Local phase from local orientation by solution of a sequence of linear systems

A technique for recovering the phase from single fringe-pattern images is presented. It is based on the estimation of the local frequency of the pattern by successive decoupled estimation of the local orientation, direction, and magnitude of the frequency field. Once this field is known, the local phase is recovered from the complex output of an adaptive quadrature filter. It is shown that by the use of Gauss-Markov measure field models all these estimation steps may be implemented by solving linear systems of equations (i.e., minimizing quadratic functions), which makes the procedure robust and computationally efficient. Examples are presented of the application of this technique to the recovery of phase fi om single electronic speckle-pattern in terferograms. (C) 1998 Optical Society of America.