“I ramp – pixel delay” grid
6. Experimental calibration studies
6.1 Application of the proposed fit function data measured with 10 x 64 pixels of a DSSC prototype
6. Experimental calibration studies was chosen, specified by the following properties (see sec. 3.1.3 and 3.1.4 were the DSSC read-out system is presented in detail):
• A strip of 10x64 pixels in the middle of the detector was operated. All other pixels readout chains were powered down.
• 2000 bursts of 800 frames each have been recorded. The signal flat top had a length of about 580 ns.
• The analog signal front-end of the read-out ASIC has been set to a medium feedback capacitor setting. A long signal integration time of about 90 ns has been selected.
• A pixel delay has not been set. The mean ADC gain was set relatively low, to a gain of about 0.5 LSB/keV (Iramp setting 16, double ramp current).
• The ADC binning has been determined before the measurement with the help of a DAC-sweep.
• The ADC gain setting and the current compensation setting have been trimmed before the measurement in order to provide as much homogeneity between the individual pixels as possible.
Fig. 6.1 shows an overview of the measurement, together with a photo of the source holder and a sketch illustrating the spatial arrangement. The most relevant result from the data analysis is given in panel (c) and (d): By applying the measured binning information and with help of the global fit-function, the asymmetric distribution of photon signal on the detector surface could be assessed. The asymmetry is expected due to the slightly off-center position of the radioactive source.
The detector was irradiated with a109Cd source with an activity of about 1.6±0.2 GBq in reference to the data sheet ([64], [65]) at a distancerof about 1.3 cm from the detector, assuming a fluorescence yield of about 85%. Each detector pixel has a surfaceApxof about 4.80·10−4cm2. The expected incident photon rateRpx in each pixel per second can be calculated with
Rpx=0.85·1.6·109γ s· 1
4π·Apx
r2 ∼3.0·104γ/px/s (6.1) withr being the distance between radioactive source and detector. The total measurement time Tmeas can be calculated by multiplying the flat-top time with the number of frames and the number of bursts. With this calculation, the numberNγ of detected X-ray photons in each pixel for the complete measurement can be estimated to be
Nγ =qe·Rpx·Tmeas =0.3·3.0·104γ/px/s·2000·800·580·10−9s=8.4·103γ/px (6.2) with a detection efficiencyqeof about 30% for the given energy levels.
Fig. 6.2 shows a fit to the spectrum of the most upper right of the 640 individual pixels that have been analyzed. As a simplification, the fit has been performed with a fit-function with only
50 60 70 80 90 100 110 LSB120
counts per LSB
1 10 102
103
104
105
106
ASIC 0 Px 4068 Fst 0
Entries 1378969
Mean 54.25 ±0.000669
Std Dev 0.7856 ±0.000473
Underflow 0
Overflow 0
/ ndf
χ2 702.4 / 16
Prob 0
noise_norm 1.591e+06 ±1.266e+03 noise_mean 54.19 ±0.00 noise_sigma 0.3211 ±0.0007 peak1_norm 993.9 ±14.9
gain 13.14 ±0.04
Px 4068
Entries 1378969
Mean 54.25 ±0.000669
Std Dev 0.7856 ±0.000473
Underflow 0
Overflow 0
/ ndf
χ2 702.4 / 16
Prob 0
noise_norm 1.591e+06 ±1.266e+03 noise_mean 54.19 ±0.00 noise_sigma 0.3211 ±0.0007 peak1_norm 993.9 ±14.9
gain 13.14 ±0.04
Figure 6.2: Example of one of the 640 individual fits performed for this measurement. The start values are given in green, the fit function is given in red. The black dashed lines mark the fit range, the red dashed line marks the middle of the fit range.
two discrete calibration lines as proposed in sec. 5.3.4 for55Fe spectra. In this case, (rounded) line energies of 22 keV and 25 keV for the combinedKαand Kβ lines have been applied with a fixed line_ratioSlof 0.14. The shape of the fit function was determined with shaping and scaling parameters (table 6.1) that have been determined on the basis of an older55Fe measurement performed with the SPIX setup (sec. 3.4.1). The scaling parameters are:
Name Symbol value
peakt_amp Nt 1.4
noise_tails Stnoise 0.8
peakp_amp Ns 3.7
line_ratio Sl 0.14
Table 6.1: Scaling parameters of the fit-function used for fitting the 109Cd measurement. In accordance to the applied global fit function (sec. 5.3.2), these parameters are without unit. They are the scaling factors and describe the quantity of photons in the respective spectral features in reference to the number of photons in theKα peakN1=peak1_norm.
