- Email: [email protected]
Threshold characterisation of the Medipix1 chip
ARTICLE IN PRESS
Nuclear Instruments and Methods in Physics Research A 509 (2003) 138–145
Threshold characterisation of the Medipix1 chip . D. Niederlohner*, Ch. Bert, J. Giersch, K.-F. Pfeiffer, G. Anton Physikalisches Institut 4, Universitat Erwin-Rommel-Strasse 1, 91058 Erlangen, Germany . Erlangen-Nurnberg, .
Abstract The Medipix1 chip is a hybrid pixel detector working in photon counting mode and has the ability to put a discriminating threshold on each photon signal. To increase the image quality the threshold voltage can be electronically fine tuned with a 3 bit threshold adjust for each pixel. This electronic adjustment can only equalise the inhomogeneities of the electronics, not those of the physical frontend (conversion material and bump bonds). The remaining noise of the threshold has an obvious impact on the image quality. To optimise the uniformity over the whole chip we did threshold scans with a cadmium X-ray source analysing every pixel. With those scans we were able to create a bit mask including the physical frontend. Comparing the results of the different methods we can judge the quality of the electronically generated mask and draw conclusions about the properties of the physical frontend. Furthermore, simulations have been carried out for comparison with the measured data. r 2003 Elsevier Science B.V. All rights reserved. PACS: 07.77; 07.85.F; 07.50.H; 07.05.T; 87.57.G Keywords: Medipix1; Characterisation; Electronic noise; Calibration; Image quality; Simulation
1. Introduction The Medipix1 chip is a hybrid pixel detector, which has been developed by the Medipix-Collaboration [1]. The pixel size is 170 170 mm2 with 64 64 pixels on one chip. Every pixel has electronics implemented to detect and count (15 bit depth) signals coming from the input. Those signals are charges that are generated by an interacting photon in the sensor layer or an electronic test pulse on the input capacity. In our case the sensor is a 300 mm thick silicon layer,
*Corresponding author. E-mail address: [email protected]. . de (D. Niederlohner).
which is bump bonded to the electronics via tin bonds. The photon counting ability is realised by a discriminator that compares the incoming charge with a given threshold. This threshold can be set globally by the voltage Vth and therefore energy sensitive images can be taken. Due to fabrication tolerances, the discriminators are not exactly equal so that the individual responses of the pixels differ over the whole chip. To overcome this problem, the discriminator threshold in every pixel can be fine tuned with a 3 bit DAC (threshold adjust bits). By the threshold adjust voltage ðVtha Þ the dimension of this correction has to be adapted to the width of the unadjusted threshold distribution. Theoretically, the threshold distribution can be narrowed by a factor of eight with a more
0168-9002/03/$ - see front matter r 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0168-9002(03)01562-6
ARTICLE IN PRESS D. Niederlohner et al. / Nuclear Instruments and Methods in Physics Research A 509 (2003) 138–145 .
139
equalised detector as result. A so-called mask holds the bit settings for the DAC of all pixels. This mask can be written into the chip before an acquisition has to be performed.
2. Standard way of mask generation The described equalisation can be realised by sending test pulses to the pixel electronics which can be used to find out the individual threshold of every pixel. Generation of the test pulse is done by the MUROS-1 (Medipix1 re-Usable Read Out System) [2] in combination with two standard commercial interface boards and the software package Medisoft [3]. 2.1. Mask generation with Medisoft Medisoft has routines for mask generation for a certain Vth ; which help the user to determine the right bit settings. The following measurements and calculations have to be performed to create a mask [4]: * *
*
*
Find the individual threshold for all pixels Select the optimal Vtha depending on the width of the unadjusted threshold distribution Measure the distribution for all eight possible adjust bit settings Generate the mask by choosing the right bit setting for every pixel
The first point is easily done by systematic variation of the test pulse height (pulse scan) and taking the 50% value of the resulting S-curve as the individual threshold of the corresponding pixel. To find the optimal Vtha ; one has to perform more pulse scans with all adjust bits set (equals a maximum correction for every pixel). Fig. 1 illustrates this procedure: vary Vtha until the distribution with no adjust bits set overlaps by an eighth the distribution with all adjust bits set (Vtha corresponds to the position of the right peak and therefore to the distance of the two uncorrected distributions). Once the correct Vtha is found, pulse scans with the eight possible bit settings have to be performed to obtain the data from which Medisoft generates the mask. Fig. 1 also shows the result of the adjustment: the distribution is narrowed by a
Fig. 1. Uncorrected threshold distributions (left peak ¼ no adjust bits set and right peak ¼ all adjust bits set) and the narrowed distribution in the middle. For optimal results the two uncorrected distributions—the distance in between them corresponds to Vtha (threshold adjust voltage)—has to overlap by an eighth (from Ref. [5]).
