Chapter 6 - Fourier Optics

Abstract

The basic task in Fourier optics is to describe the wave function in an optical field in terms of spatial frequencies, where such a description is achieved by means of the operation of Fourier transformation. This makes possible a neat and useful description of the transformation of the optical field from an input plane to an output plane in an optical system. We begin by recalling the fundamentals of Fourier transformation, with a number of examples. The important concepts of convolution and correlation are introduced, on the basis of which the convolution theorem and the correlation theorem are explained. The propagation of an optical field from a given plane to another in a source-free region is described in the Fresnel (or paraxial) approximation, with the example of a Gaussian beam. In a diffraction situation the propagation in the paraxial approximation through a large distance (or between conjugate planes of an optical system) leads to the Fraunhofer diffraction formula, which can be interpreted in terms of the Fourier transform of the field in the plane of the exit pupil.