Multi-step phase-shifting algorithm based on extended averaging technique and its error suppression characteristics comparison

In order to meet the requirements of nano or even hypo-nano measurement accuracy in phase-shifting interferometry, multi-step phase-shifting algorithms with lower sensitivity to errors are needed. Based on traditional 4 and 3 steps algorithms, class A and class B of 5 to 13 steps phase-shifting algorithms were deduced based on extended averaging technique. Take 5, 6, 7 and 13 steps algorithms as example, suppression characteristics of algorithms to PZT phase shift error and CCD non-linearity error were compared through simulation and numerical calculation. The results show that the error suppression effect to above two error sources becomes better with the increasing of its steps, but when the steps reach a certain number, the values of errors are insignificant for the measurement. Class B algorithms have enhanced phase shift error suppression effect, and as for large phase shift error, class B algorithms are preferred. Class A algorithms are almost completely immune to 2nd order CCD non-linearity error, class B algorithms have some sensitivity to this error, but the influence are very small for most high accuracy CCD in common measurement. Also, the phase noise should not be neglected in measurement, and maximum value of PV wavefront measurement error caused by phase shift noise is larger than the noise itself in many times calculation. Wavefront errors of different algorithms caused by different errors were acquired, and the research can provide favorable reference for the using or choosing of suitable phase-shifting algorithm in actual interferometry.