The highest photon count in fig. 6.1 panel (c) and (d) is around 1200 for the parameterN1 or
“peak1_norm” (table 5.2 in sec. 5.3.4). The number of X-ray eventsNγ,spec in each individual spectrum can be calculated by referring to equations 5.15 to 5.21 and eq. 5.26 by:
Nγ,spec= (N1·(1+Nt+StnoiseNt+Ns))) (1+Sl)∼1·104γ (6.3) This result is in good agreement with the expected photon count (eq. 6.2), considering the large error margin on the activity of the109Cd source and the measurement of the distance to the detector. It has to be noted though that this study was intended to be a proof of concept, both
6. Experimental calibration studies for the setting into service of a copy of the prototype detector setup (sec. 3.4.2) and irradiation of the detector with 109Cd, as well as the application of the global fit function could be tested on the measured dataset. In this case it was used to determine system offset, noise and gain “in one go” as described in sec. 5.3.9.
Fig. 6.3 shows additional results from the analysis of the spectra with the global fit function.
The following effects ([66]) can be identified in the dataset:
• The offset (panels a and b) shows a mostly homogeneous distribution over the active part of the detector. The mean is approximately 56 LSB. Down the center, a column of pixels is showing a slightly higher offset. For this chip generation, such an effect can be caused by an error in the setting of the ADC start value.
• The gain (panels c and d) can be assessed both in units of LSB, i.e. the distance between the noise peak and theKαline, and in units of LSB/keV. It shows a sligth decline starting from lower pixel rows towards upper rows. This is expected due to the inevitable supply voltage drop across the detector matrix. The voltage supply lines start at the lower rows of the detector, providing these rows with a slightly higher operation voltage. The gain of the input transistor of the analog signal front-end is correlated directly to this voltage: The higher it is, the higher the pixel gain.
• The system noise (panels e and f) is given in electrons ENC. This calculation includes both the fit providing the width of the noise peak in units of LSB and the pixel gain in units of LSB/keV. Usinge/h=3.63 eV (sec.3.1.1) the energy equivalent of the noise peak can be converted to this measure. The noise increases slightly for higher pixel rows. As the electronic system noise is dominated by the input transistor, this behavior can also be explained by the supply voltage drop: The lower the supply voltage for the analog front-end of the read-out ASIC, the higher the electronic noise.
This example shows that the offset, gain and noise value of the DSSC detector can in principle be determined by applying the global fit function. For this study only one specific ASIC setting was measured. A calibration as proposed in sec. 3.3.2 based on the comparison of multiple gain and offset settings was not performed, as a method to experimentally cross-check the resulting calibrated setting was not available for the setup configuration employed in this measurement. The following chapter will provide the result of such a cross-check, performed with the configuration the system proved to operate most stable in.
LSB
0 10 20 30 40 50 60
x [mm]
0 2 4 6 8 10 12 14
y [mm]
0 2 4 6 8 10 12
(a)
52 54 56 58 60 LSB62
nr of #hist
0 2 4 6 8 10 12 14 16
(b)
LSB
0 2 4 6 8 10 12 14
x [mm]
0 2 4 6 8 10 12 14
y [mm]
0 2 4 6 8 10 12
LSB/keV
0 0.1 0.2 0.3 0.4 0.5 0.6
(c)
LSB/keV
0.46 0.48 0.5 0.52 0.54 0.56 0.58 0.6
nr of #hist
0 2 4 6 8 10 12 14 16 18 20 22
(d)
ENC
0 20 40 60 80 100 120 140 160 180 200 220
x [mm]
0 2 4 6 8 10 12 14
y [mm]
0 2 4 6 8 10 12
(e)
160 165 170 175 180 185 190 195 200ENC
nr of #hist
0 2 4 6 8 10 12 14 16 18
(f)
Figure 6.3: Results obtained with the global fit-function, plotted pixel-wise in a 2d map (left column) and as histograms (right column):
(a), (b): offset
(c), (d): determined gain in LSB and LSB/keV (e), (f): system noise in ENC
6. Experimental calibration studies