factor of 4–5 (peak in the middle). A mask which is generated by this procedure will be called a ‘‘standard mask’’ in this article. 2.2. Limitations of the standard mask If one wants to use the variable threshold of the Medipix1 detector to take energy sensitive images, one has to discriminate photons of lower energies by placing the threshold inside the used photon spectrum. Images taken with the standard mask become very noisy as soon as the threshold is located at a rapidly and intensely changing region. This property is illustrated in Fig. 2: One can see two images taken with the same detector parameters with exception of the threshold. The left one is taken with the threshold below the photon spectrum, the right one with the threshold inside. The used photon spectrum is a 35 kV-Mo spectrum filtered by 30 mm Mo and 2 mm Al: The decrease in image quality is evident if the threshold is inside the photon spectrum.1 This decrease could 1
The structure in the images is from a phantom we used for quality tests. It is mainly made out of PMMA with rods of Teflon and PA in it.
ARTICLE IN PRESS 140
D. Niederlohner et al. / Nuclear Instruments and Methods in Physics Research A 509 (2003) 138–145 .
Fig. 2. Comparision of images taken with the standard mask. On the left side one can see an image where the threshold is below the photon spectrum ðVth ¼ 1:357 VE10 keVÞ; on the right side one where the threshold is inside the photon spectrum ðVth ¼ 1:161 VE19 keVÞ: The spectrum is from a Mo-anode, 35 kV with 30 mm Mo and 2 mm Al filtering.
be caused by a suboptimal mask and therefore an insufficient equalisation. But there could be another reason for the reduced image quality: the described equalisation concerns only the electronics of the detector and not the conversion layer and the bump bonds (the so-called ‘‘physical frontend’’). A—by the standard procedure uncorrectable—imperfect physical frontend could be a possible reason: if the conductivity of the bump bond connection differs between different pixels, then this would have an influence on the charges on the way from generation to detection. Those differences are not observable and adjustable with the electronic approach. Therefore we generated a mask including the physical frontend by using X-ray photons. This mask is called ‘‘absolute mask’’ since an energy gauging is acquired from the data.
3. Calibration with an X-ray source 3.1. Generation of the absolute mask The individual thresholds of all pixels has to be measured for the adjustment. In contrast to the standard method we use a fixed energy and vary the threshold voltage. The ideal X-ray source to be used to measure the response curves of all pixels
would be one with only one spectral line. Synchrotron radiation would be ideal, but we used a 109 Cd source with two lines in the interesting energy region: * *
At 22:1 keV with about 83 % of the intensity. At 25:0 keV with about 17 % of the intensity.
This source is almost ideal, because most of the intensity is in one of the lines. The response curve of a threshold scan for a few pixels is shown in Fig. 3. The source was placed above the chip with silicon sensor as close as possible ðE12 mmÞ and the scan ran in the interval 1:3pVth p1:8 V in steps of 0:005 V with an acquisition time of 60 s per threshold voltage. From the two Cd-lines one would expect a superposition of two error functions in the response, but due to noise the curve is smeared out and has the form of one error function. With higher statistics the response to the two lines could be resolved into two error functions, but the present statistics are a compromise of low activity of the source (338 kBq at date of measurement) and a realistic acquisition time. Analogous to the standard method, the 50% value defines the threshold of the pixel. To access these values, we assume one error function and fit the curve to f ðxÞ ¼ a erfðbðc xÞÞ þ d:
ð1Þ
ARTICLE IN PRESS D. Niederlohner et al. / Nuclear Instruments and Methods in Physics Research A 509 (2003) 138–145 .
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600 pixel 0 pixel 1000 pixel 2000 pixel 3000
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1.9
Fig. 3. The response curve of a threshold scan for a few pixels with the 109 Cd source. One of the curves is exemplarily fitted with the adapted error function. The fit parameter c corresponds to the distance from the ordinate and therefore to the individual threshold (see Eq. (1)).
The fit parameter c corresponds to the individual pixel threshold and the distribution of c therefore mirrors the threshold spread. The goal of the following procedure is a reduced width of this distribution. Fit parameter b corresponds to the electronic noise and therefore to the quality of one individual pixel. The results of the fit procedure for all pixels are Gaussian distributions for b and c: In Table 1 the mean values and RMS of the distributions are shown. They represent the unadjusted detector. For the calibration one has to find the optimal threshold adjust voltage Vtha (as in the standard method). This is done by threshold scans with varying Vtha to achieve an eighth overlap of the uncorrected distribution with the distribution with all adjust bits set. In the presented example (see Fig. 5) the overlap does not match the optimal 12.5% but rather 20%. This difference originates in a compromise one has to make due to the very time consuming threshold scans. Through these measurements we were also able to confirm the supposed linear relation between Vtha and c% (see Figs. 4 and 5). The distribution with all adjust bits set thus moves linearly with applied Vtha ; measuring the relation at two points will be sufficient in the future.
