Abstract

We consider the reconstruction of the complex transmission coefficients of screens from their projected wave fields. The technique that we use in order to recover the screen complex transmission coefficient is to solve iteratively a system of linear equations that relate the screen to the observed data. We are interested in the special case in which we have detailed a priori knowledge about the distance of the object. In this instance we constrain the solution such that the reconstructed screen conforms to a real positive function. We explicitly formulate the wave equation and demonstrate that a substantial increase in noise immunity and/or resolution enhancement of the recovered function obtainable by using this method.

© 1987 Optical Society of America

Reconstruction of a complex-valued object from the modulus of its Fourier transform using a support constraint

J. R. Fienup
J. Opt. Soc. Am. A 4(1) 118-123 (1987)

Tomography transform and inverse in geometrical optics

Anders H. Andersen
J. Opt. Soc. Am. A 4(8) 1385-1395 (1987)

Analysis of unit-magnitude constrained phasor reconstruction problems

Roque Kwok-Hung Szeto
J. Opt. Soc. Am. A 14(7) 1412-1420 (1997)

A limited-memory, quasi-Newton preconditioner for nonnegatively constrained image reconstruction

Johnathan M. Bardsley
J. Opt. Soc. Am. A 21(5) 724-731 (2004)

Reconstruction of complex-valued propagating wave fields using the Hilbert–Hankel transform

Michael S. Wengrovitz, Alan V. Oppenheim, and George V. Frisk
J. Opt. Soc. Am. A 4(1) 247-266 (1987)