TY - JOUR

T1 - Radiance and photon noise

T2 - Imaging in geometrical optics, physical optics, quantum optics and radiology

AU - Caucci, Luca

AU - Myers, Kyle J.

AU - Barrett, Harrison H.

N1 - Funding Information:
We have benefited significantly from discussions with Abhinav Jha and Eric Clarkson. This research was supported by the National Institutes of Health under grants R37 EB000803 and P41 EB002035.

PY - 2016/1/1

Y1 - 2016/1/1

N2 - 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.

AB - 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.

KW - photon noise

KW - photon processing

KW - radiance

UR - http://www.scopus.com/inward/record.url?scp=84954177606&partnerID=8YFLogxK

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U2 - 10.1117/1.OE.55.1.013102

DO - 10.1117/1.OE.55.1.013102

M3 - Article

AN - SCOPUS:84954177606

VL - 55

JO - Optical Engineering

JF - Optical Engineering

SN - 0091-3286

IS - 1

M1 - 013102

ER -