Spatial frequency‐dependent pulse‐height spectrum and method for analyzing detector DQE(f) from ensembles of single X‐ray images

Abstract

Scintillators and photoconductors used in energy integrating detectors (EIDs) have inherent variations in their imaging response to single-detected X-rays due to variations in X-ray energy deposition and secondary quanta generation and transport, which degrades DQE(f). The imaging response of X-ray scintillators to single X-rays may be recorded and studied using single X-ray imaging (SXI) experiments; however, no method currently exists for relating SXI experimental results to EID DQE(f). This work proposes a general analytical framework for computing and analyzing the DQE(f) performance of EIDs from single X-ray image ensembles using a spatial frequency-dependent pulseheight spectrum. Methods: A spatial frequency (f)-dependent gain, g(f ), is defined as the Fourier transform of the imaging response of an EID to a single-detected X-ray. A f-dependent pulse-height spectrum, Pr[ g(f )], is defined as the 2D probability density function of g(f ) over the complex plane. Pr[ g(f )] is used to define a f-dependent Swank factor, A S (f), which fully characterizes the DQE(f) degradation due to single X-ray noise. A S (f) is analyzed in terms of its degradation due to Swank noise, variations in the frequency-dependent attenuation of | g(f )|, and noise in arg g(f ) which occurs due to variations in the asymmetry in each single X-ray's imaging response. Three example imaging systems are simulated to demonstrate the impact of depth-dependent variation in g(f ), remote energy deposition, and a finite number of secondary quanta, on Pr[ g(f )], A S (f), MTF(f),and NPS(f)/NPS(0),which are computed from ensembles of single X-ray images. The same is also demonstrated by simulating a realistic imaging system; that is, a Gd 2 O 2 S-based EID. Using the latter imaging system, the convergence of A S (f) estimates is investigated as a function of the number of detected X-rays per ensemble. Results: Depth-dependent g(f ) variation resulted in A S (f) degradation exclusively due to depth-dependent optical Swank noise and the Lubberts effect. Conversely, the majority of A S (f) degradation caused by remote energy deposition and finite secondary quanta occurred due to variations in arg g(f ). When using input X-ray energies below the K-edge of Gd, variations in the frequencydependent attenuation of | g(f )| accounted for the majority of A S (f) degradation in the GOS-based EID, and very little Swank noise and variations in arg g(f ) were observed. Above the K-edge, however, A S (f) degradation due to Swank noise and variations in arg g(f ) greatly increased. The convergence of A S (f) was limited by variation in arg g(f ); imaging systems with more variation in arg g(f ) required more detected X-rays per ensemble.