6.1. Anode energy resolution
Hole trapping is significant within CZT detectors since the hole mobility in CZT is about 20 times lower than electron mobility (Erickson et al 2000
). Slowly-moving and trapped holes induce a signal component on anodes that is opposite in polarity to electrons, resulting in anode signal deficit. The effects of trapped holes beyond the immediate vicinity of anodes can be mitigated by the small-pixel effect.
The small-pixel effect is brought about by the small width of the anode, which causes the region of high sensitivity to space charge to be restricted to the immediate vicinity of the anode as reflected by the sharp lobe shown in (Ramos 1939
, Barrett et al 1995
, Luke 1996
, Eskin et al 1999
, Kalemci et al 1999
). The effectiveness of the small-pixel effect is evident through the locus of 511 keV event cluster in the scatter plot of , which is essentially horizontal and forms a band of approximately uniform variance. The slight downward curvature of the photopeak band at large cathode signal values is attributable to signal deficit due to trapping of drifting electrons for photon interactions far from the anode plane.
The photopeak tailing seen in is attributable to the downward curvature and the increase in variance of the event distribution in the photopeak at small cathode signal values (events highlighted by the circle in ). These events correspond to interactions very close to the anode plane, where after the electrons of a photon interaction have drifted away the holes can remain in the vicinity of the anode strips longer than the pulse peaking time. The prolonged presence of holes near anode strips creates a reverse-polarity induction on the anodes, since the small-pixel is no longer effective in this range.
The variation of FWHM energy resolution at 511 keV across the detector’s 5 mm DOEP thickness (z axis in ) was investigated with the aid of the C/A ratio-to-DOEP position mapping of (see section 6.3 for related discussion). The result is shown in . The spectra from which the data points in were derived can be visualised as slice cross-sections of taken along straight lines through the origin whose slope is the inverse of C/A ratio of interest. For example shows the spectrum corresponding to the slice along the diagonal line in (C/A ratio = 0.76), for which the FWHM energy resolution at 511 keV is 3.06±0.39%.
shows that the small-pixel effect helps to maintain an approximately uniform energy resolution across most of the detector’s 5 mm thickness, but the energy resolution for a single anode in fact spans a range from 3.05% at 4.02 mm from the anode plane to 8.60% at 0.76 mm from the anode plane. Along with , this illustrates that both the photopeak’s position (signal deficit) as well as its width (energy resolution at a particular DOEP position) vary with the DOEP position, and it is only in the aggregate (over all DOEP positions) that the detector exhibits the 4.09% energy resolution of .
Seeing that the photopeak position and width both vary systematically as a function of interaction depth (DOEP), which can be estimated with better than 1 mm precision (refer to section 6.3 for discussion on DOEP resolution), both effects may be addressed using the C/A ratio. In particular equation (1)
was used to correct for the shift in photopeak position due to signal deficit induced by holes near the anode plane, shows the energy spectrum of (4.09±0.19% energy resolution) after the correction (3.90±0.19% energy resolution).
Similarly, depth gating based on the DOEP position will be used to address the depth-dependent photopeak width, so that the appropriate energy gating settings can be chosen for each photon interaction based on the energy resolution at the interaction’s DOEP position.
The single-anode event specrtum and energy resolution shown in and differ from those of and in that whereas the latter are based on one specific anode, the former are based on single-anode events that could have triggered any one of the detector’s anodes read out. shows that the range of energy resolution for single and multiple-anode events are 2.65%–11.85% and 3.25%–13.31%, respectively. This slight degradation of resolution seen in and for multiple-anode events is unsurprising since the signal variance due to independent noise contribution from each individual RENA-3 channel adds in quadrature. Another factor degrading the energy resolution in this case is the signal deficit due to low hole mobility, which is magnified for charge-shared interactions near the anode plane. In this case the reverse-polarity induction on each anode comes from the full population of holes generated by an interaction that remains in the vicinity of the anode plane past the pulse peaking time, but the electron signal component comes from only the fraction of electrons collected by that anode. This asymmetry in signal contribution increases the amount of signal deficit, and in turn the photopeak tailing towards low energies in the spectrum containing multiple-anode events.
