and its cut frequency is 1 1 sRC 0 gt fE a 15 9 MHz 2 9 The effect produced by the impedance is to introduce different errors in the acquired signal depending on the frequency And it will also cause the lost of peaks that must contribute to the Photon s energy spectrum consequently this effect increases the time of acquisition To show graphically these effect two square functions with different frequencies will be shown in Figure 2 7 and Figure 2 8 in order to analyze the different effects 4 8 12 16 20 H1 V Time us Paused A Figure 2 7 Square signal f 100 kHz Amplitude 1 V Previous numerical data treatment with MatLab 17 0 6 0 8 1
51. ement modifies the cut frequency in both cases it does not change that the best option to wire our system is the EDP The total range area will be calculated using two peaks one of the minimum amplitude and one of the peaks with maximum amplitude see Table 2 2 Table 2 2 Frequency working range of the signal using At 3ps NEN 34 kHz 6 1 6 MHz Once the complete Bode diagram is understood Figure 2 15 will show the Bode diagram in the signal frequency range Previous numerical data treatment with MatLab 25 Bode diagram in the region of interest r x x x Amplification dB 5 T Frequency Hz Figure 2 15 Bode diagram over region of interest In order to obtain more information we are going to calculate in table 2 3 where are located the peaks with its energy inside the energy window filter Table 2 3 Frequency range for peaks around 14 4 keV x 0 33 If we compare the results obtained in Table 2 3 with Figure 2 15 it is possible to observe that the peaks around 14 4 keV are in frequencies around the maximum amplification see Figure 2 16 Bode diagram around the energy window levels 39 r T 38 5 x 38 1 375r EDP 4 a Coaxial D 377 E e S E 365 2 B 36 lt 35 5 4 35 1 34 5 4 34 r 10 10 10 Frequency Hz Figure 2 16 Bode diagram in the region determined by the energy window 26 Design of
52. ermitted by the energy window then appears a kind of Dirac s delta synchronized with the position of the desired peak on the amplifier s output data file if it is not then the output signal remains constant in a value near to zero 34 Design of a low cost Photon Height Analyzer for a M ssbauer Spectroscopy Energy window output data T T r r r Amplitude V T 0 r r 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 of point Figure 3 6 Energy window output data As was done in the previous sub section 3 2 2 it is interesting to observe zoomed the signal see Figure 3 7 Energy window output data t t Amplitude V o o a T r r r r r 405 410 415 420 425 430 3t of points Figure 3 7 Energy window output data zoomed The energy window output data is very well defined it is possible to observe two situation a if there is no peaks with the energy between the upper and lower limit the signal remains constant with a value of 19 mV b the energy window receives a peak with its energy between its limits then the signal has a value around 5 V Then in order to know the proper value of the peak it is necessary to take profit of the synchronization between the amplifier s output and the energy window as could be observes in Figure 3 8 in this figure it is changed the value of 5 V by 0 5 in order to obtain a clearer image Previous numerical data treatment with
53. ght Analyzer displayed as a histogram or spectrum of the radioactive source and also to obtain information about the dead time of the detector considering that we were involved in a low cost project In Chapter 2 we were conscious that although our set up using an external divisor probe instead of a coaxial cable will improve the data acquired the digital oscilloscope analogue to digital converser will increase the time of data acquisition of our Photon Height Analyzer There exists the inconvenient caused by this time increase of the data acquisition around fifteen minutes plus 45 minutes that runs the code but it is permitted because we have replaced a commercial software and acquisition system card that cost around 4000 around teen years ago by our system that has cost 200 In addition the system will be only used twice or three times every year It was determined that the amplifier is also a differentiator thanks to the image obtained of the Bode diagram 5 2 Future work There are some ideas that could improve this project and could be done as a future work but they are out of this project possibilities First of all could be a good idea to build an adapter between the amplifier and energy window and the external divisor probe in order to ensure that during the twenty minutes that takes the oscilloscope to acquire data the connexion will be the best Secondly and example of how to create a dynamic data exchange
54. hannel 100 8 354 2204 2 Channel 50 Gao 2090 2 100 8 259 CS320A 2 100 12 1200 TiePie HS3 2 10 12 1100 The decision was taken considering that the key feature was the bit number and that the project needed an oscilloscope of 10 bits Due to this to affirmations it was easy to choose PropScope as a good tool to carry out the project Circuit Analysis 55 Annex II CIRCUIT ANALYSIS The objective of this annex is to show in detail a theoretically study of the different wires that can be chosen to work in the laboratory The idea is to show theoretically how the system works in order to compare with the real data A2 1 Circuit wired with coaxial cable The objective of a circuit s analysis is to find the transfer s function of the system and to analyze how the errors introduced by the impedances in the measured data depend on the frequency or amplitude The figure below shows the circuit s scheme with the different passives elements as capacitances and resistances Figure A2 1 Circuits scheme wired with coaxial cable Vi is the output signal R is the amplifiers output resistance Ccoa is the capacitance of the coaxial cable Rosc and Cosc are referred to the oscilloscope s input To solve easily the circuit it is necessary to build an equivalent circuit It is possible to calculate the equivalent impedance of two capacitances in parallel The equivalent circuit works as a voltage divisor If we take into account that the input re
55. he code see Annex IV it contains the MatLab code is to find the positions where the discriminator indicates that will appear a peak that fulfil the energy window conditions Once we have this position the code goes to the amplifier output data vector to find the value of amplitude of this LabView program and display 47 position Then as both signals are synchronized this value is the amplitude of the peak The final part of the code applies the conversion between voltage and energy in order to obtain a histogram with its x axis in energy units The LV code ends plotting the data file in red and over their peaks is placed a white circle in order to indicate the peaks taken into account for doing the histogram Figure 4 10 the code also does two histograms a in yellow the ones who express the initial peaks detected b in red the previous peaks plus the peaks that fulfil the condition of the energy window Histogram Histogram A 0 10 20 30 40 50 Energy keV Figure 4 10 Histograms i in yellow initial peaks detected ii red the same peaks plus the new peaks detected To decide if the energy window is well placed remember that it is the main objective of the thesis we should conclude if the histogram plotted in red have the new values red over yellow in the area that corresponds to the peak placed around 14 4 keV If it does not happen then we should look which boundary of the energy windows is bad placed For example
