Instrument-limited pixel-level SNR bounds from optical throughput

The radiometric integral is the fundamental radiance–to–flux relation in imaging, whereas étendue 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 (opticalthroughput) factor Fopg,i (units m2 sr) such that, under weak radiance variation, Φi ≈ 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 ≤ p Ninc,i ∝ p Fopg,i, while in photoelectron units one has SNRi ≤ p Nph,i = p η(¯ν) Ninc,i ∝ p Fopg,i, where Nph,i is the detected photoelectron count and η(¯ν) 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. To compare throughput across wavelength bands, a throughput-normalized pixel-level phase-space proxy Mi(λ) ≡ Fopg,i/λ2 is introduced. In the paraxial unvignetted baseline, Fopg,i reduces to a compact design expression, recovering the familiar scaling SNRi ∝ app,i/(f# |M|) as a corollary. Overall, the results remain within standard radiometry but elevate pixel-resolved throughput to a first-class quantity, providing an explicit end-to-end link pixel radiometry → optical throughput → photon budget → SNR for thermography, remote sensing, and quantitative imaging.