Two sampling expansions are derived, from which the three-dimensional (3-D) field amplitude distribution in the vicinity of an axial image point can be recovered entirely from a 1-D set of amplitude samples. In the first of these expansions, the sampling points are regularly spaced along the system optical axis, whereas in the second these points lie along one radius in a plane perpendicular to this axis. The expansions are derived with a scalar diffraction theory by using the paraxial and classical approximations. Apart from leading to very efficient computational schemes, both expansions are shown to provide a good basis for analyzing the structure of this kind of diffraction pattern, and knowledge of this structure can be applied in turn to the solution of pupil synthesis problems.
© 1997 Optical Society of America
Original Manuscript: March 20, 1997
Revised Manuscript: June 16, 1997
Manuscript Accepted: June 16, 1997
Published: November 1, 1997
J. E. A. Landgrave and L. R. Berriel-Valdos, "Sampling expansions for three-dimensional light amplitude distribution in the vicinity of an axial image point," J. Opt. Soc. Am. A 14, 2962-2976 (1997)