56. he position vectors in one longer vector obtaining the result shown in the Figure 3 3 32 Design of a low cost Photon Height Analyzer for a M ssbauer Spectroscopy Amplitude V r r r r r r 0 500 1000 1500 2000 2500 3000 3500 sample number Figure 3 3 An example some packs of 1024 points of the previous position vector spread out 3 2 2 Peaks detection over amplifier s output data To understand the signal shape obtained from the amplifier s unipolar output it could be observed Figure 3 3 There it is shown that the peak consist in a fast increment of voltage from 2 us until 6us maximum followed by a negative near Gaussian peak which allow us to obtain information about the dead time The MatLab code pretends to find the position and amplitude value of the positives peaks In order to know how to detect the positives peaks it is essential to know their features therefore the data will be zoomed to obtain some key parameters see Figure 3 4 Amplifier s output data T T T T 0 04 F M 0 03 I al li 0 02 I HI y i TI Amplitude V 0 01 ul BEI MU bine ob dM E r r fi r r r r r r r 2 61 2 615 2 62 2 625 2 63 2 635 2 64 2 645 2 65 2 655 of point x 10 Figure 3 4 Signal without values greater than 50 mV excepting peaks Previous numerical data treatment with MatLab 33 Then to characterize basically th
57. i 0 posmax i 0 36 end 4 Figure 4 7 Histogram pattern code True case LabView program and display 45 The first step to do is to acquire a data file containing a statistically significant number of peaks enough to e three typical peaks observed in the decay of the radioactive cobalt isotope When the part of the code that we are explaining receives the information ou de peaks detected and the data for creating the graph then the variable with the value of the peaks is saved in a file histogramdata txt because we will need these values in the second running Finally the code creates a histogram with the x axis in voltage units In this stage we also should be able to detect the three peaks commented previously because the second part of the code will need their position values in voltage units Xy x 4 2 1 2 Final histogram false case In order to obtain the total histogram compared with the previous one the code does some steps see Figure 4 8 5 en P 58 rvm find vecmax gt u Time of execution s 59 Invm length rvm post 50 nnzvecmax2 nnz vecmax2 1 rvm2 find vecmax2 gt u m dead time 62 Invm2 length rvm2 Gua index bid Irvm2 pepe 0 7 ms smax divite D 58 else ETE 1 uu 9 newamp i vecmax2 rvm2 i Irvm 5 a2 mer A hmi H 72 eat 73 Imax ina 74 for j 1 1 Im 5 mem
58. ifier has a lineal gain it was commented in section 2 4 In consequence it is necessary to select two points that must correspond to the peaks located in 6 4 and 14 4 keV respectively then it is possible to do a lineal regression in order to obtain the straight line that contains both points in the histogram The energy value of the third peak shown in figure A 3 3 is 21 keV then substituting this value in the straight line and isolating the value of the x axes it is possible to find where the third maximum must be located in the histogram If both coincide then the supposition done with the two initial peaks are correct If was necessary it is possible to make the whole conversion between amplitude and energy on the histogram The other feature that should be commented in this annex is the number of minimum obtained 66 Design of a low cost Photon Height Analyzer for a M ssbauer Spectroscopy In section 2 3 was commented that both circuits were working as a low pass filter although the circuit wired with EDP had a cut frequency ten times higher In consequence the faster peaks cannot be obtained in a circuit with the coaxial cable concretely the peaks with frequency higher than 16 MHz cut frequency of circuit wired with CC and lower that 20 MHz bandwidth of the oscilloscope The table A3 1 shows the ratio between points obtained and minimums detected for both circuits wired with EDP and CC Table A3 1 Ratio between points analyzed a
59. igure 1 7 Typical Amplifier Pulses 10 The amplifier is a critical component on the detection stage as a consequence of its characteristics gain range output pulse shape and the relation between signal and noise that determine the output data The amplification in the area of interest is lineal maintaining the relation between energy and amplitude of the peak The amplifier used in the laboratory is the Canberra s model 2022 which uses a Near Gaussian shape working as unipolar output time to peak 2 35x shaping time and pulse width 7 3x shaping time data extracted from Operator s manual It means that if another pulse arrives before 9 65x shaping time the amplifier will suffer stacking In this case the energy window will accept events that has not the 14 4 keV needed and will discard events with the proper M ssbauer gamma ray energy 8 Design of a low cost Photon Height Analyzer for a M ssbauer Spectroscopy Vertical 2V div TAME T RUNE IINIUR rizontal TATEN TT T 9 PEA N UNIPOLAR OUTPUT 10 V Figure 1 8 Unipolar output with three different shaping time 12 4 and 1 us 11 from wider to thinner As a comment the data of the duration of the event shows that the peak s shape is not symmetric check in Figure 1 8 Previous numerical data treatment with MatLab 9 Chapter 2 MEASURING SYSTEM ARCHITECTURE AND ERRORS All the elements in a circuit either active or passive could modify introduce errors in am
60. ions provided by PhD students there would also like to thank my family and friends for their endless support throughout the development of this thesis would finally like to thank Marc and Eric for being there all this time Table of Contents INTRODUCTION 1 e lE 1 CHAPTER 1 PRINCIPLES OF M SSBAUER SPECTROSCOPY 3 1 1 M ssbauer Spectroscopy experimental configuration eese 4 LAs Radioactive source ete ae id 4 UNE Detector oiran D 5 1 1 3 Pre Amplifier and Amplifier sse eene nene eene nnne 6 CHAPTER 2 MEASURING SYSTEM ARCHITECTURE AND ERRORS 9 2 1 Architecture of the instrumentation system cc cesses seeeee ee eeeeeeeeeeseeeeeseeneeseseeeeeseseenenenseeeenes 9 2 2 Data Acquisition System n ln trea ick oae panes 10 2 2 1 Analysis of the number of bits oocoocnnnccccnnnoccccnnnoccccnnnonc cnn nnnnn cnn nano nara enne nnne 11 2 2 2 Analysis of sampling tate cerieirar enida pruina pan iaia aaa RA KE nennen nnne nenne 12 2 2 3 Oscilloscope requirements summary sse nennen 13 2 3 Errors introduced by effects of non ideal system eese 13 2 3 4 Condal Cale iia er eet creer exon Denk nene Ax Tug Pes eue der av den De Leda un a dea as 14 2 3 2 Exteirial Divisor Probe EDD dtt epe t ea de nre redes nied 18 2 4 Complete O
