Figure 1.
Photon counting works by comparing the signal out of the sensor (in this case the charge on the preamplifier, black line) against a pre-set threhsold (dashed lines). A threshold (red dashed line) is set so as to be several standard deviations from the mean of the electronic noise so false counts from noise are extremely unlikely. In an x-CSI system, additional thresholds are employed (green, blue and purple dashed lines), so that the energy of the photon can be more accurately estimated. In this instance, the incoming photon can be seen to be at some energy between 18.5 and 27 keV (the blue and purple threhsolds respectively).
Figure 1.
Photon counting works by comparing the signal out of the sensor (in this case the charge on the preamplifier, black line) against a pre-set threhsold (dashed lines). A threshold (red dashed line) is set so as to be several standard deviations from the mean of the electronic noise so false counts from noise are extremely unlikely. In an x-CSI system, additional thresholds are employed (green, blue and purple dashed lines), so that the energy of the photon can be more accurately estimated. In this instance, the incoming photon can be seen to be at some energy between 18.5 and 27 keV (the blue and purple threhsolds respectively).
Figure 2.
Schematic of the various components of CoGI, showing their name, simulation tools employed, goals, and outputs.
Figure 2.
Schematic of the various components of CoGI, showing their name, simulation tools employed, goals, and outputs.
Figure 3.
Schematics for the various count triggering schemes simulated in this work. Common symbols: Yellow rectangle (preamplifier), green/red/black numbered triangles (comparator to provide a threshold), green/red/black numbered rectangles (counter associated with same numbered/coloured comparator), straight lines (connections). Unique symbols: in (B), blue “D” shapes represent logical AND gates and the blue circle represents a device to provide an input of finite duration to the AND gates (e.g., a capacitor). In (C), the blue diamond represents a delay circuit which provides an offset, dt, between being triggered and resetting the anode (yellow rectangle). In (E), the blue diamond represents a second stage integraing circuit which counts the number of thresholds recently triggered (using an adjustable baseline) and then triggers that number of counters from lowest to highest.
Figure 3.
Schematics for the various count triggering schemes simulated in this work. Common symbols: Yellow rectangle (preamplifier), green/red/black numbered triangles (comparator to provide a threshold), green/red/black numbered rectangles (counter associated with same numbered/coloured comparator), straight lines (connections). Unique symbols: in (B), blue “D” shapes represent logical AND gates and the blue circle represents a device to provide an input of finite duration to the AND gates (e.g., a capacitor). In (C), the blue diamond represents a delay circuit which provides an offset, dt, between being triggered and resetting the anode (yellow rectangle). In (E), the blue diamond represents a second stage integraing circuit which counts the number of thresholds recently triggered (using an adjustable baseline) and then triggers that number of counters from lowest to highest.
Figure 4.
Raw counts from threshold counters (red dashed line) and the energy spectrum that is calculated as a result of counter subtraction (black solid line), as described in text. Data obtained from a simulated system with 8 energy bins, 108 X-ray photons mm−2 s−1, 2 mm thick sensor, and 400 µm pixel pitch. 8 bins were chosen as this is the most used in a commercial x-CSI ASIC to date.
Figure 4.
Raw counts from threshold counters (red dashed line) and the energy spectrum that is calculated as a result of counter subtraction (black solid line), as described in text. Data obtained from a simulated system with 8 energy bins, 108 X-ray photons mm−2 s−1, 2 mm thick sensor, and 400 µm pixel pitch. 8 bins were chosen as this is the most used in a commercial x-CSI ASIC to date.
Figure 5.
Comparison of the calculated energy spectrum produced by an ideal counting scheme (REF, black line) and the currently used counting scheme (STD). Data obtained from a simulated system with 8 energy bins, 108 X-ray photons mm−2 s−1, 2 mm thick sensor, and 400 µm pixel pitch. Blue dashed line corresponds to zero counts and is added to allow negative counts to be more easily visualised.
Figure 5.
Comparison of the calculated energy spectrum produced by an ideal counting scheme (REF, black line) and the currently used counting scheme (STD). Data obtained from a simulated system with 8 energy bins, 108 X-ray photons mm−2 s−1, 2 mm thick sensor, and 400 µm pixel pitch. Blue dashed line corresponds to zero counts and is added to allow negative counts to be more easily visualised.
Figure 6.
Energy spectrum obtained from a system with a 1.5 mm sensor thickness, a 250 µm pixel pitch, and 130 energy bins. The X-ray flux simulated was 106 photons mm−2 s−1. All spectra are plotted; however, they perform almost identically at this low flux, leading only the last line plotted visible over the top of the others.
