Evaluation of Two-Dimensional Phase Unwrapping Algorithms for Interferometric Adaptive Optics Utilizing Liquid-Crystal Spatial Light Modulators

A Twyman-Green interferometer is used to measure the phase induced by a liquid-crystal spatial light modula- tor (LC-SLM) via spatial-carrier phase measurement methods in order to characterize the phase response as a function of applied voltage. With the phase response characterized, the LC-SLM can be operated in a closed-loop adaptive optics sys- tem. Four separate phase unwrapping algorithms are evaluated for their ability to unwrap the resulting modulo 2 signal. The evaluation process consisted of measuring the response of the liquid-crystal spatial light modulator to applied volt- ages, creating a response matrix for the liquid-crystal spatial light modulator and then running the device in a closed-loop adaptive optics system using the response matrix. The results indicated that the two least-squares phase unwrapping algo- rithms, based on multigrid techniques and Fourier transform techniques, provided superior performance over a path fol- lowing algorithm and a two-dimensional extension of Itoh's method when using these algorithms in a closed-loop adap- tive optics system.