Generalized iterative phase retrieval algorithms and their applications

It is well known that the phase contains more important information about the field in comparison with the amplitude. Therefore the imaging of phase is encountered in many branches of modern science and engineering. Direct measurement of the phase is easy in the long wavelength regime of the electromagnetic spectrum, but is difficult in the short regime such as the visible light due to the limited bandwidth of imaging sensors. One must employ computational techniques to extract the phase from the captured intensity. So far many methods have been proposed for this task. These algorithms can be basically classified into three categories: Holography, deterministic algorithms such as the transport of intensity equation, and iterative algorithms such as the Gerchberg-Saxton-Fienup-type algorithm. Each of these algorithms has its own advantages and disadvantages. This paper mainly focuses on the our previous works on iterative phase retrieval techniques, and their applications in the calculation of computer-generated holograms, microscopic imaging, and optical signal processing.