Figure 6.
Energy spectrum obtained from a system with a 1.5 mm sensor thickness, a 250 µm pixel pitch, and 130 energy bins. The X-ray flux simulated was 106 photons mm−2 s−1. All spectra are plotted; however, they perform almost identically at this low flux, leading only the last line plotted visible over the top of the others.
Figure 7.
Energy spectrum obtained from a system with a 1.5 mm sensor thickness, a 250 µm pixel pitch, and 130 energy bins. The X-ray flux simulated was 107 photons mm−2 s−1. All spectra are plotted; however, they perform equally well at most energies at this flux, with only slight differences visible at the lowest and highest energies (where FDR and DLR respectively are visibly different).
Figure 7.
Energy spectrum obtained from a system with a 1.5 mm sensor thickness, a 250 µm pixel pitch, and 130 energy bins. The X-ray flux simulated was 107 photons mm−2 s−1. All spectra are plotted; however, they perform equally well at most energies at this flux, with only slight differences visible at the lowest and highest energies (where FDR and DLR respectively are visibly different).
Figure 8.
Energy spectrum obtained from a system with a 1.5 mm sensor thickness, a 250 µm pixel pitch, and 130 energy bins. The X-ray flux simulated was 108 photons mm−2 s−1.
Figure 8.
Energy spectrum obtained from a system with a 1.5 mm sensor thickness, a 250 µm pixel pitch, and 130 energy bins. The X-ray flux simulated was 108 photons mm−2 s−1.
Figure 9.
Energy spectrum obtained from a system with a 1.5 mm sensor thickness, a 250 µm pixel pitch, and 130 energy bins. The X-ray flux simulated was 109 photons mm−2 s−1.
Figure 9.
Energy spectrum obtained from a system with a 1.5 mm sensor thickness, a 250 µm pixel pitch, and 130 energy bins. The X-ray flux simulated was 109 photons mm−2 s−1.
Figure 10.
Normalised energy spectrum obtained from a system with a 1.5 mm sensor thickness, a 250 µm pixel pitch, and 130 energy bins. The X-ray flux simulated was 108 photons mm−2 s−1.
Figure 10.
Normalised energy spectrum obtained from a system with a 1.5 mm sensor thickness, a 250 µm pixel pitch, and 130 energy bins. The X-ray flux simulated was 108 photons mm−2 s−1.
Figure 11.
Normalised energy spectrum obtained from a system with a 1.5 mm sensor thickness, a 250 µm pixel pitch, and 130 energy bins. The X-ray flux simulated was 109 photons mm−2 s−1.
Figure 11.
Normalised energy spectrum obtained from a system with a 1.5 mm sensor thickness, a 250 µm pixel pitch, and 130 energy bins. The X-ray flux simulated was 109 photons mm−2 s−1.
Figure 12.
Energy spectrum normalised after removing data from the last energy bin, obtained from a system with a 1.5 mm sensor thickness, a 250 µm pixel pitch, and 130 energy bins. The X-ray flux simulated was 109 photons mm−2 s−1.
Figure 12.
Energy spectrum normalised after removing data from the last energy bin, obtained from a system with a 1.5 mm sensor thickness, a 250 µm pixel pitch, and 130 energy bins. The X-ray flux simulated was 109 photons mm−2 s−1.
Figure 13.
Plot showing the spectral efficiency and counting performance of the various count-triggering schemes considered on a system with pixel pitch 250 µm, sensor thickness 1.5 mm, and 130 energy bins, at an X-ray flux of 106 photons mm−2 s−1. The y-axis has been zoomed in to allow schemes to be more clearly differentiated as comprising 3 groups: top group (REF, DLR and SR), middle group (STD, FDR(Inst) and PCS), and bottom group (FDR(DT)).
Figure 13.
Plot showing the spectral efficiency and counting performance of the various count-triggering schemes considered on a system with pixel pitch 250 µm, sensor thickness 1.5 mm, and 130 energy bins, at an X-ray flux of 106 photons mm−2 s−1. The y-axis has been zoomed in to allow schemes to be more clearly differentiated as comprising 3 groups: top group (REF, DLR and SR), middle group (STD, FDR(Inst) and PCS), and bottom group (FDR(DT)).
Figure 14.
Plot showing the spectral efficiency and counting performance of the various count-triggering schemes considered on a system with pixel pitch 250 µm, sensor thickness 1.5 mm, and 130 energy bins, at an X-ray flux of 107 photons mm−2 s−1. The y-axis has been zoomed in to allow schemes to be more clearly differentiated as comprising 3 groups: top group (REF, DLR and SR), middle group (STD, FDR(Inst) and PCS), and bottom group (FDR(DT)).