Table 1 Resulting fit parameters for the unadjusted detector Parameter
Mean
RMS
b c
0.0932 1.72
0.007625 0.04029
Another interesting point which can be seen in Fig. 4 is the constant width of the distribution (the bars mirror the RMS of the threshold distribution). The spread in the thresholds is independent of the applied Vtha : This was already known [4], but only as a property of the electronics and not of the whole detector. Once the proper threshold adjust voltage is found one more threshold scan has to be taken for each adjustment bit setting. At that point the necessary data is available to generate an absolute mask by selecting the best bit setting for every pixel. A final threshold scan with the new mask shows the resulting distribution which is obviously narrowed. This effect can be nicely seen in Fig. 6, which shows all fitted error functions before and after the equalisation. Fig. 7 shows the effect of the absolute mask in form of the change to the threshold distributions.
ARTICLE IN PRESS D. Niederlohner et al. / Nuclear Instruments and Methods in Physics Research A 509 (2003) 138–145 .
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1.62
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mean of c with RMSc [V]
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1.46 0.765
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0.775
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0.79
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Vtha [V]
Fig. 4. Relation of c% and Vtha : The bars mirror the RMS of the (unadjusted) threshold distributions.
ratio gives a quantitative evaluation: 140
RMSbefore ¼ 4:71: RMSafter
120
Therefore with the new calibration technique the same narrowing is possible as with the standard one. The question is whether the masks are really equivalent and produce images with the same quality. To answer this question, a standard mask with the same voltage settings as the absolute one was built with Medisoft and compared with the new one. This comparison additionally allows a judgement of the physical frontend.
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Fig. 5. The uncorrected threshold distribution (no adjust bits set, right side) and the threshold distribution with all adjust bits set (left side) with the overlap.
The mean of the histogram at the right side ð22:91 keVÞ corresponds to the energy of the Cd source’s main line ð22:1 keVÞ with a slight shift upwards due to the second line of the source ð25:0 keVÞ: Because the RMS is a measure for the achieved reduction of the widths, the following
3.2.1. Bit settings A direct comparison is easily achieved by taking the difference of the two masks pixel-wise and filling the absolute value in a histogram. The result can be seen in Fig. 8. The evaluation of that histogram shows that almost 50% of the pixels have an identical setting and less than 10% differ by more than one. Hence the conversion layer and the bump bonds are not the main reason for the noisy images when the threshold is inside the photon spectrum. The spread of the individual response of the pixels
ARTICLE IN PRESS D. Niederlohner et al. / Nuclear Instruments and Methods in Physics Research A 509 (2003) 138–145 .
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Fig. 6. Comparison of the fitted error functions before (left side) and after (right side) the equalisation. Obviously the distribution is narrowed.
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Fig. 7. Comparison of the threshold distributions before (left side) and after (right side) the equalisation. The change in RMS is a measure for the quality of the absolute mask. The ratio before/after is about 4.71.
that cannot be completely corrected by the 3 bit adjustment is the dominant factor for the insufficient equalisation.
seems that this small difference is important for the image quality.
4. Simulations on the threshold properties 3.2.2. Image quality A comparison can also be made by looking at the image quality. Therefore, we took acquisitions with identical parameters except the masks used. The results are shown in Fig. 9: the quality of the image taken with the absolute mask is obviously better. This is surprising, because only a small difference is found by the pixel-wise comparison. It
The width of the Gaussian threshold distribution is known from the final threshold scan of the mask generation (see Fig. 7, right side). The data were evaluated in keV and so the RMS of the distribution equals directly the physical threshold spread, namely 0:51 keV: In Ref. [5] the threshold distribution width was electronically determined to
ARTICLE IN PRESS D. Niederlohner et al. / Nuclear Instruments and Methods in Physics Research A 509 (2003) 138–145 .
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This value is generated from a Gaussian distribution around zero. Thereby a noisy preamplifier is modelled.
