Phase retrieval algorithms in the Fresnel domain

There are several known iterative algorithms, which reconstruct the phase of an unknown wavefront from two intensity measurements. These algorithms are based on a Fourier connection between the input and output plane. An algorithm based on a Fourier connection must contain additional optical setup for the implementation and in addition needs more longitudinal space. Since a wavefront is a function that obeys the wave equation, it is only natural to implement the iterative algorithms using free space propagation relation between two intensity planes. We propose to make phase retrieval calculations between any two arbitrary planes interrelated through the Fresnel domain. Since any two arbitrary parallel planes are interconnected by the Fresnel domain, no additional setup is needed. The calculation of the free space propagation is based on the angular spectrum approach, which is calculated using the fast Fourier transform (FFT). This approach can be applied with any of the algorithms that rely on a Fourier connection between the input and the output planes.