61. ircuit wired with an external divisor probe In this section the external divisor probe EDP replaces the coaxial cable The EDP includes a coaxial cable and a RC front net with an adjustable capacitance it offers a higher input resistance and lower capacity in parallel than the oscilloscope alone figure A2 3 Figure A2 3 Circuit s scheme wired with EDP Viis the output signal Ra is the amplifier s output resistance R is the resistance of the RC net C is the adjustable capacitance Cedp is the capacitance of the coaxial cable Rosc and Cosc are referred to the oscilloscope The circuit will be separated in two parts the first study will consist in to find an equivalent circuit of the elements that do not belong to the amplifier In consequence it is necessary to calculate the impedance of a capacitance and a resistance in parallel 60 Design of a low cost Photon Height Analyzer for a M ssbauer Spectroscopy ty 34 5 A2 24 Ds 1 sRC N m mie And to calculate the impedance of two capacitances in parallel both in parallel with a resistance Ceq edp ICosc Ceap t Cosc A2 25 1 1 1 1 SRoscCeq Rosc Z2 Rosc sCeq Rosc 2 1 SRoscCeq Then it is possible to represent the circuit as figure A2 4 Figure A2 4 Equivalent circuit s scheme with impedance At that point it is possible to adapt the expression A2 6 substituting R by Z1 and Zeg by Zo obtaining directly Vose Z2 A2 27 Vi
62. is shown in Annex VI just in case the manufacturer decide to send us a software that can allow us to work in streaming mode as they promised us Third the possibility to change the hardware of the digital oscilloscope in order to permit to obtain data faster could also be studied It would be necessary a faster analogue to digital converter and also a bigger internal memory for the oscilloscope 52 Design of a low cost Photon Height Analyzer for a M ssbauer Spectroscopy Finally it could be done a complete study of the LabView and MatLab code in order to check some options for reducing the time that the program is running References A SS REFERENCES 1 M ssbauer R L Z Physik 151 124 1958 Naturwissenschaften 45 538 1958 Z Naturforsch 14a 211 1959 2 Morris R V et al M ssbauer mineralogy of rock soil and dust at Gusev Crater Mars Spirits journey through weakly altered olivine basalt on the Plains and pervasively altered basalt in the Columbia Hills NASA publication revised for Journal of Geophysical Research Planets October 2005 3 Heiman N Hester R K and Weeks S P M ssbauer Effect Measurement of the Relaxation Time of Ultrasonic Vibrations in Fe Foils Phys Rev B 8 3145 3150 1973 4 Gummer A W Smolders J W T and Klinke R Basilar membrane motion in the pigeon measured with the M ssbauer technique Hearing Research Volume 29 Issue 1 1987 Pages 63 92
63. l be necessary to acquire twice data files a the first time the display will show an histogram statistically significant with its x axis in voltage b the second time the display will show an histogram with the previous peaks and also with the new ones which will be only those that would pass through the energy window This step will also calculate the linear equivalence between voltage and energy in order to have the peaks value expressed in energy units ready for the histogram 4 2 1 1 Histogram pattern true case Figure 4 7 shows the code done for the case that we are acquiring the histogram statistically significant b length x Time of execution s dro 3 up 0 035 4 lowz 0 005 5 threshold 0 06 dead time 5 vecmax2 b 0 7 posmax2 b 0 8 vecmax b 0 9 posmax b 0 10 for i 2 1 b 1 11 ify i gt threshold amp y i y i 1 0 amp y i y i 1 gt 0 vecmax i y i posmax i x 1 vecmax2 i y i i posmax2 i x i errorout a En Signal Histogram Histogram vecmax i 0 posmax i 0 m 01m H vecmay2 i 0 p a l i 8 Data Graphic posmax2 i 0 j E end mee on ree oa acer Senco E CAwork histogramdata be f 8 a ee 1s ER 28 for i 3 1 b 3 30 if vecmax i gt up amp y i 1 lt up El y i 1 gt low vecmax i y i posmax i x i else vecmax
64. mma rays 14 4 keV the most efficient detector is a gas proportional counter A gas proportional counter consists in a metallic recipient connected to the ground and an inner metallic wire between which a high voltage difference around 2 kV is stablished The detector has a Beryllium window transparent to the photons that ionize an inert gas in the detector of our laboratory is a mixture of Xe and CO causing an electron avalanche It is possible to observe in figure 1 5 the spectrum of all the received photons and it is easy to realize that not all the photons with a very well known energy level are located in a single value they are spread around it That happens because not all the photons travel the same distance as they enter into detector with different input angles The high energy photons produced in the Fe decay 122 and 136 keV are not enough amplified in the detector because of the gain of the proportional detectors at these energies is too small As was argued before it works successfully in events involving maximum energies of 40 keV nevertheless some of these gamma rays provokes Compton s effect 9 that produces emission in the zone of tens keV In consequence this zone is more pronounced for smaller energies 6 Design of a low cost Photon Height Analyzer for a M ssbauer Spectroscopy Intensity counts Figure 1 5 Spectrum obtained with a commercial photon height analyzer The output data of the detecto
65. nction The transfer function permits understanding the output signal and also to see how the input signal changes depending its amplitude and frequency Then the first circuit studied is shown in the figure below Figure 2 5 Circuit wired with a coaxial cable To make easy the lecture of the thesis this section will show a schematic study of the circuit Annex Il contains a deeper explanation and it also shows and explains all the steps performed Previous numerical data treatment with MatLab 15 The first step to do in order to solve easily the circuit is to find an equivalent circuit Then the equivalent capacitance of two capacitances in parallel is calculated obtaining an equivalent circuit that works as a voltage divisor The resistance of the oscilloscope is much bigger 10 000 times than the output resistance of the amplifier in consequence the equivalent resistance of the circuit is simply the output resistance of the amplifier Figure 2 6 Req Vosc Ceq Figure 2 6 Equivalent circuit Where the equivalents elements are Cog Ccoa Cos 100 pF 2 2 R lt Rosc Req R 1000 2 3 The solution of the circuit shown in figure 2 6 is Vose Vi Req I 2 4 Vosc Coq 2 5 Reordering equation 2 4 and 2 5 it is possible to express the relation between the output signal and the input signal equation 2 6 in the time domain Ooa 2 6 Vi CeqtR To obtain the frequency s dependence on the signal it is n
