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

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, (Formula presented.), 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, (Formula presented.), is defined as the 2D probability density function of (Formula presented.) over the complex plane. (Formula presented.) 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 (Formula presented.), and noise in (Formula presented.) 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 (Formula presented.), remote energy deposition, and a finite number of secondary quanta, on (Formula presented.), 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 Gd₂O₂S-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 (Formula presented.) 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 (Formula presented.). When using input X-ray energies below the K-edge of Gd, variations in the frequency-dependent attenuation of (Formula presented.) accounted for the majority of A_S(f) degradation in the GOS-based EID, and very little Swank noise and variations in (Formula presented.) were observed. Above the K-edge, however, A_S(f) degradation due to Swank noise and variations in (Formula presented.) greatly increased. The convergence of A_S(f) was limited by variation in (Formula presented.); imaging systems with more variation in (Formula presented.) 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 (Formula presented.), and quantified using A_S(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.