2000 1800 1600 1400 1200 1000 800 600 400 200 0 0
1
2
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adjust bit difference
Fig. 8. Histogram of the absolute value of the pixel-wise difference of the masks.
be 120 to 180 e : With an energy for electron–hole pair production in silicon of 3:6 eV; that leads to a threshold distribution width around 0:5370:1 keV: In order to get a better understanding we did simulations on the threshold properties. 4.1. Description of simulation model The simulations were performed entirely with ROSI [6] and were intended to model the final threshold scan in the procedure for the generation of the absolute mask. Therefore all parameters (distance, X-ray source, sensor material) were chosen as in the measurement. Additionally the following assumptions were made for the detector properties: Every pixel has an individual threshold, slightly varying from the global threshold. Those differences follow a Gaussian distribution. The noise amplitude is identical for all pixels.2 For every incoming photon a random value is added to the individual threshold of the pixel.
*
*
2
This does not comply with reality, but the differences are so small that this effect is negligible for the fitting procedure and the results.
If a photon arrives at the detector, its energy is compared with the sum of global threshold, individual threshold (per pixel) and randomly generated noise. This is done for 10 different widths of the individual threshold distribution and for 10 different widths of the distribution that is used to generate the noise. Therefore for every global threshold (13 up to 33 keV in 0:5 keV steps) the photons are compared with 10 10 different values and we obtain 100 threshold scans with varying detector properties. These were—analogue to the measurement—fitted with the function f ðxÞ ¼ a erfðbðc xÞÞ þ d: When searching the best match of the parameters one has to consider that the width of the threshold distribution corresponds to the RMS of parameter c; the width of the noise distribution is mirrored by the mean of parameter b: 4.2. Results of simulations Since the used 109 Cd source is not monoenergetic these simulations are not very well suited for determining the noise properties of the detector. Therefore we will not discuss that topic and concentrate on the results concerning the threshold distribution. For the evaluation of the parameter c; we plotted the dependence of the fit parameter on the distribution width in Fig. 10. The curve was fitted with a linear function with the following functional equation: RMSc ¼ 0:945 keV1 sthreshold þ 0:056:
ð3Þ
The best match of the measured and simulated fit parameter can be calculated based on this equation: With a RMSc ¼ 0:5083 one will find a distribution width of sthreshold ¼ 0:478: This value is consistent with the results of our measurements and the electronically determined width and therefore confirms our measurements and simulation model.
ARTICLE IN PRESS D. Niederlohner et al. / Nuclear Instruments and Methods in Physics Research A 509 (2003) 138–145 .
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Fig. 9. Images with identical parameters except the mask: standard mask (left side) and absolute mask (right side). It is quite evident that the image quality is higher with the absolute mask.
1
modelling the threshold scan with an X-ray source, we were able to find the same magnitude for the threshold distribution width.
simulated values 0.945*x + 0.056
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References
0.5 0.4 0.3 0.2 0.1
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width of threshold distribution [keV] Fig. 10. Dependency of RMSc on the width of the threshold distribution in the simulation. The points are fitted with a linear function.
5. Conclusions The mask generation with an X-ray source including the physical frontend has the potential to increase the image quality of the Medipix1 detector. This is especially important when the threshold cuts into the photon spectrum near a rapidly and intensely changing region, which can be necessary for energy sensitive imaging [7]. The remaining noise in the images seems not to be caused by the physical frontend. With a simulation
[1] M. Campbell, E.H.M. Heijne, G. Meddeler, E. Pernigotti, W. Snoeys, Readout for a 64 64 pixel matrix with 15-bit single photon counting, IEEE Trans. Nucl. Sci. 45 (3) (1998) 751. [2] G. Bardelloni, T. Boerkamp, D. Calvet, H. Verkooijen, J.L. Visschers, MUROS-1, Medipix-1 re-Usable Read Out System, NIKHEF, March 2002. [3] G. Bardelloni, E. Bertolucci, A.L.J. Boerkamp, D. Calvet, M. Conti, M. Maiorino, P. Russo, J.L. Visschers (Eds.), A new read-out system for an imaging pixel detector, IEEE Nuclear Science Symposium and Medical Imaging Conference, 2000. [4] B. Mikulec, Single photon detection with semiconductor pixel arrays for medical imaging applications, Ph.D. Thesis, University of Vienna, Austria, June 2000. [5] C. Schwarz, Digital X-ray imaging using hybrid semiconductor pixel detectors in single photon counting mode, Ph.D. Thesis, Albert-Ludwigs-Universit.at Freiburg i. Brsg, August 2001. [6] J. Giersch, Rosi: an object-oriented and parallel computing Monte Carlo simulation for X-ray imaging, Nucl. Instr. and Meth. A, (2003) these proceedings, September 2002. [7] C. Bert, Computed tomography using the Medipix1 chip, Nucl. Instr. and Meth. A, (2003) these proceedings, September 2002.