66. nd minimum detected 1 329 152 1 348 608 11 487 0 85 As was predicted by the theory the ratio between the number of points acquired ant the peaks detected is more than four time greater for the circuit wired with the external divisor probe The main consequence of this observation is that changing the cable that wires the circuit then the acquisition time can be reduced four times maintaining the statistics This is a great improvement more if it is taken into account the limitation that the oscilloscope imposes over the acquisition time MatLab Code Annex IV MATLAB CODE Code created to obtain all the peaks from the amplifier unipolar output data without overlapped peaks clear all a load finalhisto2amplfine3 txt b length a 1 a 1 1 b x a 1 y a 3 z a 4 threshold 0 06 u 0 035 1 0 005 vecmax2 posmax2 vecmax b posmax b for i 2 1 b 2 if y i gt threshold amp y i y i 1 gt 0 amp y i y i 1 gt 0 0 0 b b 0 0 vecmax i y i posmax i x i vecmax2 i y i posmax2 i x i else vecmax 1 0 posmax i 0 vecmax2 i 0 posmax2 1 0 end if y i gt u y 1 lt 1 xdt 1 x 1 else xdt 1 0 end end nnzxdt nnz xdt for 1 3 1 b 3 if vecmax i gt u amp vecmax 1 y posmax 1 x else vecmax i 0 posmax i 0 end if vecmax2 i gt u amp y i 2 u amp y i 2 gt 1 vecm
67. nnnnnnnnnnnns 47 Figure 4 11 E3DVIOW dISDIBy insista tiia iain 48 Figure 4 12 Initial display set up 49 Figure 4 13 The figure shows the intermediate step between the first running and the SOCONMG M PES 50 Figure 4 T4 Final GISplay anos 50 Figure A2 1 Circuit s scheme wired with coaxial cable Viis the output signal R is the amplifier s output resistance Ccoa is the capacitance of the coaxial cable Rosc and Cosc are referred to the oscilloscope s input ssssseeueuuuuus 55 Figure A2 2 Equivalent circuits scheme using coaxial cable 56 Figure A2 3 Circuits scheme wired with EDP Vi is the output signal Ra is the amplifiers output resistance R is the resistance of the RC net C is the adjustable capacitance Cedp is the capacitance of the coaxial cable Rosc and Cosc are referred to the oscilloscope oconnnnnnnnnnncccccoccnonnccncnnnaccnnncnnnnnn 59 Figure A2 4 Equivalent circuits scheme with impedance ssssses 60 Figure A2 5 Scheme of equivalent circuit wired with EDP sessess 62 Figure A2 6 Equivalent circuit s scheme using coaxial cable 62 Figure A3 1 Measures done with coaxial Cable ooooooccccnnnnocccccnnnoccncnonnnannncnnnanancnno 64 Figure A3 2 Measures done with EDP oooooonccccccccnccccccononananncncnoncnonannnnnnnnnnncnnn
68. of the energy levels see Figure 1 2 The information obtained from these interactions is useful not only in physics and chemistry but also in a wide range of disciplines as biology geology or archaeology for instance study mineralogy of rock soil and dust at Gusev crater in Mars 2 measurement of the relaxation time of ultrasonic vibrations in Fe foils 3 study of the 4 Design of a low cost Photon Height Analyzer for a M ssbauer Spectrosco basilar membrane motion in the pigeon 4 measure of the astrophysical parameter red shift in Earth 5 y PY Ff f A Lak Relative Velocity Free IS IS ER atom No OS With QS A Spas Figure 1 2 Characteristics of Mossbauer spectra related to nuclear energy levels Hyperfine Splitting includes IS QS and DI 6 In this chapter we will present the most relevant aspects of the MS experimental setup used in the laboratory 1 1 Mossbauer Spectroscopy experimental configuration This is the scheme of a typical M ssbauer spectrometer S Collimator Detector M ssbauer Drive Tli 9 Co Source Sample Figure 1 3 Basic scheme of MS instrumentation It is worth to explain in depth the three main elements radioactive source detector and the amplifier at which the detector is connected 1 1 1 Radioactive source It is possible to work with a lot of different isotopes in MS but the most used and the one that it is used in the l
69. oooococcccccccccococonoccnoncccconanananancnnncnnncnnnnnnns 36 Figure 3 11 Amplifier output histogram including overlapped peaks 37 Figure 3 12 Previous histogram without overlapped peaks oooccccccncccccccccccccccnanannns 38 Figure 3 13 Energy window peaks selected histograM oooooccccccccccccccccoocccnononccnnannnns 38 Figure 3 14 Comparison between the histograms obtained by the amplifier and the energy WNdOW et 39 Figure 4 1 signal generated 2 MHz frequency 1 Vpp ccccccoonoocccccnnancnnnnnnnanononananacenanas 42 Figure 4 2 Square signal acquired point by point with LV sssseessesessse 42 Figure 4 3 Sawtooth signal generated 2 MHz frequency 1 vpy sess 42 Figure 4 4 Signal acquired in streaming mode with LV ssssesssssssss 42 Figure 4 5 Data acquired kA dos 43 Figure 4 6 Creation of the time axis and obtaining the amplitude axis 43 Figure 4 7 Histogram pattern code True case cccccccccnnnncoooocccnnncncnnnnnnnnnnnnnnnnnnnnnannnns 44 Figure 4 8 Final histogram code False case oooococccccccccconococcncncnccnnnnnnnnnnnnnnnnncnnnannnns 45 Figure 4 9 MatLab script Case False ooooononcccccccccnncccccnonononncnnnnnccnnnnnnnnnnnnnnnnncnnnnnnnns 46 Figure 4 10 Histograms i in yellow initial peaks detected ii red the same peaks plus the new peaks detected ocooconnonnccccccnncccccccconncccnnccnnnnnnnnnnnnnncnnn
70. ow cost Photon Height Analyzer for a M ssbauer Spectroscopy Before to start analyzing the acquired data it is necessary to analyze the errors in amplitude and frequency introduced on the signal due to the impedance of the passives elements The output impedance of the amplifier and the impedance of the coaxial cable were both commented in section 2 1 Now that has been chosen the data acquisition system of our system it is necessary to detail which impedance has been added The USB PropScope oscilloscope introduces input impedance consisting in a resistance 1 MQ and a capacitance 20 pF As was commented in section 2 1 the output impedance of the amplifier and the input impedance of the DAS are fixed Along this section the actual circuit and also a modification of it will be study that will consist in changing the coaxial cable by an external divisor probe with the objective to compensate both the capacitance of the coaxial and the capacitance of the oscilloscope 2 3 1 Coaxial cable In order to establish clearly the effects introduced by the impedances This sub section will contain two parts i the first part will study theoretically the circuit that forms the system ii the second part will compare the theoretical study with experimental images extracted from the system The objective of a circuit s theoretical study is to find its response in time domain and also in frequency complex domain this feature is called transfer fu
71. ows the intermediate step between the first running and the second At this point it is essential to observe the histogram obtained because we need to introduce the parameters x V x V with the help of a cursor indicator in this case the values are 0 35 V and 0 7 V respectively We obtain the display shown in Figure 4 13 when these two parameters are introduced Before the second running we should switch off the Boolean that asks if we are running for the first time or not the code and also to introduce the path file of the new data file which acquires data that have passed through the energy window The final display is shown in Figure 4 14 Path File C work finalhisto2amplfine3 tt md First Iteration i E Histogram Histogram Ez 4531 20 6 Cursor Om Histog 0 76347 0 i 1 1 20 30 50 Energy keV mao x1 keV aw a keV V 64 jos 19 0476 32 keV 2M Amplitude keV a Amplitude V b b kev ha 9jo 16 007615 a3 key 21 Figure 4 14 Final display gt la or peaks 1st of peaks 2nd 1356 dead time Time of execution s 159 62 S It is possible to observe that the methodology has been chosen to make the use of the code as simple as possible Conclusion and future work 51 Chapter 5 CONCLUSION AND FUTURE WORK 5 1 Conclusion The main objectives of the projects have been determined since the beginning and they are to obtain and design a Photon Hei
