Random phase-shifting interferometry without accurately controlling or calibrating the phase shifts

A random phase-shifting interferometry insensitive to environmental noises is proposed. The relationship between intensity and phase in each pixel is obtained from a large amount of phase-shifting interferograms. In the phase-solving algorithm, the phase shift step length is not taken as a parameter, but the temporal intensity maximum and minimum in each pixel are needed. For finding the extreme values, random passive phase shifts caused by environmental noises are adopted to make the intensity ergodic. Supplementary active phase shifts, which are not accurately controlled or calibrated, are performed to shorten the measurement cycle. Finally, averaging statistically uncorrelated data over a long enough period of time can effectively reduce most random errors. A minitype Fizeau interferometer applying this random phase-shifting method demonstrated the feasibility of it.