Nuclear Instruments and Methods in Physics Research A 509 (2003) 138–145
Threshold characterisation of the Medipix1 chip . D. Niederlohner*, Ch. Bert, J. Giersch, K.-F. Pfeiffer, G. Anton Physikalisches Institut 4, Universitat Erwin-Rommel-Strasse 1, 91058 Erlangen, Germany . Erlangen-Nurnberg, .
Abstract The Medipix1 chip is a hybrid pixel detector working in photon counting mode and has the ability to put a discriminating threshold on each photon signal. To increase the image quality the threshold voltage can be electronically fine tuned with a 3 bit threshold adjust for each pixel. This electronic adjustment can only equalise the inhomogeneities of the electronics, not those of the physical frontend (conversion material and bump bonds). The remaining noise of the threshold has an obvious impact on the image quality. To optimise the uniformity over the whole chip we did threshold scans with a cadmium X-ray source analysing every pixel. With those scans we were able to create a bit mask including the physical frontend. Comparing the results of the different methods we can judge the quality of the electronically generated mask and draw conclusions about the properties of the physical frontend. Furthermore, simulations have been carried out for comparison with the measured data. r 2003 Elsevier Science B.V. All rights reserved. PACS: 07.77; 07.85.F; 07.50.H; 07.05.T; 87.57.G Keywords: Medipix1; Characterisation; Electronic noise; Calibration; Image quality; Simulation
1. Introduction The Medipix1 chip is a hybrid pixel detector, which has been developed by the Medipix-Collaboration [1]. The pixel size is 170 170 mm2 with 64 64 pixels on one chip. Every pixel has electronics implemented to detect and count (15 bit depth) signals coming from the input. Those signals are charges that are generated by an interacting photon in the sensor layer or an electronic test pulse on the input capacity. In our case the sensor is a 300 mm thick silicon layer,
*Corresponding author. E-mail address: [email protected]. . de (D. Niederlohner).
which is bump bonded to the electronics via tin bonds. The photon counting ability is realised by a discriminator that compares the incoming charge with a given threshold. This threshold can be set globally by the voltage Vth and therefore energy sensitive images can be taken. Due to fabrication tolerances, the discriminators are not exactly equal so that the individual responses of the pixels differ over the whole chip. To overcome this problem, the discriminator threshold in every pixel can be fine tuned with a 3 bit DAC (threshold adjust bits). By the threshold adjust voltage ðVtha Þ the dimension of this correction has to be adapted to the width of the unadjusted threshold distribution. Theoretically, the threshold distribution can be narrowed by a factor of eight with a more
0168-9002/03/$ - see front matter r 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0168-9002(03)01562-6
ARTICLE IN PRESS D. Niederlohner et al. / Nuclear Instruments and Methods in Physics Research A 509 (2003) 138–145 .
139
equalised detector as result. A so-called mask holds the bit settings for the DAC of all pixels. This mask can be written into the chip before an acquisition has to be performed.
2. Standard way of mask generation The described equalisation can be realised by sending test pulses to the pixel electronics which can be used to find out the individual threshold of every pixel. Generation of the test pulse is done by the MUROS-1 (Medipix1 re-Usable Read Out System) [2] in combination with two standard commercial interface boards and the software package Medisoft [3]. 2.1. Mask generation with Medisoft Medisoft has routines for mask generation for a certain Vth ; which help the user to determine the right bit settings. The following measurements and calculations have to be performed to create a mask [4]: * *
*
*
Find the individual threshold for all pixels Select the optimal Vtha depending on the width of the unadjusted threshold distribution Measure the distribution for all eight possible adjust bit settings Generate the mask by choosing the right bit setting for every pixel
The first point is easily done by systematic variation of the test pulse height (pulse scan) and taking the 50% value of the resulting S-curve as the individual threshold of the corresponding pixel. To find the optimal Vtha ; one has to perform more pulse scans with all adjust bits set (equals a maximum correction for every pixel). Fig. 1 illustrates this procedure: vary Vtha until the distribution with no adjust bits set overlaps by an eighth the distribution with all adjust bits set (Vtha corresponds to the position of the right peak and therefore to the distance of the two uncorrected distributions). Once the correct Vtha is found, pulse scans with the eight possible bit settings have to be performed to obtain the data from which Medisoft generates the mask. Fig. 1 also shows the result of the adjustment: the distribution is narrowed by a
Fig. 1. Uncorrected threshold distributions (left peak ¼ no adjust bits set and right peak ¼ all adjust bits set) and the narrowed distribution in the middle. For optimal results the two uncorrected distributions—the distance in between them corresponds to Vtha (threshold adjust voltage)—has to overlap by an eighth (from Ref. [5]).