Figure 14.
Plot showing the spectral efficiency and counting performance of the various count-triggering schemes considered on a system with pixel pitch 250 µm, sensor thickness 1.5 mm, and 130 energy bins, at an X-ray flux of 107 photons mm−2 s−1. The y-axis has been zoomed in to allow schemes to be more clearly differentiated as comprising 3 groups: top group (REF, DLR and SR), middle group (STD, FDR(Inst) and PCS), and bottom group (FDR(DT)).
Figure 15.
Plot showing the spectral efficiency and counting performance of the various count-triggering schemes considered on a system with pixel pitch 250 µm, sensor thickness 1.5 mm, and 130 energy bins, at an X-ray flux of 108 photons mm−2 s−1.
Figure 15.
Plot showing the spectral efficiency and counting performance of the various count-triggering schemes considered on a system with pixel pitch 250 µm, sensor thickness 1.5 mm, and 130 energy bins, at an X-ray flux of 108 photons mm−2 s−1.
Figure 16.
Plot showing the spectral efficiency and counting performance of the various count-triggering schemes considered on a system with pixel pitch 250 µm, sensor thickness 1.5 mm, and 130 energy bins, at an X-ray flux of 109 photons mm−2 s−1.
Figure 16.
Plot showing the spectral efficiency and counting performance of the various count-triggering schemes considered on a system with pixel pitch 250 µm, sensor thickness 1.5 mm, and 130 energy bins, at an X-ray flux of 109 photons mm−2 s−1.
Figure 17.
Plot of count scheme performance as a function of pixel pitch. Other system parameters were: sensor thickness 1.5 mm, 130 energy bins, and an X-ray flux of 108 photons mm−2 s−1.
Figure 17.
Plot of count scheme performance as a function of pixel pitch. Other system parameters were: sensor thickness 1.5 mm, 130 energy bins, and an X-ray flux of 108 photons mm−2 s−1.
Figure 18.
Plot of count scheme performance as a function of sensor thickness. Other system parameters were: pixel pitch 250 µm, 130 energy bins, and an X-ray flux of 108 photons mm−2 s−1.
Figure 18.
Plot of count scheme performance as a function of sensor thickness. Other system parameters were: pixel pitch 250 µm, 130 energy bins, and an X-ray flux of 108 photons mm−2 s−1.
Figure 19.
Plot of count scheme performance as a function of X-ray flux. Other system parameters were: sensor thickness 1.5 mm, pixel pitch of 250 µm, and 130 energy bins.
Figure 19.
Plot of count scheme performance as a function of X-ray flux. Other system parameters were: sensor thickness 1.5 mm, pixel pitch of 250 µm, and 130 energy bins.
Figure 20.
Plot of count scheme performance as a function of number of energy bins. Other system parameters were: sensor thickness 1.5 mm, 250 µm pixel pitch, and X-ray flux 108 photons mm−2 s−1.
Figure 20.
Plot of count scheme performance as a function of number of energy bins. Other system parameters were: sensor thickness 1.5 mm, 250 µm pixel pitch, and X-ray flux 108 photons mm−2 s−1.
Figure 21.
Plot showing how pulse pileup can cause negative counts to register in a system. The first photon (lower peak starting around 400 ns) causes the lowest 3 counters (red, green, and blue thresholds) to increment. The second photon (higher peak starting around 420 ns) arrives after the charge falls below the blue threshold, but is still above the red and green thresholds. As a result, the second event triggers the 3rd and 4th counters (blue and purple thresholds) but not the lower 2 (red and green). How this leads to a negative count is further explained in
Table 6.
Figure 21.
Plot showing how pulse pileup can cause negative counts to register in a system. The first photon (lower peak starting around 400 ns) causes the lowest 3 counters (red, green, and blue thresholds) to increment. The second photon (higher peak starting around 420 ns) arrives after the charge falls below the blue threshold, but is still above the red and green thresholds. As a result, the second event triggers the 3rd and 4th counters (blue and purple thresholds) but not the lower 2 (red and green). How this leads to a negative count is further explained in
Table 6.
Figure 22.
Data used to produce
Figure 8 (sensor thickness 1.5 mm, pixel pitch 250 µm, and X-ray flux 10
8 photons mm
−2 s
−1) processed with 8 energy thresholds instead of 130. Note that the negative counts seen when 130 thresholds are used now appear simply as lower counts in the lowest of 8 energy bins. The REF data set lies almost exactly behind the SR data set.
Figure 22.
