Characteristics of an Optical System in the Fourier Domain

An imaging system can be characterized by its point spread function (PSF), which in most cases is space-variant. The final image is the result of the convolution of the PSF with the object (2d representation). Also, we know that the operation of convolution can achieved by multiplication in the Fourier domain.

So the question is: Can an optical system be described by a single unique matrix operator in the Fourier Domain which we can multiply with the object's Fourier transform to achieve the final image (in Fourier space, of course)?

EDIT: I've been doing some thinking about my topic, and it occurred to me for every PSF there's a corresponding MTF (modulation transfer function), that determines how well can a certain feature in the object plain will be imaged be the optical system. So it follows that to characterize an optical system in Fourier space, each point\matrix element needs to have a MTF curve. So instead of a single unique matrix of constants, we need a unique matrix of functions (MTFs), which are modulation dependent. This suggests to me that this operator cannot be multiplied be the object's Fourier transform (which was the assumption in the original question), but rather, we need a modulation representation of the object, to go with the MTFs elements.

• Evidently, as you've proved, this is possible. Have you got more specific questions about this? – Emilio Pisanty Sep 25 '15 at 22:26
• Taking the Fourier transform from the spatial domain to spatial frequency domain gives the optical transfer function , which is certainly used in optical analysis. I think the question may be a bit too broad. – paisanco Sep 26 '15 at 0:13