An analytical model of NPS and DQE comparing photon counting and energy integrating detectors

Abstract

ABSTRACT 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 Four ier 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 in tensity. 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 exis ts such that NPS PC • NPS EI and hence DQE PC ” DQE EI . 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. Keywords: Energy integrating detector, photon counting detector, point spread function (PSF), optical transfer function (OTF), modulation transfer function (MTF), noise power spectra (NPS), detective quantum efficiency (DQE).