Data used to produce
Figure 8 (sensor thickness 1.5 mm, pixel pitch 250 µm, and X-ray flux 10
8 photons mm
−2 s
−1) processed with 8 energy thresholds instead of 130. Note that the negative counts seen when 130 thresholds are used now appear simply as lower counts in the lowest of 8 energy bins. The REF data set lies almost exactly behind the SR data set.
Figure 23.
Plot of count scheme performance as a function of number of energy bins. Parameters were the same as for
Figure 20, with the exception of the reset delay in FDR schemes (10 ns here vs. 100 ns in
Figure 20) and the integration time of the digital adder in the SR scheme (10 ns here, 1 ns in
Figure 20).
Figure 23.
Plot of count scheme performance as a function of number of energy bins. Parameters were the same as for
Figure 20, with the exception of the reset delay in FDR schemes (10 ns here vs. 100 ns in
Figure 20) and the integration time of the digital adder in the SR scheme (10 ns here, 1 ns in
Figure 20).
Table 1.
List of parameters used in the Monte Carlo simulations in Component 1.
Table 1.
List of parameters used in the Monte Carlo simulations in Component 1.
Parameter | Value | Unit |
---|
X-ray source type | Monoenergetic | - |
X-ray energy | 80 | keV |
Irradiation type | Flatfield | - |
Sensor material | CdTe | - |
Sensor density | 5850 | kg m−3 |
Sensor cross-sectional area | 21 × 21 | mm2 |
Sensor thickness | 1 to 3 (steps of 0.5) | mm |
Table 2.
List of material properties used in the Finite Element Method simulations in Component 2.
Table 2.
List of material properties used in the Finite Element Method simulations in Component 2.
Parameter | Symbol | Value | Unit |
---|
Mobility, electrons | µe | 1100 | cm2 V−1 s−1 |
Mobility, holes | µh | 100 | cm2 V−1 s−1 |
Lifetime, electrons | τe | 3.0 | µs |
Lifetime, holes | τh | 2.0 | µs |
Density | Ρ | 5850 | kg m−3 |
Diffusion coefficient, electrons | De | 2.84 × 10−3 | m2 s−1 |
Diffusion coefficient, holes | Dh | 2.58 × 10−4 | m2 s−1 |
Relative permittivity | ε | 11.0 | - |
Pixel pitch | SP | 100 to 600 (in steps of 50) | µm |
Sensor thickness | ST | 1 to 3 (steps of 0.5) | mm |
Table 3.
Summary of the timing parameters used in modelling the count-triggering schemes.
Table 3.
Summary of the timing parameters used in modelling the count-triggering schemes.
Parameter | Value |
---|
Signal decay model | Exponential |
Decay time (to 1%) | 100 ns |
AND gate open time (PCS only) | 10 ns |
Reset delay (FDR(Inst) and FDR(DT)) | 100 ns |
Reset deadtime (FDR(DT) only) | 10 ns |
Table 4.
Summary of the count triggering schemes modeled.
Table 4.
Summary of the count triggering schemes modeled.
Acronym | Full Name | Quick Description |
---|
STD | Standard approach | Each threshold is linked directly to its corresponding counter. |
PCS | Premature Count Suppression | Higher counters can only be incremented if the lowest counter was recently incremented. |
FDR | Forced Delay Reset | A fixed time after the lowest threshold is crossed, the charge on the anode is reset to zero. |
DLR | Descending Line Responder | When a counter is incremented, any untriggered counters below it are also incremented. |
SR | Shift Register | The number of thresholds recently crossed is counted and then distributed across counters, starting from the lowest to the highest. |
Table 5.
List of the bins which constitute Np in Equation (3).
Table 5.
List of the bins which constitute Np in Equation (3).
Number of Energy Bins Simulated | Bin Numbers Containing Photopeak |
---|
3 | 2 |
5 | 3 |
8 | 5 |
24 | 13–15 |
130 | 70–81 |
Table 6.
Conversion from number of times a threshold is crossed to the counts recorded in that energy bin shows how negative counts can originate from the data shown in
Figure 21.
Table 6.
Conversion from number of times a threshold is crossed to the counts recorded in that energy bin shows how negative counts can originate from the data shown in
Figure 21.
Threshold–Counter Pair | Counts | Energy Bin | Calculated Counts |
---|
1 (1.5 keV) | 1 | 1.5–10 keV | 0 |
2 (10 keV) | 1 | 10–18.5 keV | −1 |
3 (18.5 keV) | 2 | 18.5–27 keV | 1 |
4 (27 keV) | 1 | >27 keV | 1 |