Generalized-Mode Averaging Technique for Wrapped Phase

In this paper, a generalized-mode phase averaging technique is proposed to suppress air turbulence and random noise in optical shop testing. This approach eliminates the need to repeatedly unwrap and thus greatly improves processing efficiency. By removing the random tilt component of the wrapped phase, a set of wrapped phases that are corrupted by random vibrations can be unified into the same mode, some of which obey a circular distribution. Therefore, the circular mean technique can be used for wrapped phase averaging; only one unwrapping process is required for a set of wrapped phases. A criterion based on maximum likelihood estimation is proposed to determine scenarios for the use of this method. The effects of noise and air disturbances on this method are discussed. Finally, the effectiveness of the method is demonstrated by simulations and experiments.