Instrument-limited pixel-level SNR bounds from optical throughput
Abstract
The radiometric integral is the fundamental radiance--to--flux relation in imaging, whereas \'etendue is typically used as a compact system-level descriptor. For quantitative imaging and calibration, however, the operative mapping must be explicit at the level of individual detector pixels, including pixel acceptance and field-dependent pupil visibility. This work packages the pixel-restricted radiometric integral into a reusable geometric throughput factor by defining a per-pixel optogeometric (optical-throughput) factor Fopg,i (units m2.sr) such that, under weak radiance variation, i ≈ Li\,Fopg,i. Making throughput explicit at the pixel scale yields an optics-delivered photon budget in which the incident photon count at the detector, Ninc,i (before quantum efficiency), scales linearly with geometry: Ninc,i Fopg,i for a given scene radiance distribution and fixed acquisition settings (bandwidth, integration time, and optical transmission). The corresponding optics-delivered (pre-detection) shot-noise ceiling is set by the incident photon count Ninc,i, with SNRinc,i Ninc,i Fopg,i, while in photoelectron units one has SNRi Nph,i=η()\,Ninc,i Fopg,i, where Nph,i is the detected photoelectron count and η() is the (narrowband) quantum efficiency; additional detector/electronics noise sources (e.g.\ dark current and read noise) can only reduce the achieved SNR below these shot-noise limits.
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