Abstract

This paper describes a fast direct algorithm for obtaining least-squares phase estimates from arrays of noisy phase differences. The algorithm uses the fast Fourier transform to diagonalize and decouple the system of equations which results from the application of the least-squares criterion. It is accurate and stable, and is perhaps an order of magnitude faster than the best iterative method. The effectiveness of the algorithm has been demonstrated by using it in connection with the Knox–Thompson speckle-imaging procedure to restore an optical object perturbed by simulated atmospheric turbulence. Representative results are discussed in the paper.

© 1979 Optical Society of America

Speckle imaging and hidden phase

Gregory C. Dente
Appl. Opt. 39(10) 1480-1485 (2000)

Matrix formulation of the reconstruction of phase values from phase differences

B. R. Hunt
J. Opt. Soc. Am. 69(3) 393-399 (1979)

Speckle imaging, photon by photon

Lawrence N. Mertz
Appl. Opt. 18(5) 611-614 (1979)

Signal-to-noise comparison of deconvolution from wave-front sensing with traditional linear and speckle image reconstruction

Byron M. Welsh and Michael C. Roggemann
Appl. Opt. 34(12) 2111-2119 (1995)

Phase-gradient reconstruction from photon-limited stellar speckle images

George J. M. Aitken and Robert Johnson
Appl. Opt. 26(19) 4246-4249 (1987)