72. plitude or frequency the output data that is going to be measured This is the reason why before analyzing in depth the data to obtain the photon s energy spectrum it is always advisable to study the architecture of the instrumentation system to receive the signal in order to be sure that the data have as less error as possible This chapter contains four well differentiate parts Section 2 1 will be dedicated to analyze the architecture of the measuring system necessary to obtain the signal in order to determine which elements make up the system analyzed In section 2 2 the actual system used in the laboratory will be compared with the different devices that allow acquiring the amplifier s signal This section also contains the study of the amplifier s signal because it should ensure that the data acquisition system DAS that is going to be bought complies all the requirements of the project It is essential to determine device s features as the sampling frequency fs necessary to obtain a good digital reconstruction of the signal the number of bits n to obtain accurate data and finally the bandwidth without forgetting that one of the goals of the project is to design a low cost equipment Section 2 3 will compare the errors caused by the actual type of wiring with the effects obtained with an external divisor probe Finally Section 2 4 will analyze the whole system 2 1 Architecture of the instrumentation system The system use
73. r offers the possibility to study two different characteristics depending on the electronics used after it it is possible to study the amplitude and shape of the gamma rays emitted in order to get information about the properties of the source and configuration of the experiment this is also called Photon analyzer it is also possible to study the different hyperfine interaction in the absorber with a MCA Multi Channel Analyzer also called spectrum analyzer As was discussed in the introduction we are going to analyze the energy of the photon emitted by the radioactive source photon analyzer 1 1 3 Pre Amplifier and Amplifier The pre amplifier normally consists in a charge integrator The charge collected in a capacitor is proportional to the photon energy A resistance situated in parallel with the capacitor produce an exponential discharge the time that takes the capacitor to discharge is a key parameter because if during that time other photon arrive then its energy amplitude will we modified as shown in figure 1 6 Principles of M ssbauer Spectrosco 7 a N ae i ana b Figure 1 6 Scheme of preamplifier and amplifier output The way to avoid that effect is either decreasing the arrival s rate not useful due to the increment of measure time or changing the shape of the pulse which is done by the amplifier see Figure 1 7 Differentiation Energy Baseline Reference Integration Energy AA LN F
74. refore the system acts as an equivalent resistance and an equivalent capacitance in parallel with the following values Req Rose R 10 MO 10 MQ 2 24 Previous numerical data treatment with MatLab 21 Rosc 100 pF Coys Cog Sys ed RosctR 10 10pF 2 25 Hence the equivalent circuit is shown in Figure 2 11 As was commented at the beginning of the sub section the equivalent system has a bigger input resistance and a smaller capacitance than the case of the coaxial cable Although both are analogues taking profit of this fact only the key expressions in the analysis of the circuit will be shown For further explanations see Annex II Figure 2 11 Scheme of equivalent circuit wired with EDP Accordingly the transfer function is 2 8 T s 2 26 1 SCsysR It is dependent on frequency as it is in 2 10 but in that case the value of the cut s frequency is EDP 1 __ 10 04 159 MHz 2 27 cut 2TRCsys It is a great improvement because just changing the wire type the system is able to obtain data with a frequency ten times bigger without being modified It means that the peaks with higher frequency will be detected with this wire A table with this feature of the system is shown in Annex ll To find the transfer function in the time domain the expression found in the previous sub section is going to be used equation 2 12 with the only change of Csys instead Of Ceg Obtaining
75. rvm2 index lrvm lrvm2 for i 1 1 index if i lt lrvm newamp i vecmax rvm i newpos i posmax rvm i else newamp i vecmax2 rvm2 i lrvm newpos 1 posmax2 rvm2 i lrvm end end amplitude 0 0 05 5 5 hist newamp amplitude figure plot x y b x z g newpos newamp ro 70 Design of a low cost Photon Height Analyzer for a M ssbauer Spectroscopy Annex V ALTERNATIVE PEAK DETECTION AND HISTOGRAM Since the beginning of the project we thought that could be possible to obtain the spectrum of the radioactive sample using the peak that has a near Gaussian shape instead of the peak that is similar to a Dirac s delta We also thought that the information about dead time could be obtained first detecting all the peaks and then impose an overlapping condition to remove the peaks overlapped Finally we realize that the most reliable way of work should be the ones presented in Chapter 3 As the final histogram is very similar to the histogram obtained in Chapter 3 then here will be presented the alternative work Some of the previous information necessary to follow this explanation is offered in Chapter 3 since the beginning until section 3 2 2 Peaks detection would like to explain that at the first stage of numerical treatment the idea was to simulate the signal observed in the analogue oscilloscope this MatLab code was done before the analysis that will be shown later section A 1 w
76. s its maximums values more concentrated than Figure A 3 1 where they are more scattered Before to analyze both histograms it is interesting to compare them with a previous work to be able to give an opinion depending on what we are observing Figure A 3 3 shows the data obtained in the laboratory with the previous acquisition card Comparing Data Obtained Using Coaxial Cable and External Divisior Probe 65 2500 Enn Figure A3 3 Laboratory data histogram spectrum The figure A 3 3 has it x axes in energy units it is possible to convert the data shown in Figure A 3 2 to energy just using theoretical results The idea is identify a maximum in the histogram with its energy very well known That is why the histogram A 3 2 is more clear than the histogram A 3 1 where is more difficult to be able to determine a maximum This is the reason why from here in advance it is just commented histogram A 3 2 Comparing histograms A 3 2 and Figure A 3 3 it is possible comment that The maximum located around 0 35 V Figure A 3 2 must correspond to the peak located around 6 4 keV in Figure A 3 3 The maximum located around 0 7 V Figure A 3 2 must correspond to the peak located around 14 4 keV in Figure A 3 3 The maximum located around 0 9 V Figure A 3 2 must correspond to the peak located around 21 keV in Figure A 3 3 To ensure that the identification has been well done it is necessary to remember that the ampl
