Acciavatti Raymond J, Maidment Andrew D A
University of Pennsylvania, Department of Radiology, 3400 Spruce St., Philadelphia PA 19104.
Proc SPIE Int Soc Opt Eng. 2010 Feb;7622. doi: 10.1117/12.845310. Epub 2010 Mar 22.
In this work, analytical models of the optical transfer function (OTF), noise power spectra (NPS), and detective quantum efficiency (DQE) are developed for two types of digital x-ray detectors. The two detector types are (1) energy integrating (EI), for which the point spread function (PSF) is interpreted as a weighting function for counting x-rays, and (2) photon counting (PC), for which the PSF is treated as a probability. The OTF is the Fourier transform of the PSF. The two detector types, having the same PSF, possess an equivalent OTF. NPS is the discrete space Fourier transform (DSFT) of the autocovariance of signal intensity. From first principles, it is shown that while covariance is equivalent for both detector types, variance is not. As a consequence, provided the two detector types have equivalent PSFs, a difference in NPS exists such that NPS ≥ NPS and hence DQE ≤ DQE. The necessary and sufficient condition for equality is that the PSF is either zero or unity everywhere. A PSF modeled as the convolution of a Lorentzian with a rect function is analyzed in order to illustrate the differences in NPS and DQE. The Lorentzian models the blurring of the x-ray converter, while the rect function reflects the sampling of the detector. The NPS difference between the two detector types is shown to increase with increasing PSF width. In conclusion, this work develops analytical models of OTF, NPS, and DQE for energy integrating and photon counting digital x-ray detectors.
在这项工作中，针对两种类型的数字X射线探测器，开发了光学传递函数（OTF）、噪声功率谱（NPS）和探测量子效率（DQE）的分析模型。这两种探测器类型分别是：（1）能量积分（EI）型，其点扩散函数（PSF）被解释为对X射线计数的加权函数；（2）光子计数（PC）型，其PSF被视为一种概率。OTF是PSF的傅里叶变换。这两种具有相同PSF的探测器类型拥有等效的OTF。NPS是信号强度自协方差的离散空间傅里叶变换（DSFT）。从基本原理出发，可以看出虽然两种探测器类型的协方差是等效的，但方差并非如此。因此，假设这两种探测器类型具有等效的PSF，则存在NPS的差异，使得NPS≥NPS，进而DQE≤DQE。相等的充要条件是PSF在任何地方要么为零要么为一。分析了一个建模为洛伦兹函数与矩形函数卷积的PSF，以说明NPS和DQE的差异。洛伦兹函数模拟X射线转换器的模糊，而矩形函数反映探测器的采样。两种探测器类型之间的NPS差异随着PSF宽度的增加而增大。总之，这项工作为能量积分型和光子计数型数字X射线探测器开发了OTF、NPS和DQE的分析模型。
