Department of Radiological Sciences, UCLA, Los Angeles, CA, 90024, USA.
Departments of Radiology, Stanford University, Stanford, CA, 94305, USA.
Med Phys. 2018 Apr;45(4):1433-1443. doi: 10.1002/mp.12799. Epub 2018 Mar 1.
Photon-counting detectors using CdTe or CZT substrates are promising candidates for future CT systems but suffer from a number of nonidealities, including charge sharing and pulse pileup. By increasing the pixel size of the detector, the system can improve charge sharing characteristics at the expense of increasing pileup. The purpose of this work is to describe these considerations in the optimization of the detector pixel pitch.
The transport of x rays through the CdTe substrate was simulated in a Monte Carlo fashion using GEANT4. Deposited energy was converted into charges distributed as a Gaussian function with size dependent on interaction depth to capture spreading from diffusion and Coulomb repulsion. The charges were then collected in a pixelated fashion. Pulse pileup was incorporated separately with Monte Carlo simulation. The Cramér-Rao lower bound (CRLB) of the measurement variance was numerically estimated for the basis material projections. Noise in these estimates was propagated into CT images. We simulated pixel pitches of 250, 350, and 450 microns and compared the results to a photon counting detector with pileup but otherwise ideal energy response and an ideal dual-energy system (80/140 kVp with tin filtration). The modeled CdTe thickness was 2 mm, the incident spectrum was 140 kVp and 500 mA, and the effective dead time was 67 ns. Charge summing circuitry was not modeled. We restricted our simulations to objects of uniform thickness and did not consider the potential advantage of smaller pixels at high spatial frequencies.
At very high x-ray flux, pulse pileup dominates and small pixel sizes perform best. At low flux or for thick objects, charge sharing dominates and large pixel sizes perform best. At low flux and depending on the beam hardness, the CRLB of variance in basis material projections tasks can be 32%-55% higher with a 250 micron pixel pitch compared to a 450 micron pixel pitch. However, both are about four times worse in variance than the ideal photon counting detector. The optimal pixel size depends on a number of factors such as x-ray technique and object size. At high technique (140 kVp/500 mA), the ratio of variance for a 450 micron pixel compared to a 250 micron pixel size is 2126%, 200%, 97%, and 78% when imaging 10, 15, 20, and 25 cm of water, respectively. If 300 mg/cm of iodine is also added to the object, the variance ratio is 117%, 91%, 74%, and 72%, respectively. Nonspectral tasks, such as equivalent monoenergetic imaging, are less sensitive to spectral distortion.
The detector pixel size is an important design consideration in CdTe detectors. Smaller pixels allow for improved capabilities at high flux but increase charge sharing, which in turn compromises spectral performance. The optimal pixel size will depend on the specific task and on the charge shaping time.
使用 CdTe 或 CZT 衬底的光子计数探测器是未来 CT 系统的有前途的候选者，但存在许多不理想的情况，包括电荷共享和脉冲堆积。通过增加探测器的像素尺寸，系统可以提高电荷共享特性，但代价是增加堆积。本工作的目的是描述在优化探测器像素间距时的这些考虑因素。
使用 GEANT4 以蒙特卡罗方式模拟 x 射线通过 CdTe 衬底的传输。沉积的能量转换为电荷，分布为高斯函数，其大小取决于相互作用深度，以捕获扩散和库仑排斥引起的扩展。然后以像素化的方式收集电荷。单独使用蒙特卡罗模拟来合并脉冲堆积。使用数值估计了基础材料投影的测量方差的克拉美罗下限（CRLB）。将这些估计中的噪声传播到 CT 图像中。我们模拟了 250、350 和 450 微米的像素间距，并将结果与具有堆积但具有理想能量响应和理想双能系统（80/140 kVp 加锡过滤）的光子计数探测器进行了比较。模拟的 CdTe 厚度为 2 毫米，入射光谱为 140 kVp 和 500 mA，有效死时间为 67 ns。未模拟电荷求和电路。我们将模拟限制在厚度均匀的物体上，并且没有考虑在高空间频率下使用较小像素的潜在优势。
在非常高的 x 射线通量下，脉冲堆积占主导地位，小像素尺寸表现最佳。在低通量或对于厚物体，电荷共享占主导地位，大像素尺寸表现最佳。在低通量且取决于束的硬度下，与 450 微米像素间距相比，基础材料投影任务的 CRLB 方差在 250 微米像素间距时可以高 32%-55%。但是，两者的方差都比理想的光子计数探测器差四倍。最佳像素尺寸取决于许多因素，例如 x 射线技术和物体尺寸。在高技术（140 kVp/500 mA）下，当对 10、15、20 和 25 cm 的水进行成像时，与 450 微米像素相比，450 微米像素的方差比为 2126%、200%、97%和 78%。如果物体中还添加了 300 mg/cm 的碘，则方差比分别为 117%、91%、74%和 72%。非谱任务，例如等效单能成像，对光谱失真的敏感性较低。
探测器像素尺寸是 CdTe 探测器的一个重要设计考虑因素。较小的像素可以提高在高通量下的性能，但会增加电荷共享，这反过来又会影响光谱性能。最佳像素尺寸将取决于特定任务和电荷成形时间。
