  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.
