PHASE RETRIEVAL WITH THE TRANSPORT-OF-INTENSITY EQUATION - MATRIX SOLUTION WITH USE OF ZERNIKE POLYNOMIALS
TE GUREYEV, A ROBERTS, KA NUGENT
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION | OPTICAL SOC AMER | Published : 1995
A new technique is proposed for the recovery of optical phase from intensity information. The method is based on the decomposition of the transport-of-intensity equation into a series of Zernike polynomials. An explicit matrix formula is derived, expressing the Zernike coefficients of the phase as functions of the Zernike coefficients of the wave-front curvature inside the aperture and the Fourier coefficients of the wave-front boundary slopes. Analytical expressions are given, as well as a numerical example of the corresponding phase retrieval matrix. This work lays the basis for an effective algorithm for fast and accurate phase retrieval. © 1995 Optical Society of America.