PHASE RETRIEVAL WITH THE TRANSPORT-OF-INTENSITY EQUATION - MATRIX SOLUTION WITH USE OF ZERNIKE POLYNOMIALS

A new technique is proposed for the recovery of optical phase from int ensity information. The method is based on the decomposition of the tr ansport-of-intensity equation into a series of Zernike polynomials. An explicit matrix formula is derived, expressing the Zernike coefficien ts of the phase as functions of the Zernike coefficients of the wave-f ront curvature inside the aperture and the Fourier coefficients of the wave-front Analytical expressions are given, as well as a numerical e xample of the corresponding phase retrieval matrix. This work lays the basis for an effective algorithm for fast and accurate phase retrieva l.