factor of 4–5 (peak in the middle). A mask which is generated by this procedure will be called a ‘‘standard mask’’ in this article. 2.2. Limitations of the standard mask If one wants to use the variable threshold of the Medipix1 detector to take energy sensitive images, one has to discriminate photons of lower energies by placing the threshold inside the used photon spectrum. Images taken with the standard mask become very noisy as soon as the threshold is located at a rapidly and intensely changing region. This property is illustrated in Fig. 2: One can see two images taken with the same detector parameters with exception of the threshold. The left one is taken with the threshold below the photon spectrum, the right one with the threshold inside. The used photon spectrum is a 35 kV-Mo spectrum filtered by 30 mm Mo and 2 mm Al: The decrease in image quality is evident if the threshold is inside the photon spectrum.1 This decrease could 1
The structure in the images is from a phantom we used for quality tests. It is mainly made out of PMMA with rods of Teflon and PA in it.
ARTICLE IN PRESS 140
D. Niederlohner et al. / Nuclear Instruments and Methods in Physics Research A 509 (2003) 138–145 .
Fig. 2. Comparision of images taken with the standard mask. On the left side one can see an image where the threshold is below the photon spectrum ðVth ¼ 1:357 VE10 keVÞ; on the right side one where the threshold is inside the photon spectrum ðVth ¼ 1:161 VE19 keVÞ: The spectrum is from a Mo-anode, 35 kV with 30 mm Mo and 2 mm Al filtering.
be caused by a suboptimal mask and therefore an insufficient equalisation. But there could be another reason for the reduced image quality: the described equalisation concerns only the electronics of the detector and not the conversion layer and the bump bonds (the so-called ‘‘physical frontend’’). A—by the standard procedure uncorrectable—imperfect physical frontend could be a possible reason: if the conductivity of the bump bond connection differs between different pixels, then this would have an influence on the charges on the way from generation to detection. Those differences are not observable and adjustable with the electronic approach. Therefore we generated a mask including the physical frontend by using X-ray photons. This mask is called ‘‘absolute mask’’ since an energy gauging is acquired from the data.
3. Calibration with an X-ray source 3.1. Generation of the absolute mask The individual thresholds of all pixels has to be measured for the adjustment. In contrast to the standard method we use a fixed energy and vary the threshold voltage. The ideal X-ray source to be used to measure the response curves of all pixels
would be one with only one spectral line. Synchrotron radiation would be ideal, but we used a 109 Cd source with two lines in the interesting energy region: * *
At 22:1 keV with about 83 % of the intensity. At 25:0 keV with about 17 % of the intensity.
This source is almost ideal, because most of the intensity is in one of the lines. The response curve of a threshold scan for a few pixels is shown in Fig. 3. The source was placed above the chip with silicon sensor as close as possible ðE12 mmÞ and the scan ran in the interval 1:3pVth p1:8 V in steps of 0:005 V with an acquisition time of 60 s per threshold voltage. From the two Cd-lines one would expect a superposition of two error functions in the response, but due to noise the curve is smeared out and has the form of one error function. With higher statistics the response to the two lines could be resolved into two error functions, but the present statistics are a compromise of low activity of the source (338 kBq at date of measurement) and a realistic acquisition time. Analogous to the standard method, the 50% value defines the threshold of the pixel. To access these values, we assume one error function and fit the curve to f ðxÞ ¼ a erfðbðc xÞÞ þ d:
ð1Þ
ARTICLE IN PRESS D. Niederlohner et al. / Nuclear Instruments and Methods in Physics Research A 509 (2003) 138–145 .
141
600 pixel 0 pixel 1000 pixel 2000 pixel 3000
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400
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1.65
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1.8
1.85
1.9
Fig. 3. The response curve of a threshold scan for a few pixels with the 109 Cd source. One of the curves is exemplarily fitted with the adapted error function. The fit parameter c corresponds to the distance from the ordinate and therefore to the individual threshold (see Eq. (1)).