77. se the equation of the transfer function in the complex frequency domain equation 2 8 and apply the inverse Laplace transform the result is 1 Voss 1 Re 2 12 Vi Rug 18 Design of a low cost Photon Height Analyzer for a M ssbauer Spectroscopy The transfer function in the time domain shows that for an observed peak the transfer function applied on the signal is an exponential decay with a discharge time constant t RCeq 10 ns 2 13 Hence if the results of equations 2 11 and 2 13 are compared then the conclusion of this sub section is that the theoretical and graphical results do not agree It means that probably the system has some other elements that would affect the data Analyzing the equation 2 12 it is possible to conclude that as lowest the value of r is is the better will be rebuilt the shape of the signal Hence the idea is to find an equivalent circuit diminishing either the equivalent capacitance or the equivalent resistance In this case it has been explained that the output resistance of the amplifier is fixed then the solution will be to use an external divisor probe EDP 2 3 2 External Divisor Probe EDP To reduce the impedance introduced by the amplifier and the oscilloscope an EDP is used to wire the system instead of the coaxial cable In this case it is just necessary to comment the impedance introduced by the EDP because the amplifier and the oscilloscopes are the same see Figure 2 9
78. sistance is ten thousands time bigger than the output resistance of the amplifier then it is clear than the equivalent resistance for the equivalent circuit is the output resistance of the amplifier Ceg CeoallCosc Ccoa Cosc A2 1 Re R A2 2 56 Design of a low cost Photon Height Analyzer for a M ssbauer Spectroscopy Then the equivalent circuit see Figure A2 2 is formed by a resistance in series with a capacitance that is the classical configuration of a low pass filter Req Vosc Vi Ceq Figure A2 2 Equivalent circuit s scheme using coaxial cable This is a basic circuit to solve Vosc Vi Req sd A2 3 Vosc Ceq d A2 4 Isolating the intensity in equation A2 4 and substituting in equation A2 3 it is obtained fa uy t eR ose A2 5 Ceq ea Ceq Reordering equation A2 5 it is possible to obtain the transfer s function of the circuit E N Re V 1 V Ce Ce ee 1 2 2 V gt sc n gt ose q q A2 6 Zeq Vi 4424 Vi Ceq Req Ceg R IB In order to express the transfer s function in the complex frequency domain it is necessary to express the impedance in terms of frequency because resistance does not depend on frequency then Zcapacitance Sp S jw A2 7 Introducing A2 7 in A2 6 Circuit Analysis 57 1 1 gt V sc 1 C 1 T S 8 pO quse a A2 8 Vi iste SCeq eq 1 SRCeq sCeq Equation A2 8 shows that the func
79. some peak that should be count when comparing two consecutives relative minimums exist the probability than both peaks are absolutes minimums but the statistics of these events is so small that this error can be accepted A5 2 2 Overlap One key parameter of the program is to give an idea of how the dead time of the system is in other words to know if the distance between the radioactive source and the sample to analyze is optimum On the one hand if the source is too close to the sample then the detector will receive a number of photons too big to be able to have a good response in consequence the information of the photons will be overlapped it means that the second photon arrived to the detector will contribute to the histogram with a wrong energy quantity On the other hand if the distance from the source to the sample is too big a fraction of the information could be lost because the photons emitted by the source will not impact on the sample It is easy to understand that the worst option of both is to have the set up explained in the first case where the source is too close to the sample Then for avoiding counting this photons in the histogram with their modified energy the program incorporates an option that could be used when the user decide In order to explain this idea easily it is important to know how is the behaviour of the data when appears an emission peak Alternative peak detection and histogram 75 In figure
80. st iteration x V and X2 V Instead as an indicator work of peaks 1st total of peaks 2nd dead time time of execution s a keV V b keV x keV x keV and xs keV The function of each element either control or indicator will be explained Path file its function is to introduce the data file acquired First iteration this Boolean fix if the data file used is going to be the ones which will work as a histogram pattern or the ones which will be used to confirm where is placed the energy window X1 V x2 V After the first time that the program runs we should identify the three peaks with physical meaning The first two are x and x Once we have indentified the peak we should use the value of the x axis of peaks 1st shows the length of the array containing the peaks detected in the first data file of peaks 2nd shows the length of the array containing the peaks detected thanks to the energy window discriminator dead time 96 shows the percentage of dead time at the detector LabView program and display 49 time of execution s shows the time that takes MatLab to do the whole data treatment a keV V shows the slope value of the linear equivalence between voltage and amplitude b keV shows the constant term of the linear equivalence between voltage and amplitude X1 keV x2 keV xs keV shows the position of the peaks placed in 6 4 keV 14 4 and 21 respectively 4 3
81. sults The idea to use MatLab has a clear explanation considering the interest of the author of the project in increase their knowledge about LabView LV programming was decided to use MatLab because LV contains a function called MatLab script which allows to pass directly the MatLab code to LV In Chapter 4 it has been also determined some other parameters necessaries for the right work of the code such us the minimum value accepted for a maximum peak detected 50 mV or the threshold values to measure dead time V 0 35 mV to avoid dead time In Chapter 4 it is shown step by step the final LV block diagram explaining all the highlights it is also presented a kind of user s manual in order to proportionate to the laboratory worker all the information needed to do a good energy window calibration Finally Chapter 5 includes the main conclusion obtained during the project and also some ideas about what could be the future work in order to improve the project Principles of M ssbauer Spectroscopy 3 Chapter 1 PRINCIPLES OF MOSSBAUER SPECTROSCOPY Rudolf Ludwig M ssbauer discovered at the end of the 50 s the recoilless resonant absorption of gamma rays 1 also known as Mossbauer effect ME It consists in the recoilless emission of gamma rays by a radioactive nucleus followed by the absorption of these rays by other nucleus of the same species see Figure 1 1 Excited State Nucleus Ees Gamma Ground State Nucleus Egs
