All the characterizations presented here were carried out at the surface diffraction station of the material science beamline X04SA of the SLS (Patterson et al.
), since better results are obtainable using monochromatic X-rays than using the internal calibration signal (CAL, cf.
Fig. 2) of the readout chip. Either the direct synchrotron beam in combination with absorbing filters or an elastic scatterer for homogeneous detector illumination was used.
3.1. Threshold scan
Many detector characteristics can be derived from threshold scans. For that purpose the module is homogeneously illuminated with monochromatic X-rays. Images of equal exposure time are taken while the global threshold (E
th) is increased with respect to energy for each frame.
The s-curve method (Dinapoli, 2004
) is used to analyze the threshold scans. In our case the s-curve is extended by a linear factor to take into account the charge-sharing2
contribution. This representation of the s-curve is empirically based on observations and describes the data well. A previous energy calibration of the V
bias controlling the global threshold of the module in order to convert the abscissa from voltage to energy is required,
The s-curve (1)
has a well defined inflection point a
which is the threshold of the pixel for the incident X-ray energy (E
) that was used. The parameter a
is related to the electronic noise, charge sharing and energy spectrum3
of the incident X-rays. The magnitude of a
is determined by the flux of the source and the exposure time. The slope a
in the linear term models the charge sharing of the sensor.
Threshold scans of an individual PILATUS pixel for five different beam energies as a function of the global threshold are shown in Fig. 3. For the purpose of comparison, the data of each scan in Fig. 3 are normalized to the number of counts recorded with the global threshold set at 50% of E
Threshold scans of a pixel with low-gain CSA settings for different incident X-ray energies.
3.2. Charge sharing
Incident photons are converted into charge clouds inside the sensor, which are transported by the applied electrical field to the collection electrodes. Owing to diffusion and Coulomb repulsion, the diameter of the charge cloud increases while it drifts towards the collection electrode. In the case of conversion close to or at the border between pixels, the signal will therefore be shared among adjacent pixels (Ponchut et al.
; Bergamaschi et al.
Charge sharing in the predecessor of the current PILATUS detector system was characterized using an infrared laser to determine the effective charge collection area (Broennimann et al.
). Alternatively, the influence of charge sharing on the count rate can be directly derived from threshold scans (Tlustos et al.
). However, the method of measuring the charge sharing by means of threshold scans with monochromatic X-rays is advantageous over the laser method with respect to real operation conditions, because the infrared photons convert into charge at the surface of the sensor, whereas X-rays convert throughout the bulk of the silicon.
The parameter a
represents the slope of the linear decrease in count rate of the threshold scans occurring for global threshold settings below the incident photon energy. This slope is due to charge sharing among adjacent pixels. Since (1)
describes a threshold scan in absolute counts, a
is normalized becoming independent of exposure time and photon flux, thus thereby being comparable. For the normalization, the count N
is used, which is registered with the global threshold set to 50% of E
. At this particular threshold setting, the count rate is independent of charge sharing and represents the number of correctly counted photons. Thus the normalized charge sharing slope is k
Since charge sharing occurs at the borders of the sensor pixel, its effect depends on the ratio between the perimeter and pixel area. In a simple model, the normalized charge-sharing slope is associated with a corresponding fraction of area of the sensor pixel in which the charge of converting photons is shared, e.g. for k = 4.5% keV−1 at E
in = 12 keV the corresponding area is k
in/2 = 27.2% of the pixel. Regarding this area to be a strip along the pixel border, we can calculate its width. Using the example above, the strip width is 12.6 µm for a normal PILATUS pixel. Assuming the width to be the same for any pixel size, k can be calculated for different pixel sizes from the known k of a particular pixel size.
The normalized charge-sharing slopes of the PILATUS were determined from threshold scans taken with 8, 10, 12, 14 and 16 keV X-rays. The above-mentioned geometrical considerations were applied to calculate the k
value for the large sensor pixels spanning the gaps between the readout chips4
Fig. 4) and compared with the measurements. The averaged k
value for normal-sized pixels and the averaged k
value for the larger pixels with the calculated k
value according to the above model are shown in Fig. 5.
Light microscope image of the sensor flip side with normal pixels (square) and large pixels (rectangular) spanning the gaps between readout chips.
Average normalized charge-sharing slope (k) at different X-ray energies for normal-sized and large pixels including the calculated k for large pixels.
3.3. Energy resolution
A threshold scan curve of a pixel corresponds to the integrated energy spectrum of the X-ray source above the threshold. The electronic noise of the sensor, and the analog and digital front-end, further broaden the spectrum. Hence, the derivative of a threshold scan performed with monochromatic X-rays yields a spectral peak in which the apparent width is a measure of the energy resolution of the pixel. In addition to the resolution of a single pixel, the pixel-to-pixel threshold dispersion has to be included for the overall energy resolution (OER) of the detector system. Since noise in the threshold scan data is enhanced by numeric differentiation, several thousand incident photons per pixel are required to obtain a reliable peak. To achieve better statistics, the threshold scans of a module were averaged before differentiation, i.e. the average count of all pixels was calculated for each threshold value. Thereby, the threshold dispersion is also taken into account.
The derivative of an averaged threshold scan of a trimmed5
module for 12 keV X-rays is shown in Fig. 6. The constant tail towards low threshold energies stems from charge-sharing effects which only marginally affect the peak shoulder towards high energies. A Gaussian is fitted to the data in the region of the right shoulder including the peak. The OER of the system is given by the full width at half-maximum [FWHM = 2(2ln2)1/2
σ] of the peak, where σ2
is the variance of the fitted Gaussian.
