Gerchberg-Saxton algorithm applied to a translational-variant optical setup.

The standard Gerchberg-Saxton (GS) algorithm is normally used to find the phase (measured on two different parallel planes) of a propagating optical field (usually far-field propagation), given that the irradiance information on those planes is known. This is mostly used to calculate the modulation function of a phase mask so that when illuminated by a plane wave, it produces a known far-field irradiance distribution, or the equivalent, to calculate the phase mask to be used in a Fourier optical system so the desired pattern is obtained on the image plane. There are some extensions of the GS algorithm that can be used when the transformations that describe the optical setup are non-unitary, for example the Yang-Gu algorithm, but these are usually demonstrated using nonunitary translational-invariant optical systems. In this work a practical approach to use the GS algorithm is presented, where raytracing together with the Huygens-Fresnel principle are used to obtain the transformations that describe the optical system, so the calculation can be made when the field is propagated through a translational-variant optical system (TVOS) of arbitrary complexity. Some numerical results are shown for a system where a microscope objective composed by 5 lenses is used.