82. t that avoiding overlap in the histogram the program takes more time running consequently the user may decide when it is necessary normally when the source is changed or the set up moved or when is not important In order to be able to choose easily which mode is going to be used a parameter is introduced on the code and also a visual indicator on the LabView display In order to have an idea of this difference of time a comparison has been done it and will be shown in Table A5 2 76 Design of a low cost Photon Height Analyzer for a M ssbauer Spectroscopy Table A5 2 Time running comparison between a code with or without the overlap condition File length 0 4 M points Overlapped peaks No overlapped peaks Peaks number 1490 1253 Time running s 148 997 148 357 Considering the table above consider that it should be usual to use the condition of avoid overlap because the histogram obtained will be clearer and the time difference it is not big enough A5 2 3 Histogram s bar width The main objective of this project is to obtain a histogram of the different photon s energy expressed trough the oscilloscope as voltage In order to establish the bar s width it is necessary to see which are the upper and lower values that are going to be pictured To do this long data files containing one and a half million points were taken and it was possible to determine that the maxim
83. technical limitations As was commented in the introduction of the chapter it is necessary to understand how the digital oscilloscope works For this reason it is essential to distinguish between the two modes of work On one hand if the TS is slow enough bigger than 20ms div to continuously send all samples over the USB connexion then the PropScope goes into streaming mode where it is possible to see all samples moving from right to left On the other hand when the TS knob is to set into faster TS the scope takes a set of samples and transfers them to be displayed The sampling rate SR is calculated to return twenty divisions of data over 1024 samples in consequence it is necessary to make a balance between the maximum TS possible against the idea to obtain the full peak inside the 1024 samples vector The following table shows the correspondence between SR TS and the time acquired in one 1024 sample vector Table 3 1 Dependence of the time acquired in a vector against SR TS 25 2 40 10 5 100 5 10 200 2 5 20 400 1 50 1000 0 5 100 2000 Looking on the table 3 1 and taking into account that the maximum amplitude peak it means around 5 V see Figure 3 1 is around 40 points equivalent to 80 us width it does not have too much sense to use a TS faster than 100 us because if not we will lose information about the dead time it probably could cut any peak by the half 30 Design of a low cost Pho
84. the first thing to do is to observe the signal and characterize it with a commercial analogue oscilloscope Amplitude V m T 1 r r r r r r f 3800 4000 4200 4400 4600 4800 5000 Time us Figure 2 2 Example of the digital signal With a signal example see figure 2 2 it is possible to determine the features that will decide the optimum device 2 2 1 Analysis of the number of bits The first parameter to analyze was the required amplitude s signal range This parameter determines the maximum value of peak to peak voltage v admitted The output signal had a maximum value of 5 V and a minimum of 2 V thus the minimum v accepted would be 10 V in order to avoid the clipping effect that could saturate the oscilloscope Once the value of v is known it is possible to know the needed n number of bits fixing previously the required data resolution using EN Vmax V min Vop Vresotution gt 2n mE 2n 2 1 lt is known that the electronic devices use an even number of bits therefore the discussion was focused between 8 10 or 12 bits In Table 1 the resolution obtained is shown as a function of the bit s number for v equal to 10 V 12 Design of a low cost Photon Height Analyzer for a M ssbauer Spectroscopy Table 2 1 Resolution offered depending on the number of bits 10 9 8 12 2 4 It is clear that this parameter will affect directly the final photon s energy spectrum an
85. the previous paragraph will make easier the data treatment It must be commented that this feature does not happens with the coaxial cable where the noise values were much more scattered Then to characterize basically the signal there exists two different behaviours i when there is not emission the signal remain around zero with a minimum value of 0 065 V very well determinate see figure A5 3 ii when there is a peak the values are all of them getting bigger absolute value As the objective is to determine the peaks due to emission process the region i allows to determine properly the minimum value accepted to consider a minimum Then using a for loop it is very simple to just hold on the minimum values smaller more negatives than the no emission level Consequently the next step is to distinguish between two areas on the signal i where the points are getting smaller more negatives until arrive to the minimum value ii where the points start getting bigger less negatives If the idea is understood then it is easy to decide that a good way to analyze the signal is making small length vectors with eight points and to calculate their minimum value it permits to obtain a vector eight times shorter than the samples vector with all the minimum values of each small segment Amplitude V o coll a i li ii Jl al Wi 0 2 t r r r r t p r i3 2000 2100 2200 2300 2400 2500 2600 2700 2800 290
86. time in microseconds because the data format is prepared to starts in zero at each new pack Getting the third row of the file at code appears as a 2 because it starts to count since 0 the y axis amplitude in Volts is obtained and then the data are ready for being used in the MatLab script In order to have time as a x axis the code place the first pack in a new array for the others packs the idea is to obtain the last value of the previous pack and add this quantity plus 2 us because the pack starts at zero and the mean time separation between points with this time scale is 2 us to the complete pack ENERGY WINDOW OUTPUT s TI TIME AXIS OUTPUT AMPLITUDE AXIS OUTPUT Figure 4 6 Creation of the time axis and obtaining the amplitude axis 44 Design of a low cost Photon Height Analyzer for a M ssbauer Spectroscopy 4 2 Data Treatment The objective of this section is basically to explain the few small corrections done over the MatLab previous code due to the goal to take profit of all possible LabView s skills These changes could be essentially expressed in one section The final histogram is it the first 4 2 1 Histogram The final objective of this thesis is to be able to identify and decide if the energy window is well placed along the energy axis in order to work exclusively with the photons with 14 4 keV energy In order to be able to show a graphic with its x axes in energy units it wil