Derivative of an averaged threshold scan for 12 keV X-rays fitted with a Gaussian.
The PILATUS module was trimmed for three different CSA gain settings and for each setting a threshold scan was taken using 8 keV X-rays. The OERs obtained by the described method from the scans are listed in Table 2. The module was also trimmed at 8, 10, 12, 14 and 16 keV for low-gain CSA settings, and a threshold scan was recorded for each energy to study the energy dependence of the OER. The resulting OER as a function of incident X-ray energy is shown in Fig. 7.
Overall energy resolution of a trimmed PILATUS module for 8 keV X-rays and three different CSA gain settings
Overall energy resolution of a trimmed PILATUS module for different X-ray energies using low-gain CSA settings. Inset: relative overall energy resolution.
Since electronic noise scales with the reciprocal of the CSA gain, and the achieved threshold dispersion after trimming is smaller for high-gain CSA settings (Kraft et al.
), the OER improves with an increase in gain.
The counting behaviour of the PILATUS detector for high-intensity synchrotron beams was investigated at the surface diffraction station of the material science beamline X04SA of the SLS. The beamline features 15 filter sheets of Al, Ti and Mo of different thicknesses to control the attenuation of the beam. To avoid beam hardening owing to absorbers, the monochromator was set to 16 keV, because the higher harmonics (≥32 keV) are greatly suppressed by the lower wiggler flux at high energy, the low mirror reflectivity and the low Si scattering factors (Patterson et al.
). The remaining radiation from higher harmonics is further suppressed, since the efficiency of the Si sensor is less than 10% above 30 keV. Therefore the use of filter sheets to create different beam intensities is justified. The transmissions of the sheets were previously calibrated using the PILATUS detector at low intensity (<100000 counts pixel−1
). In doing so, the direct synchrotron beam was defocused on the module such that the spot size was several millimetres in diameter. The same set-up was used to investigate the counting behaviour of the detector. For each filter transmission which was increased in small steps, a frame was recorded. The exposure time was set to 20 ms, preventing the counter overflow at very high intensities. Data were recorded with medium- and low-gain CSA settings at E
= 6, 8 and 10.7 keV.
The time structure of the SLS during the experiment was a flat-filled electron beam of t
= 780 ns with 390 electron bunches of approximately 50 ps length every 2 ns, followed by a gap of 180 ns containing a single bunch. Regarding the X-ray delivery as being Poisson distributed during t
from the detector point of view and considering the given time structure of the beam, a Monte Carlo (MC) model can be employed to simulate the response of the detector to the incident rate (Bateman, 2000
MC data were generated for 100 different dead-times between 50 and 250 ns. The MC data for each dead-time were parameterized and the parameterizations compared with the experimental data of a pixel (cf.
Fig. 8). By means of minimum χ2
between parameterization and experimental data, the corresponding dead-time (τ) was determined. The average τ, obtained in this way, with respect to the relative global threshold setting (E
), are presented in Fig. 9. The shorter τ for low-gain CSA settings originates from leaner pulses entering the comparator, hence the time to resolve two successive pulses is less than for medium-gain CSA settings. Common for both CSA settings is a monotone drop in τ for increasing E
. Experimental data taken at E
= 83% show a significant deviation from the Monte Carlo model at incident rates above 1 × 106
, meaning that pile-up effects become dominant and thus the experimental data are insufficiently described by the utilized model (Laundy & Collins, 2003
Detected count rate of a pixel as a function of the incident rate for 16 keV X-rays using 50% relative global threshold and medium-gain CSA settings. The Monte Carlo model prediction agrees well with the data.
Figure 9 Average dead-times (τ) for 12 and 16 keV X-rays with respect to the relative global threshold settings for medium gain (a) and low gain (b) CSA settings. The black error bars represent the statistical errors on the average τ, the (more ...)
In case of a flat-filled synchrotron beam without gap or an X-ray tube, the photon delivery in time can be considered as uniform, and the loss in counting efficiency at high rates can be calculated using the analytic model (Bateman, 2000
depicts the detected rate and N
the true incident photon rate. Therefore an offline rate correction in software can be applied. In order to minimize computing time for large series of exposures with constant exposure time (t
), the rate correction is accomplished by means of a look-up table. A look-up table mapping recorded counts (N
) to the corresponding incident counts (N
) using (2)
is created for a specific dead-time and a specific exposure time, when either of them is changed. After an image is transferred to the data acquisition computer, the counts of each pixel are replaced according to the look-up table. The incident rate per pixel should stay at least below the detectable maximum rate given by N
= 1/τ, since a higher rate becomes ambiguous in terms of the detected rate and would lead to misinterpretation. The exposure time has to be adapted to the detected rate in order to avoid overflow of the counter because the counter starts to count again from zero after its range is exceeded. Also noteworthy is the loss of statistics owing to the reduced counting efficiency at high rates, meaning that the relative statistical counting error of a pixel is given by the number of detected photons, which is larger than the same error of the number of incident photons. This leads to a decrease of the signal-to-noise ratio in the data for an increase in rate. This simple rate correction will fail if the incident rate changes during an exposure, since the correction method assumes a constant rate per pixel. In the case of the above-mentioned time structure of the SLS, the error between (2)
and the Monte Carlo model is approximately 2% for an input rate of 420000 photons s−1
(630000 photons s−1
) at 50% relative global threshold for low (medium) gain CSA settings.