Discontinuous phase unwrapping based on the minimization of Zernike gradient polynomial residual

In many certain optical metrology cases, the pupil is usually divided into multiple connected domains by secondary mirror spiders, thus producing segment piston errors and leaving a false phase unwrapping result. In this paper, a method based on minimization of Zernike gradient polynomial residual (MZGR) is proposed to estimate segment piston errors and correct erroneous phase unwrapping results. Simulations and experiments demonstrated that this method can obtain the segment piston errors precisely under complex aberration forms and varied obscurations, indicating reliable practicality. Comparison to the 4D commercial solution, the RMS (root-mean-square) of the residual decreased from 0.154 λ to 0.020 λ.