This report shows how the pattern information in an object through which a coherent beam of light is passed can be transformed into information existing in the focal plane. The information in the focal plane can be interpreted as sidebands of a zero-frequency carrier. There is also a close connection between the sideband interpretation and the sampling theorem of information theory and this connection is derived and discussed.
The mathematical methods used in the first (one-dimensional) part of the following analysis are an application to optics of certain classical methods in modulation and communication theory. These are the method of symmetrical and antisymmetrical sideband distribution, the method of paired echoes and sampling theorem analysis.
In the two dimensional analysis, a more general method of separating functions into symmetrical and antisymmetrical parts is used. This leads to a new general analysis of the diffraction patterns of unsymmetrical pupil functions. In the course of the analysis a two-dimensional quadrature function is used. The quadrature function in one dimension is the Hilbert transform.
STANFORD GOLDMAN, "Sideband Interpretation of Optical Information and the Diffraction Patterns of Unsymmetrical Pupil Functions," J. Opt. Soc. Am. 52, 1131-1142 (1962)