Instrument-limited pixel-level SNR bounds from optical throughput
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| Format: | Preprint |
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2025
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| _version_ | 1866914368371818496 |
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| author | Sova, Jan Kolaříková, Marie |
| author_facet | Sova, Jan Kolaříková, Marie |
| contents | 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 (optical-throughput) factor $F_{\mathrm{opg},i}$ (units \si{m^2.sr}) such that, under weak radiance variation, $Φ_i \approx L_i\,F_{\mathrm{opg},i}$. Making throughput explicit at the pixel scale yields an optics-delivered photon budget in which the incident photon count at the detector, $N_{\mathrm{inc},i}$ (before quantum efficiency), scales linearly with geometry: $N_{\mathrm{inc},i}\propto F_{\mathrm{opg},i}$ 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 $N_{\mathrm{inc},i}$, with $\mathrm{SNR}_{\mathrm{inc},i}\le \sqrt{N_{\mathrm{inc},i}}\propto \sqrt{F_{\mathrm{opg},i}}$, while in photoelectron units one has $\mathrm{SNR}_i \le \sqrt{N_{\mathrm{ph},i}}=\sqrt{η(\barν)\,N_{\mathrm{inc},i}}\propto \sqrt{F_{\mathrm{opg},i}}$, where $N_{\mathrm{ph},i}$ is the detected photoelectron count and $η(\barν)$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_09335 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Instrument-limited pixel-level SNR bounds from optical throughput Sova, Jan Kolaříková, Marie Optics Applied Physics Instrumentation and Detectors 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 (optical-throughput) factor $F_{\mathrm{opg},i}$ (units \si{m^2.sr}) such that, under weak radiance variation, $Φ_i \approx L_i\,F_{\mathrm{opg},i}$. Making throughput explicit at the pixel scale yields an optics-delivered photon budget in which the incident photon count at the detector, $N_{\mathrm{inc},i}$ (before quantum efficiency), scales linearly with geometry: $N_{\mathrm{inc},i}\propto F_{\mathrm{opg},i}$ 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 $N_{\mathrm{inc},i}$, with $\mathrm{SNR}_{\mathrm{inc},i}\le \sqrt{N_{\mathrm{inc},i}}\propto \sqrt{F_{\mathrm{opg},i}}$, while in photoelectron units one has $\mathrm{SNR}_i \le \sqrt{N_{\mathrm{ph},i}}=\sqrt{η(\barν)\,N_{\mathrm{inc},i}}\propto \sqrt{F_{\mathrm{opg},i}}$, where $N_{\mathrm{ph},i}$ is the detected photoelectron count and $η(\barν)$ 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. |
| title | Instrument-limited pixel-level SNR bounds from optical throughput |
| topic | Optics Applied Physics Instrumentation and Detectors |
| url | https://arxiv.org/abs/2508.09335 |