Department of Physics, University of British Columbia Okanagan, Kelowna, BC, V1Y 1V7, Canada.
Imaging Research Laboratories, Robarts Research Institute, The University of Western Ontario, London, ON, N6A 5B7, Canada.
Med Phys. 2018 May;45(5):1926-1941. doi: 10.1002/mp.12853. Epub 2018 Mar 31.
Single-photon-counting (SPC) and spectroscopic x-ray detectors are under development in academic and industry laboratories for medical imaging applications. The spatial resolution of SPC and spectroscopic x-ray detectors is an important design criterion. The purpose of this article was to extend the cascaded systems approach to include a description of the spatial resolution of SPC and spectroscopic x-ray imaging detectors.
A cascaded systems approach was used to model reabsorption of characteristic x rays, Coulomb repulsion, and diffusion in SPC and spectroscopic x-ray detectors. In addition to reabsorption, diffusion, and Coulomb repulsion, the model accounted for x-ray conversion to electron-hole (e-h) pairs, integration of e-h pairs in detector elements, electronic noise, and energy thresholding. The probability density function (PDF) describing the number of e-h pairs was propagated through each stage of the model and was used to derive new theoretical expressions for the large-area gain and modulation transfer function (MTF) of CdTe SPC x-ray detectors, and the energy bin sensitivity functions and MTFs of CdTe spectroscopic detectors. Theoretical predictions were compared with the results of MATLAB-based Monte Carlo (MC) simulations and published data. Comparisons were also made with the MTF of energy-integrating systems.
Under general radiographic conditions, reabsorption, diffusion, and Coulomb repulsion together artificially inflate count rates by 20% to 50%. For thicker converters (e.g. 1000 μm) and larger detector elements (e.g. 500 μm pixel pitch) these processes result in modest inflation (i.e. ∼10%) in apparent count rates. Our theoretical and MC analyses predict that SPC MTFs will be degraded relative to those of energy-integrating systems for fluoroscopic, general radiographic, and CT imaging conditions. In most cases, this degradation is modest (i.e., ∼10% at the Nyquist frequency). However, for thicker converters, the SPC MTF can be degraded by up to 25% at the Nyquist frequency relative to EI systems. Additionally, unlike EI systems, the MTF of spectroscopic systems is strongly dependent on photon energy, which results in energy-bin-dependent spatial resolution in spectroscopic systems.
The PDF-transfer approach to modeling signal transfer through SPC and spectroscopic x-ray imaging systems provides a framework for understanding system performance. Application of this approach demonstrated that charge sharing artificially inflates the SPC image signal and degrades the MTF of SPC and spectroscopic systems relative to energy-integrating systems. These results further motivate the need for anticharge-sharing circuits to mitigate the effects of charge sharing on SPC and spectroscopic x-ray image quality.
单光子计数（SPC）和光谱 X 射线探测器正在学术和工业实验室中开发，用于医学成像应用。SPC 和光谱 X 射线探测器的空间分辨率是一个重要的设计标准。本文的目的是扩展级联系统方法，以包括 SPC 和光谱 X 射线成像探测器的空间分辨率描述。
使用级联系统方法来模拟特征 X 射线的再吸收、库仑排斥和扩散。除了再吸收、扩散和库仑排斥之外，该模型还考虑了 X 射线转换为电子-空穴（e-h）对、探测器元件中 e-h 对的积分、电子噪声和能量阈值。描述 e-h 对数量的概率密度函数（PDF）通过模型的每个阶段进行传播，并用于推导出 CdTe SPC X 射线探测器的大面增益和调制传递函数（MTF）以及 CdTe 光谱探测器的能量-bin 灵敏度函数和 MTF 的新理论表达式。理论预测与基于 MATLAB 的蒙特卡罗（MC）模拟和已发表数据的结果进行了比较。还与能量积分系统的 MTF 进行了比较。
在一般射线照相条件下，再吸收、扩散和库仑排斥共同使计数率人为地增加 20%至 50%。对于较厚的转换器（例如 1000μm）和较大的探测器元件（例如 500μm 像素间距），这些过程会导致表观计数率适度增加（即约 10%）。我们的理论和 MC 分析预测，与能量积分系统相比，SPC MTF 将在透视、一般射线照相和 CT 成像条件下降级。在大多数情况下，这种退化是适度的（即在奈奎斯特频率处约为 10%）。然而，对于较厚的转换器，SPC MTF 相对于 EI 系统在奈奎斯特频率处可能会降低 25%。此外，与 EI 系统不同，光谱系统的 MTF 强烈依赖于光子能量，这导致光谱系统中的能量-bin 依赖性空间分辨率。
用于模拟 SPC 和光谱 X 射线成像系统中信号传输的 PDF 传输方法为理解系统性能提供了一个框架。该方法的应用表明，电荷共享会人为地增加 SPC 图像信号，并降低 SPC 和光谱系统的 MTF，相对于能量积分系统。这些结果进一步证明需要反电荷共享电路来减轻电荷共享对 SPC 和光谱 X 射线图像质量的影响。