As for anode energy resolution as a function of photon interaction position transverse to the anode strips within one anode pitch, demonstrates that there is no drastic change in FWHM energy resolution at 511 keV as the electronically collimated slit beam is scanned across the detector’s edge-face. The relatively constant FWHM energy resolution (~5% on average) confirms that in spite of the spatial pixel decomposition of the CZT detector volume by anodes and steering electrodes, the device can continue to operate as a continuous detector with uniform energy resolution performance throughout.
It is expected that these energy resolution results can be improved since they were based on measurements made with a prototype system that was not optimised for low electronic noise. Nevertheless, current results suffice in demonstrating that CZT is capable of providing excellent energy resolution for PET.
6.2. Efficacy of steering electrodes
The lines of reflect relative photon sensitivity across one anode pitch as explained in section 5.2. Using a sum-energy window of 662 keV±14%, shows that the photon sensitivity increases across the entire anode pitch with increasing steering bias. This verifies that when biased at a more negative potential compared to the anode strips the steering electrodes are more effective at repelling electrons towards the anodes. The photon sensitivity profile across the anode pitch also appears approximately uniform beyond about −100 V of steering bias, at which point the number of photon interactions with near-complete charge collection becomes an approximately constant function of the interaction position.
When a narrower sum-energy window of 662 keV±4% was used (), the sensitivity profile displays clear peaks and a valley, which is centred on the steering electrode and remains visible even at high steering bias values. This indicates that more photon interactions fall outside of the nominal photopeak energy range when they occur near the centre of a steering electrode. This is likely due to the occurrence of small amounts of charge loss to non-metalized areas on the detector face between the narrow anode strips and the steering electrode, resulting in a charge falling just outside the photopeak i.e. not falling in the 662 keV±4% window, but falling in the 662 keV±14% window. Nevertheless, the photon sensitivity increases with increasing steering bias in , but only up to approximately −100 V, after that there is no increase and the valley remains.
These results verify the efficacy of steering electrode in enhancing the detector sensitivity by mitigating charge loss, but they also reveal sub-pitch-scale variations in the detector’s capability for complete charge collection. The sub-pitch variations (the sensitivity dips over steering electrodes) will be corrected during the detector efficiency normalization procedure of image reconstruction.
6.3. Spatial resolution along the direction orthogonal to the electrode planes (DOEP)
Two important observations can be made from and . Firstly, it is clear that the variation in the mean of the C/A ratio is almost linear with position of photon interaction along the DOEP. It should be noted that this does not hold for semiconductor detectors in general e.g. Si or Ge, instead it is a fortuitous result of a number of factors. Firstly, as mentioned above CZT has very different mean drift length values for electrons and holes so that hole trapping is significant within the detector. Secondly, in spite of hole trapping, the small-pixel effect causes the anode signal to be essentially proportional to the photon interaction energy. Finally, due to their larger widths the cathodes do not exhibit the small-pixel effect i.e. the weighting potential lobe rolls off slowly in , so that trapped holes cause the cathode signal to be proportional to the product of photon interaction energy and the DOEP position. The net effect of these factors is that the C/A ratio is approximately linearly proportional to the DOEP position.
This linearity suggests a simple model for inferring the position of a photon interaction along the DOEP based on an interaction’s C/A ratio. shows how this inverse relationship of true DOEP position as function of C/A ratio can be captured using a simple quadratic polynomial. The polynomial was optimally fitted in the least squared error sense with an R2 error value of 0.9997, and enables estimation of an event’s true DOEP position if its C/A ratio is known e.g. used in converting the energy resolution as a function of C/A ratio to a function of the true DOEP position (section 6.1).
Secondly, we see from the fitted Gaussian curves that the spread of the C/A ratio in each position is sufficiently tight to allow positions 1 mm apart to be resolved. In fact, across the 5 Gaussian curves fitted to C/A ratio distributions for pencil-beam-collimated photon interactions positioned 1 mm apart along the DOEP (), the FWHM of the fitted curves is 0.44±0.07 mm. This tells us that we can readily achieve 1 mm resolution along the DOEP, so the desired voxel size of 1 mm × 1 mm × 5 mm for the high-resolution small animal PET system can be realised.
