### Abstract

The statistics of detector outputs produced by an imaging system are derived from basic radiometric concepts and definitions. We show that a fundamental way of describing a photon-limited imaging system is in terms of a Poisson random process in spatial, angular, and wavelength variables. We begin the paper by recalling the concept of radiance in geometrical optics, radiology, physical optics, and quantum optics. The propagation and conservation laws for radiance in each of these domains are reviewed. Building upon these concepts, we distinguish four categories of imaging detectors that all respond in some way to the incident radiance, including the new category of photon-processing detectors (capable of measuring radiance on a photon-by-photon basis). This allows us to rigorously show how the concept of radiance is related to the statistical properties of detector outputs and to the information content of a single detected photon. A Monte-Carlo technique, which is derived from the Boltzmann transport equation, is presented as a way to estimate probability density functions to be used in reconstruction from photon-processing data.

Original language | English (US) |
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Article number | 013102 |

Journal | Optical Engineering |

Volume | 55 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2016 |

### Keywords

- photon noise
- photon processing
- radiance

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Engineering(all)

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## Cite this

*Optical Engineering*,

*55*(1), [013102]. https://doi.org/10.1117/1.OE.55.1.013102