The fit parameter c corresponds to the individual pixel threshold and the distribution of c therefore mirrors the threshold spread. The goal of the following procedure is a reduced width of this distribution. Fit parameter b corresponds to the electronic noise and therefore to the quality of one individual pixel. The results of the fit procedure for all pixels are Gaussian distributions for b and c: In Table 1 the mean values and RMS of the distributions are shown. They represent the unadjusted detector. For the calibration one has to find the optimal threshold adjust voltage Vtha (as in the standard method). This is done by threshold scans with varying Vtha to achieve an eighth overlap of the uncorrected distribution with the distribution with all adjust bits set. In the presented example (see Fig. 5) the overlap does not match the optimal 12.5% but rather 20%. This difference originates in a compromise one has to make due to the very time consuming threshold scans. Through these measurements we were also able to confirm the supposed linear relation between Vtha and c% (see Figs. 4 and 5). The distribution with all adjust bits set thus moves linearly with applied Vtha ; measuring the relation at two points will be sufficient in the future.
Table 1 Resulting fit parameters for the unadjusted detector Parameter
Mean
RMS
b c
0.0932 1.72
0.007625 0.04029
Another interesting point which can be seen in Fig. 4 is the constant width of the distribution (the bars mirror the RMS of the threshold distribution). The spread in the thresholds is independent of the applied Vtha : This was already known [4], but only as a property of the electronics and not of the whole detector. Once the proper threshold adjust voltage is found one more threshold scan has to be taken for each adjustment bit setting. At that point the necessary data is available to generate an absolute mask by selecting the best bit setting for every pixel. A final threshold scan with the new mask shows the resulting distribution which is obviously narrowed. This effect can be nicely seen in Fig. 6, which shows all fitted error functions before and after the equalisation. Fig. 7 shows the effect of the absolute mask in form of the change to the threshold distributions.
ARTICLE IN PRESS D. Niederlohner et al. / Nuclear Instruments and Methods in Physics Research A 509 (2003) 138–145 .
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1.62
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mean of c with RMSc [V]
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Fig. 4. Relation of c% and Vtha : The bars mirror the RMS of the (unadjusted) threshold distributions.
ratio gives a quantitative evaluation: 140
RMSbefore ¼ 4:71: RMSafter
120
Therefore with the new calibration technique the same narrowing is possible as with the standard one. The question is whether the masks are really equivalent and produce images with the same quality. To answer this question, a standard mask with the same voltage settings as the absolute one was built with Medisoft and compared with the new one. This comparison additionally allows a judgement of the physical frontend.
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3.2. Comparison of absolute and standard mask 1.45
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Fig. 5. The uncorrected threshold distribution (no adjust bits set, right side) and the threshold distribution with all adjust bits set (left side) with the overlap.
The mean of the histogram at the right side ð22:91 keVÞ corresponds to the energy of the Cd source’s main line ð22:1 keVÞ with a slight shift upwards due to the second line of the source ð25:0 keVÞ: Because the RMS is a measure for the achieved reduction of the widths, the following
3.2.1. Bit settings A direct comparison is easily achieved by taking the difference of the two masks pixel-wise and filling the absolute value in a histogram. The result can be seen in Fig. 8. The evaluation of that histogram shows that almost 50% of the pixels have an identical setting and less than 10% differ by more than one. Hence the conversion layer and the bump bonds are not the main reason for the noisy images when the threshold is inside the photon spectrum. The spread of the individual response of the pixels
ARTICLE IN PRESS D. Niederlohner et al. / Nuclear Instruments and Methods in Physics Research A 509 (2003) 138–145 .
143
Fig. 6. Comparison of the fitted error functions before (left side) and after (right side) the equalisation. Obviously the distribution is narrowed.
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Fig. 7. Comparison of the threshold distributions before (left side) and after (right side) the equalisation. The change in RMS is a measure for the quality of the absolute mask. The ratio before/after is about 4.71.
that cannot be completely corrected by the 3 bit adjustment is the dominant factor for the insufficient equalisation.
seems that this small difference is important for the image quality.
4. Simulations on the threshold properties 3.2.2. Image quality A comparison can also be made by looking at the image quality. Therefore, we took acquisitions with identical parameters except the masks used. The results are shown in Fig. 9: the quality of the image taken with the absolute mask is obviously better. This is surprising, because only a small difference is found by the pixel-wise comparison. It
The width of the Gaussian threshold distribution is known from the final threshold scan of the mask generation (see Fig. 7, right side). The data were evaluated in keV and so the RMS of the distribution equals directly the physical threshold spread, namely 0:51 keV: In Ref. [5] the threshold distribution width was electronically determined to
ARTICLE IN PRESS D. Niederlohner et al. / Nuclear Instruments and Methods in Physics Research A 509 (2003) 138–145 .
144
This value is generated from a Gaussian distribution around zero. Thereby a noisy preamplifier is modelled.
