Phase Retrieval Problem is very common and has a lot of applications in fields such as microscope, astronomy, crystallography, optical imaging etc.. In this problem, PSF and the pupil function are given, and the goal is to reconstruct the phase of the object. For camera which has 8 bits color depth, the maximum number of colors that can be displayed at any one time is 2^8 , i.e. 256. When the minimal exposure time of the camera is longer than "correct" exposure time or the intensity is changing, e.g. dynamic focusing, too much intensity is measured by the camera and causes saturation, i.e. over-exposure. Over-exposure causes distortion of the image, thereby losing the information. However, on the other hand, the overall brightness of the PSF image will be enhanced due to over-exposure. It highlight structure and increase the number of informative pixels of the image. We can use this to enhance the information in the PSF image to offset the negative effects of noise or background in the image.
Gerchberg-Saxton algorithm is a solution to phase retrieval problem and is a nice example of projection based algorithm. The algorithm has a perfect performance in the case that the PSF is the modules square of the object, i.e. without noise or other preconditioners effect. It is demonstrated in [Nishizaki, 2019] that an over-exposure preconditioner can improve the performance for phase restoration of a machine-learning model based algorithm. In this master thesis, we propose modification of the model of PSF amplitude in Gerchbrg-Saxton algorithm to make the algorithm be able to cope with over-exposed PSF image. This approach is tested both by numerical simulation and with experimental data.