A detective quantum efficiency for spectroscopic X‐ray imaging detectors

Abstract Purpose Spectroscopic X‐ray detectors (SXDs) are under development for X‐ray imaging applications. Recent efforts to extend the detective quantum efficiency (DQE) to SXDs impose a barrier to experimentation and/or do not provide a task‐independent measure of detector performance. The purpose of this article is to define a task‐independent DQE for SXDs that can be measured using a modest extension of established DQE‐metrology methods. Methods We defined a task‐independent spectroscopic DQE and performed a simulation study to determine the relationship between the zero‐frequency DQE and the ideal‐observer signal‐to‐noise ratio (SNR) of low‐frequency soft‐tissue, bone, iodine, and gadolinium signals. In our simulations, we used calibrated models of the spatioenergetic response of cadmium telluride (CdTe) and cadmium–zinc–telluride (CdZnTe) SXDs. We also measured the zero‐frequency DQE of a CdTe detector with two energy bins and of a CdZnTe detector with up to six energy bins for an RQA9 spectrum and compared with model predictions. Results The spectroscopic DQE accounts for spectral distortions, energy‐bin‐dependent spatial resolution, interbin spatial noise correlations, and intrabin spatial noise correlations; it is mathematically equivalent to the squared SNR per unit fluence of the generalized least‐squares estimate of the height of an X‐ray impulse in a uniform noisy background. The zero‐frequency DQE has a strong linear relationship with the ideal‐observer SNR of low‐frequency soft‐tissue, bone, iodine, and gadolinium signals, and can be expressed in terms of the product of the quantum efficiency and a Swank noise factor that accounts for DQE degradation due to, for example, charge sharing (CS) and electronic noise. The spectroscopic Swank noise factor of the CdTe detector was measured to be 0.81 0.04 and 0.83 0.04 with and without anticoincidence logic for CS suppression, respectively. The spectroscopic Swank noise factor of the CdZnTe detector operated with four energy bins was measured to be 0.82 0.02 which is within 5% of the theoretical value. Conclusions The spectroscopic DQE defined here is (1) task‐independent, (2) can be measured using a modest extension of existing DQE‐metrology methods, and (3) is predictive of the ideal‐observer SNR of soft‐tissue, bone, iodine, and gadolinium signals. For CT applications, the combination of CS and electronic noise in CdZnTe spectroscopic detectors will degrade the zero‐frequency DQE by 10 %–20 % depending on the electronic noise level and pixel size.

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