Abstract

Bounds on the intensity and the variation of the far field F(u,v) of a given object f(x,y) are developed in terms of the energy and the area of the object. An amplitude function f(x,y) is determined for maximizing F(u₀,v₀). The results are extended to objects with circular symmetry. The analysis is applied to the following apodization problem: Given a pupil of specified boundary R, a transmission function f(x,y) of energy E is sought such that the energy of its far field in a region S of the u–v plane is maximum.

© 1967 Optical Society of America

Detectability of Coherent Optical Signals in a Heterodyne Receiver

Carl W. Helstrom
J. Opt. Soc. Am. 57(3) 353-361 (1967)

Integral-Transform Formulation of Diffraction Theory*

George C. Sherman
J. Opt. Soc. Am. 57(12) 1490-1498 (1967)

Optical Systems, Singularity Functions, Complex Hankel Transforms

A. Papoulis
J. Opt. Soc. Am. 57(2) 207-213 (1967)

Random Lorentz Band Model with Exponential-Tailed S⁻¹ Line-Intensity Distribution Function*

W. Malkmus
J. Opt. Soc. Am. 57(3) 323-329 (1967)

Optical Transfer of the Three-Dimensional Object*†

B. Roy Frieden
J. Opt. Soc. Am. 57(1) 56-66 (1967)