Extending the Optogeometric Factor to Non-Thermal Sources: Fundamental SNR in X-ray Imaging

The optogeometric factor, introduced as a pixel-level form of étendue, provides a compact measure of the spatial angular throughput of a detector element. In previous work, optogeometric factor was combined with Bose Einstein statistics to derive a fundamental limit for the signal-to-noise ratio (SNR) in thermal infrared imaging. Here this framework is extended to non-thermal sources, with a focus on bremsstrahlung (X-ray) radiation. By interpreting optogeometric factor as a mode count, and replacing the thermal occupancy with the spectral photon flux of an X-ray tube, a fundamental shot-noise limit for SNR is obtained. In the geometry-limited regime relevant for X-ray detectors, the result shows that the pixel-level SNR scales with 1/f\# but is independent of pixel pitch. This extension demonstrates the generality of the optogeometric factor and provides a unified mode-based framework for evaluating quantum-limited performance across both thermal and non-thermal imaging modalities.