Phase retrieval and Zernike decomposition using measured intensity data and the estimated electric field

A new direct search phase retrieval technique for determining the optical prescription of an imaging system in terms of Zernike coefficients is described. The technique provides coefficient estimates without the need to defocus point source images to generate phase diversity by using electric field (E-field) estimates in addition to intensity data. Numerical analysis shows that E-field patterns in the image plane produced by the Zernike polynomials are less correlated with each other than the intensity patterns. Therefore, the E-field pattern provides more information for Zernike coefficient estimation than the intensity pattern alone. The phase retrieval is accomplished through an iterative process that uses the measured point source data to estimate the E-field pattern in the image plane with the Gerchberg-Saxton (GS) algorithm. The estimated E-field is correlated with a modeled E-field to produce estimates of the Zernike coefficients. Then the coefficients that minimize the error between measured data and the intensity model are selected. By using E-field estimates rather than phase estimates from the GS algorithm, the limitations of phase unwrapping for Zernike decomposition are avoided. Simulated point source data shows the new phase retrieval algorithm avoids getting trapped in local minima over a wide range of random aberrations. Experimental point source data are used to demonstrate the phase retrieval effectiveness.