Contrast resolution of few-photon detectors

We investigate the minimum acquisition time, expressed as the number of image frames, and the minimum number of absorbed photons per pixel required to achieve a predefined contrast resolution in a monochromatic, pixelated image acquisition system at low light intensities (from well below one photon, to several hundred photons per pixel and frame). Primarily we compare systems based on the pixels of the photon-number-resolving (PNR) type of detectors and detectors that discriminate, in a binary fashion, between zero and non-zero photon numbers (so-called click detectors). We find that our model can seamlessly interpolate between the two. We also model detectors with intrinsic PNR capabilities and integrating detectors with a simple saturation model, derive the probability of errors in assigning the correct intensity (or 'gray level') and finally discuss how the estimated levels, which need to be based on threshold levels due to the stochastic nature of the detected photon number, should be assigned. Overall, we find that non-ideal PNR-detector-based systems offer advantages even over ideal click-detector-based systems when the incident mean photon number is sufficiently large, which is guaranteed to occur around ten photons per pixel and frame.