From \'Etendue to the Lowest Fundamental SNR: Pixel \'Etendue (Optogeometric Factor) Interpreted as Mode Count

TL;DR

This paper interprets the pixel optogeometric factor as the number of accessible optical modes, linking it to quantum photon statistics to establish a fundamental SNR limit for imaging sensors.

Contribution

It extends the interpretation of the optogeometric factor by relating it to optical mode count, providing a quantum-based benchmark for sensor performance.

Findings

Derived explicit formulas for minimal SNR based on optical mode count.

Linked radiometric throughput to quantum photon statistics.

Provided a benchmark for evaluating sensors against quantum noise limits.

Abstract

The optogeometric factor, recently introduced as a pixel level form of \'etendue, quantifies the spatial angular throughput of a detector element. In this work its interpretation is extended by identifying optogeometric factor with the number of accessible optical modes per pixel. This mode based perspective establishes a direct link between radiometric throughput and quantum photon statistics. By combining optogeometric factor with the Bose Einstein distribution, an estimate of the lowest achievable signal to noise ratio (SNR) at the pixel level is derived. Explicit formulas are presented in both scene-based and sensor based forms, showing how the minimal SNR depends on aperture geometry, pixel pitch, f-number, wavelength, and source temperature. This formulation provides a compact and physically transparent benchmark for evaluating imaging sensors against the lowest expected quantum noise limit.