Spatial frequency‐dependent pulse‐height spectrum and method for analyzing detector DQE(f) from ensembles of single X‐ray images
Authors: Dow Scott , Howansky Adrian , Lubinsky Anthony R. , Zhao Wei 
Published: November 2021

Purpose

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 pulse‐height spectrum.

Methods

A spatial frequency (f)‐dependent gain, , 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, , is defined as the 2D probability density function of over the complex plane. is used to define a f‐dependent Swank factor, AS(f), which fully characterizes the DQE(f) degradation due to single X‐ray noise. AS(f) is analyzed in terms of its degradation due to Swank noise, variations in the frequency‐dependent attenuation of , and noise in 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 , remote energy deposition, and a finite number of secondary quanta, on , AS(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 Gd2O2S‐based EID. Using the latter imaging system, the convergence of AS(f) estimates is investigated as a function of the number of detected X‐rays per ensemble.

Results

Depth‐dependent variation resulted in AS(f) degradation exclusively due to depth‐dependent optical Swank noise and the Lubberts effect. Conversely, the majority of AS(f) degradation caused by remote energy deposition and finite secondary quanta occurred due to variations in . When using input X‐ray energies below the K‐edge of Gd, variations in the frequency‐dependent attenuation of accounted for the majority of AS(f) degradation in the GOS‐based EID, and very little Swank noise and variations in were observed. Above the K‐edge, however, AS(f) degradation due to Swank noise and variations in greatly increased. The convergence of AS(f) was limited by variation in ; imaging systems with more variation in required more detected X‐rays per ensemble.

Conclusions

An analytical framework is proposed that generalizes the pulse‐height spectrum and Swank factor to arbitrary f. The impact of single X‐ray noise sources, such as the Lubberts effect, remote energy deposition, and finite secondary quanta on detector performance, may be represented using , and quantified using AS(f). The approach may be used to compute MTF(f), NPS(f), and DQE(f) from ensembles of single X‐ray images and provides an additional tool to analyze proposed EID designs.