Fourier optics

The Fourier optics ( after Jean Baptiste Joseph Fourier ) is a part of the field of optics, in which the propagation of light with the help of Fourier analysis is investigated. The Fourier optics into account the wave nature of light, but neglects, for example, the polarization.

Background

The origin of Fourier optics is the finding that the Fraunhofer diffraction pattern of the Fourier transform of the diffracting object is equivalent. If coherent light with the spatial amplitude distribution of a structure with the spatial transmission distribution, the field distribution is immediately behind the diffractive structure

In the far field of the structure is valid for the amplitude distribution

Is the distance from the diffractive structure, are the transverse coordinates. is a phase factor. Analogous to the frequency in the temporal Fourier transform is defined as spatial frequencies

As follows

The field distribution in the far field is given by the two-dimensional Fourier transform of the field distribution immediately after the diffractive structure:

Importance of spatial frequencies

A ray from the point in the observation plane to a point in the plane of the diffractive structure includes the angle with the axis, and a. For not too large angles (ie, for not too large ) it follows:

Light, which is close to the optical axis in the far field corresponds low spatial frequencies, while further outboard light belongs to high spatial frequencies.

Fine structures in the object, ie those that change rapidly in space, belong to high spatial frequencies. Larger structures represent correspondingly smaller spatial frequencies