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Spectroscopic x-ray detectors (SXDs) are poised to play a substantial role inthe next generation of medical x-ray imaging. Evaluating their performance interms of the detective quantum efficiency (DQE) requires normalization of thefrequency-dependent signal-to-noise ratio (SNR) by that of an ideal SXD. Weprovide mathematical expressions of the SNR of ideal SXDs for quantificationand detection tasks and tabulate their numeric values for standardized tasks.We propose using standardized RQA-series x-ray spectra. We define ideal SXDs asthose that (1) have an infinite number of infinitesimal energy bins, (2) do notdistort the incident distribution of x-ray photons in the spatial or energydomains, and (3) do not decrease the frequency-dependent SNR of the incidentdistribution of x-ray quanta. We derive analytic expressions for the noisepower spectrum (NPS) of such ideal detectors for detection and quantificationtasks. We tabulate the NPS of ideal SXDs for RQA x-ray spectra for detectionand quantification of aluminum, PMMA, iodine, and gadolinium basis materials.Our analysis shows that a single matrix determines the noise power of idealSXDs in detection and quantification tasks, including basis materialdecomposition and line-integral estimation for pseudo-mono-energetic imaging.This NPS matrix is determined by the x-ray spectrum incident on the detectorand the mass-attenuation coefficients of the set of basis materials. Combiningexisting tabulated values of the mass-attenuation coefficients of basismaterials with standardized RQA x-ray spectra enabled tabulating numeric valuesof the NPS matrix for selected spectra and tasks. The numeric values andmathematical expressions of the NPS of ideal SXDs reported here can be used tonormalize measurements of the frequency-dependent SNR of SXDs for experimentalstudy of the task-dependent DQE.

Normalization of the task-dependent detective quantum efficiency of spectroscopic x-ray imaging detectors