On spatial resolution, signal-to-noise and information capacity of linear imaging systems

TL;DR

This paper presents a theoretical analysis linking the spatial resolution, signal-to-noise ratio, and information capacity of linear imaging systems, providing bounds on information retrieval based on system parameters and particle statistics.

Contribution

It introduces a model connecting signal-to-noise ratio and spatial resolution volume, and relates the invariant to information capacity in imaging systems, with applications to weakly scattering objects.

Findings

Signal-to-noise ratio squared is proportional to the resolution volume.

The invariant relates to the information capacity of the system.

Upper limits of information about samples depend on particle count and sample properties.

Abstract

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.