Fundamentals of Diffraction and Image Formation

Telecommunication systems - such as optical systems dedicated to image formation - are conceived to collect, treat and transport information. In the first case, information is generally encoded temporally (for example a modulated voltage), whereas in the second case it is encoded spatially (amplitude or intensity spatial profile). On a fundamental point of view, this difference is rather minimal.

A common point between the two disciplines lies in the mathematics used to describe them: system theory and Fourier analysis. The fundamental reason for this similarity is not only the word “information” but rather some properties such as linearity or invariance. Any (electronic, optic, or other) system or device which verifies those two properties can be mathematically described in a surprisingly easily fashion by using the techniques of frequency analysis. In the same way as it is convenient to describe amplifiers in terms of their temporal frequency responses, it is often convenient to describe image formation systems in terms of their spatial frequency responses.

It is particularly important to notice that this mathematical similarity can be exploited not only to analyze the phenomenons at stake but also to synthesize new functions. Similarly to the spectrum of a temporal function which can be intentionally manipulated using electrical filtering, the spectrum of a spatial function can be modified in diverse ways. The example of Zernike's contrast phase microscope (Noble Prize) is the best piece of evidence.