Abstract

A wave field of finite cross section and angular spread has, in effect, a finite number of degrees of freedom. A knowledge of the degrees of freedom provides structural information. This paper is concerned with the propagation of structural information in optical wave fields. The fields considered are those that arise in the diffraction and scattering of quasimonochromatic and polychromatic light by fixed objects. In all cases, the light originates at a point source. To each point of a wave field we assign an information-flow vector J, so defined that its time-integrated flux through a surface of observation yields the number of degrees of freedom of the wave field incident on that surface. Thus J represents the number of independent real data that can be found in unit time on a unit area whose normal is oriented in the direction of information flow. The set of all J values comprises a vector field, which we call the structure field. The structure field can be represented by field lines; these are lines of structural-information flow. The structure field has the following additional properties. (1) In a homogeneous transparent medium, the structure field is solenoidal. Hence structural information behaves like an incompressible fluid. Elementary tubes of flow may be defined such that each tube corresponds to one spatial degree of freedom. (2) The structure field is not, in general, irrotational. However, since J and its curl are orthogonal, there exists a family of surfaces orthogonal to the lines of J. These are surfaces of maximum structural-information density. (3) The normal component of the field vector J is continuous across a smooth boundary separating homogeneous transparent media. Examples of field lines are presented. Applications of the theory include information-density mapping of holographic and conventional image-wave fields, and the determination of minimum sampling intervals.

© 1971 Optical Society of America

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