87. tion s transfer in the complex frequency domain depends on frequency represented as s the circuit works as a low pass filter To find the cut frequency of the low pass filter it is necessary to find the zero of the transfer function s divisor A2 7 1 sRC 20 gt s RC S Weut T A2 9 Using w 2nf A2 10 Finally coa _ __ 15 9MHz A2 11 2r RCeq To determine the transfer s function at time domain it is necessary to do the reverse Laplace transform the expression A2 8 could be rewritten as T s boe A2 12 i RCeq S eGR RCeq a It is simple to do the reverse Laplace s transform using the two following properties L i a F s a 1 F s A2 13 pot 5 zy A2 14 Therefore the transfer s function expressed at time domain is 1 Mose 1 QUE A2 15 Vi RCeq This equation shows that for a peak observed the transfer function applied in it is an exponential decay with a discharge time constant 58 Design of a low cost Photon Height Analyzer for a M ssbauer Spectroscopy T RC4 100 100 107 10ns A2 16 It is possible to see in equation A2 8 that the function s transfer is a function of frequency as it has been commented before the circuit works as a low pass filter and at this point it is possible to calculate the cut s frequency A2 7 _ E e M 1 SRCeq 0 gt s Resa gt Wet Ron A2 17 Using w 2nf A2 18 Th
88. tion was finished the USB oscilloscope arrived to the laboratory in consequence there was no reason to continue working on this idea instead to work with original data from the M ssbauer experiment A3 2 MatLab code A3 2 1 Peaks detection The signal shows peaks in both amplitude zones positive and negative created by the differentiator of the amplifier We are going to work with the peak with near Gaussian shape in consequence the signal can be modified in the positive area in order to make easier the data treatment see Figure A5 2 RTT ATAN Wo AMplitude V r r r r r 0 500 1000 1500 2000 2500 3000 3500 samples number Figure A5 2 Signal without values greater than 65 mV excepting peaks To work just with the lower part of the signal does not mean that the data is being altered to make it clear every time that the signal would be shown it is going to be use the full original signal and will be possible to check visually that the peak are perfectly detected in amplitude and time 72 Design of a low cost Photon Height Analyzer for a M ssbauer Spectroscopy When the signal is amplified around the zero amplitude value it is possible to realize that the signal remains swinging around the zero with a minimum value of 65 mV this allows to determinate perfectly the minimum value acceptable for a peak In other words it is like creating a filter for amplitudes smaller than 65 mV The feature commented in
89. ton Height Analyzer for a M ssbauer Spectroscopy losing its information In addition looking the figure below it can be concluded that the parameter of the amplitude is well measured Example of a peak shape T c a a ar gt a e a e Amplitude V m a 2 um cd o a o L L L L L L L L 1 062 1 064 1 066 1 068 1 07 1 072 1 074 1 076 of point x1 o Figure 3 1 The width of this peak is around 40 points it means 80 us 3 1 2 Transfer data velocity USB PropScope hardware like all digital instruments puts limitations on what can be done Main issues are PropScope analogue to digital convertor velocity memory size and USB connexion speed These features translated to our system means that exists a limited transfer data velocity in that case it is 35Kb s low although in consequence of its cost For example in order to obtain a file which size is 22 352 KB PropScope took twenty minutes approximately 3 1 3 Clipped signal When a signal exceed the amplitude allowed 10 Vp by the oscilloscope it is said that the signal is clipped in this case PropScope just remains with the maximum value permitted until it starts to descends when the signal value is lower than 10 Vpp It does not produce any kind of problem it just saturate the signal during the time that the signal exceeds the maximum value allowed 3 2 MatLab code In the introduction chapter 1 w
90. ual or higher frequencies than the cut frequency will be modified in amplitude as analogous to equation A2 23 1 1 1 R2C3 gw x 100 x 100 A2 40 Vi Vosc Erei Ex tse With the study done above we can conclude that the use of the EDP instead of the coaxial cable will suppose an improvement of our data measuring system 64 Design of a low cost Photon Height Analyzer for a M ssbauer Spectroscopy Annex lll COMPARING DATA OBTAINED USING COAXIAL CABLE AND EXTERNAL DIVISOR PROBE In Chapter 2 section 2 3 were analyzed graphically two options to wire the amplifier and the USB oscilloscope coaxial cable CC and external divisor probe EDP In section 2 4 was done the same study for the whole system analyzing both circuits with their different elements In both cases were clear that the introduction of an EDP instead of a CC will improve the quality of the measures In consequence this annex pretends to express these improvements on data observing the effects on the final result the amplitude histogram The figure below shows both histograms 500 T r r T 2500 2000 F 1500 F of counts np a o of peaks 1000 500r r L t 0 r j 2 5 2 1 5 1 0 5 0 2 5 2 1 5 1 0 5 0 Amplitude V Amplitude V Figure A3 1 Measures done with coaxial Figure A3 2 Measures done with EDP cable Just observing both images it is clear that the histogram of Figure A 3 2 ha
91. um amplitude voltage to represent will be 2 V the lower limit was previously determined by the noise level on the signal its value is 65 mV In order to choose the bar s width it is going to be represented the same data sample obtained in a measure with an external divisor probe with different thicknesses see Figures A5 6 and A5 7 Then it will be easier to choose the bar size to observe clearer the peak s histogram 2500 y T T T 2000 2000 1500 of peaks of peaks E e o 1000 500 0 L 1 5 2 1 5 1 0 5 0 2 5 2 1 5 1 0 5 0 Amplitude V Amplitude V Figure A5 6 Amplitude histogram 0 03 V Figure A5 7 Amplitude histogram 0 05 V bar s width bar s width Figure A5 6 shows clearer the results that we expected to obtain And it is possible to check that increasing the bar s width the histogram shows worst the result In conclusion the best bar s width size for our set up is 0 03 V Dynamic Data Exchange in LabView DDE Annex VI Dynamic Data Exchange in LabView DDE In chapter 4 it is commented that could exist the possibility to obtain the data from LabView directly via DDE instead of how it is performed at the moment The objective of this annex is to show Figure A6 1 how should be established a DDE connexion between the USB digital oscilloscope and the LabView REOST D Removes empty element P command line

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