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Fig. 8. Histogram of the absolute value of the pixel-wise difference of the masks.
be 120 to 180 e : With an energy for electron–hole pair production in silicon of 3:6 eV; that leads to a threshold distribution width around 0:5370:1 keV: In order to get a better understanding we did simulations on the threshold properties. 4.1. Description of simulation model The simulations were performed entirely with ROSI [6] and were intended to model the final threshold scan in the procedure for the generation of the absolute mask. Therefore all parameters (distance, X-ray source, sensor material) were chosen as in the measurement. Additionally the following assumptions were made for the detector properties: Every pixel has an individual threshold, slightly varying from the global threshold. Those differences follow a Gaussian distribution. The noise amplitude is identical for all pixels.2 For every incoming photon a random value is added to the individual threshold of the pixel.
*
*
2
This does not comply with reality, but the differences are so small that this effect is negligible for the fitting procedure and the results.
If a photon arrives at the detector, its energy is compared with the sum of global threshold, individual threshold (per pixel) and randomly generated noise. This is done for 10 different widths of the individual threshold distribution and for 10 different widths of the distribution that is used to generate the noise. Therefore for every global threshold (13 up to 33 keV in 0:5 keV steps) the photons are compared with 10 10 different values and we obtain 100 threshold scans with varying detector properties. These were—analogue to the measurement—fitted with the function f ðxÞ ¼ a erfðbðc xÞÞ þ d: When searching the best match of the parameters one has to consider that the width of the threshold distribution corresponds to the RMS of parameter c; the width of the noise distribution is mirrored by the mean of parameter b: 4.2. Results of simulations Since the used 109 Cd source is not monoenergetic these simulations are not very well suited for determining the noise properties of the detector. Therefore we will not discuss that topic and concentrate on the results concerning the threshold distribution. For the evaluation of the parameter c; we plotted the dependence of the fit parameter on the distribution width in Fig. 10. The curve was fitted with a linear function with the following functional equation: RMSc ¼ 0:945 keV1 sthreshold þ 0:056:
ð3Þ
The best match of the measured and simulated fit parameter can be calculated based on this equation: With a RMSc ¼ 0:5083 one will find a distribution width of sthreshold ¼ 0:478: This value is consistent with the results of our measurements and the electronically determined width and therefore confirms our measurements and simulation model.
ARTICLE IN PRESS D. Niederlohner et al. / Nuclear Instruments and Methods in Physics Research A 509 (2003) 138–145 .
24000
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Fig. 9. Images with identical parameters except the mask: standard mask (left side) and absolute mask (right side). It is quite evident that the image quality is higher with the absolute mask.
1
modelling the threshold scan with an X-ray source, we were able to find the same magnitude for the threshold distribution width.
simulated values 0.945*x + 0.056
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References
0.5 0.4 0.3 0.2 0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
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width of threshold distribution [keV] Fig. 10. Dependency of RMSc on the width of the threshold distribution in the simulation. The points are fitted with a linear function.
5. Conclusions The mask generation with an X-ray source including the physical frontend has the potential to increase the image quality of the Medipix1 detector. This is especially important when the threshold cuts into the photon spectrum near a rapidly and intensely changing region, which can be necessary for energy sensitive imaging [7]. The remaining noise in the images seems not to be caused by the physical frontend. With a simulation
[1] M. Campbell, E.H.M. Heijne, G. Meddeler, E. Pernigotti, W. Snoeys, Readout for a 64 64 pixel matrix with 15-bit single photon counting, IEEE Trans. Nucl. Sci. 45 (3) (1998) 751. [2] G. Bardelloni, T. Boerkamp, D. Calvet, H. Verkooijen, J.L. Visschers, MUROS-1, Medipix-1 re-Usable Read Out System, NIKHEF, March 2002. [3] G. Bardelloni, E. Bertolucci, A.L.J. Boerkamp, D. Calvet, M. Conti, M. Maiorino, P. Russo, J.L. Visschers (Eds.), A new read-out system for an imaging pixel detector, IEEE Nuclear Science Symposium and Medical Imaging Conference, 2000. [4] B. Mikulec, Single photon detection with semiconductor pixel arrays for medical imaging applications, Ph.D. Thesis, University of Vienna, Austria, June 2000. [5] C. Schwarz, Digital X-ray imaging using hybrid semiconductor pixel detectors in single photon counting mode, Ph.D. Thesis, Albert-Ludwigs-Universit.at Freiburg i. Brsg, August 2001. [6] J. Giersch, Rosi: an object-oriented and parallel computing Monte Carlo simulation for X-ray imaging, Nucl. Instr. and Meth. A, (2003) these proceedings, September 2002. [7] C. Bert, Computed tomography using the Medipix1 chip, Nucl. Instr. and Meth. A, (2003) these proceedings, September 2002.