Quantifying photon counting detector (PCD) performance using PCD-CT images. Part II. detector spectral response...

An earlier publication, Med. Phys. 52:2796 (2025), reported a method for estimating the mean output counts of photon-counting detectors (PCDs) from reconstructed PCD-CT images. This capability provides a foundation for end users of clinical PCD-CT systems to characterize PCD performance without access to raw data. Building on the previous work, the present manuscript introduces an image-domain approach for characterizing the spectral response function (SRF) of PCDs. The SRF strongly influences the spectral imaging performance of PCD-CT and can vary across PCD-CT platforms, even when the same semiconductor sensor material is used.

To calibrate and validate a theoretical PCD SRF model for a clinical whole-body PCD-CT system (Siemens NAEOTOM Alpha) using DICOM images of physical phantoms.

PMMA slabs with thicknesses ranging from 1 to 13 inches were placed in the scanner as x-ray spectrum modifiers, while the tube voltage was varied from 70 to 140 kV. The Alpha PCD-CT was operated in static-gantry mode, such that the x-ray spectrum incident on the detector remained static during each scan. The acquired projections were reconstructed by the scanner into DICOM images as if they had been acquired over a full 360 ${}^{\circ }$ rotation. For each PCD energy bin, the mean detector output count was estimated from the noise power spectrum of the reconstructed images. Ratios of the estimated mean counts between energy bins were then used to calibrate the free parameters of a theoretical SRF model developed based on the semiconductor material and pixel geometry of the Alpha PCD. This approach is analogous to calibrating a parametric x-ray spectrum model to the actual spectrum of a radiographic or CT imaging system using experimentally measured half-value layers or quarter-value layers. The calibrated SRF model was subsequently validated using PCD-CT energy-bin images acquired under different x-ray spectral conditions generated with copper (Cu) filters (0.5-4.5 mm) instead of PMMA slabs, by comparing the theoretical and experimentally estimated count ratios between energy bins.

For the PMMA-based calibration data, the model-predicted total-energy-bin to high-energy-bin count ratios yielded a mean percent error (MPE) of -0.48% (95% CI: [-8.00%, 7.03%]). For the independent Cu-based validation data, the model-predicted count ratios remained in close agreement with the experimental measurements, yielding an MPE of -2.27% (95% CI: [-10.76%, 6.22%]). The calibrated SRF model showed that the mean energy separations between the low-energy and high-energy bins of the Alpha PCD were 10.4, 16.5, 24.4, and 28.7 keV for 70, 90, 120, and 140 kV beams, respectively, indicating greater spectral separation at higher tube voltages.

It is feasible for end users of PCD-CT systems to estimate the SRF from reconstructed images without access to raw detector counts. The estimated Alpha PCD SRF curves are provided in a MATLAB software package, PCD-SPECTRA, which is made available to the research community to facilitate characterization of the spectral performance of PCD-CT systems and support further research and application development.