PHASE RETRIEVAL WITH THE TRANSPORT-OF-INTENSITY EQUATION .2. ORTHOGONAL SERIES SOLUTION FOR NONUNIFORM ILLUMINATION

In a previous paper [J. Opt. Sec. Am. A 12, 1932 (1995)] we presented a method for phase recovery with the transport-of-intensity equation b y use of a series expansion. Here we develop a different method for th e solution of this equation, which allows recovery of the phase in the case of nonuniform illumination. Though also based on the orthogonal series expansion, the new method does not require any separate boundar y conditions and can be more easily adjusted for apertures of various shapes. The discussion is primarily for the case of a circular apertur e and Zernike polynomials, but we also outline the solution for a rect angular aperture and Fourier harmonics. The latter example may have so me substantial advantages, given the availability of the fast Fourier transform. (C) 1996 Optical Society of America.