A subset of ’s data points that are spaced 0.5 mm apart are plotted in . Judging by the R2 error values of , the fitted parameters account reasonably well for the data points’ Gaussian distribution. Note that the left-most three fitted Gaussian lobes in intersect below the half-maximum level, while the right-most two lobes intersect above or approximately at the half-maximum level. The inconclusiveness of this result is attributable to the poorer statistics of data points of than those of , but it is consistent with previous results of 0.44±0.07 mm FWHM resolution since 0.5 mm falls within this range. The finding is promising as it points to the system’s potential of achieving 0.5 mm resolution along the DOEP. In fact, if the data are collected in list mode, the C/A ratio enables selectable DOEP resolution as determined by the choice of bin size along that direction.
6.4. Anode spatial resolution
shows that a clear margin exists between the half-maximum level and the level at which the curves intersect. The point spread function curves shown include the contribution from the finite size of the 250 µm diameter 22Na point source used. The anodes are therefore well-resolved as the source is stepped across the detector face, confirming that the 1 mm anode pitch enables ≤1 mm FWHM spatial resolution along that direction.
6.5. PET imaging with CZT and future work
Compared to scintillation detectors commonly used in PET systems, the preceding energy and spatial resolution results verify that CZT can offer superior 511 keV photopeak energy resolution (~3% vs. ~15% FWHM) and comparable effective detector voxel size needed for 1 mm3 resolution PET imaging (1 mm × 1 mm × 5 mm). The small detector voxels allow for narrow lines or tubes of response for high resolution image reconstruction, and given the detector arrangement of , the CZT detector’s 3-D positioning capability also provides precise depth of interaction information, which reduces parallax error. These translate to not only high resolution but also improved resolution uniformity throughout the FOV.
CZT’s high energy resolution presents an opportunity to further enhance the system sensitivity by utilizing multiple interaction photon events in PET imaging. In particular, by using the position, energy and time measurements of the individual photon interactions in a multiple interaction photon event, Bayesian estimation can be applied to identify the initial photon interaction based on Compton kinematics and CZT’s Klein–Nishina differential cross section. The position of the initial photon interaction in turn determines the positioning of the event’s LOR; PET imaging utilizing multiple interaction photon events has been seen to improve the contrast-to-noise ratio of reconstructed images (Gu et al 2010
). CZT would be preferred in this context over scintillation detectors, since the accuracy of Bayesian estimation correlates with the detector energy resolution i.e. increasing with more accurate measurements of interaction energy (Pratx and Levin 2009
Unlike its scintillation crystal counterpart, small voxels within a CZT detector crystal also has no associated dead area between them because of e.g. reflector material, air gaps, or photodetector dead area. This serves to enhance the packing fraction (and hence system sensitivity) as well as sensitivity uniformity throughout the detector volume (Habte et al 2007
). In fact the system can achieve coincidence sensitivity as high as ~20% for a point source at the centre of the FOV (Levin et al 2006
), which is an order of magnitude higher than reported for high-resolution PET systems based on other detector technologies (Missimer et al 2004
, Yang et al 2004
, Vaska et al 2005a
, Sempere Roldan 2007
, Spanoudaki et al 2007
, Bergeron et al 2009
). For a given injected dose or a fixed scan time, the CZT system is therefore expected to yield images with improved statistics and signal-to-noise ratio performance.
In future work, studies will focus on potential methods for improvements in energy resolution, and schemes to achieve sub-electrode-pitch spatial resolution. Although the timing performance of a large volume CZT detector as presented is expected to be poorer than that of scintillation crystals, prior study suggests that at fixed activity and for events in the photopeak, CZT’s high energy resolution can effectively compensate for its poorer timing by reducing the effects of single photons that undergo scatter on the randoms fraction (Levin et al 2006
). Nevertheless, prospective studies will also investigate methods to obtain accurate time pick-off for single photon events in CZT.