Phase retrieval of optical gratings in transparent media

While calculating intensity patterns from a given phase distribution is a straight forward task, the inverse problem requires sophisticated algorithms often referred to as phase retrieval algorithms. Especially, the Gerchberg-Saxton algorithm is widely used, e.g. for the design of beam shapers, and is well suited for two-dimensional holographic structures where it provides a good approximation to the desired intensity distributions. It was demonstrated by Berlich et al. that the Gerchberg-Saxton algorithm is capable of retrieving phase distributions in already existing thin gratings. However, the search for solutions to form a given intensity distribution in the diffraction maxima of a phase-only grating is a one-dimensional problem which generates a large number of solutions. In this work, we utilize an alternative iterative algorithm that was first published by Farn. In comparison to the Gerchberg-Saxton algorithm, Farn's algorithm provides various advantages in the one-dimensional case which is the focus in this work. We especially discuss the influence of resolution and initial phase on the fit performance and the validity of the obtained solutions.