TY - JOUR

T1 - Spatial resolution, signal-to-noise and information capacity of linear imaging systems

AU - Gureyev, Timur

AU - Nesterets, Yakov

AU - De Hoog, Frank

PY - 2016/7/25

Y1 - 2016/7/25

N2 - A simple model for image formation in linear shift-invariant systems is considered, in which both the detected signal and the noise variance are varying slowly compared to the point-spread function of the system. It is shown that within the constraints of this model, the square of the signal-to-noise ratio is always proportional to the "volume" of the spatial resolution unit. In the case of Poisson statistics, the ratio of these two quantities divided by the incident density of the imaging particles (e.g. photons) represents a dimensionless invariant of the imaging system, which was previously termed the intrinsic imaging quality. The relationship of this invariant to the notion of information capacity of communication and imaging systems, which was previously considered by Shannon, Gabor and others, is investigated. The results are then applied to a simple generic model of quantitative imaging of weakly scattering objects, leading to an estimate of the upper limit for the amount of information about the sample that can be obtained in such experiments. It is shown that this limit depends only on the total number of imaging particles incident on the sample, the average scattering coefficient, the size of the sample and the number of spatial resolution units.

AB - A simple model for image formation in linear shift-invariant systems is considered, in which both the detected signal and the noise variance are varying slowly compared to the point-spread function of the system. It is shown that within the constraints of this model, the square of the signal-to-noise ratio is always proportional to the "volume" of the spatial resolution unit. In the case of Poisson statistics, the ratio of these two quantities divided by the incident density of the imaging particles (e.g. photons) represents a dimensionless invariant of the imaging system, which was previously termed the intrinsic imaging quality. The relationship of this invariant to the notion of information capacity of communication and imaging systems, which was previously considered by Shannon, Gabor and others, is investigated. The results are then applied to a simple generic model of quantitative imaging of weakly scattering objects, leading to an estimate of the upper limit for the amount of information about the sample that can be obtained in such experiments. It is shown that this limit depends only on the total number of imaging particles incident on the sample, the average scattering coefficient, the size of the sample and the number of spatial resolution units.

UR - http://www.scopus.com/inward/record.url?scp=84979561967&partnerID=8YFLogxK

U2 - 10.1364/OE.24.017168

DO - 10.1364/OE.24.017168

M3 - Article

AN - SCOPUS:84979561967

VL - 24

SP - 17168

EP - 17182

JO - Optics Express

JF - Optics Express

SN - 1094-4087

IS - 15

ER -