Phase detection algorithm using step lengths deviation errors and Hough transform in phase-shifting interferometry

In phase-shifting interferometry (PSI), a set of interferograms with a known phase step displacement is necessary, but incorrect calibration deviation errors can occur in shifter devices. We present a method to recover the phase distribution in the presence of this deviation error through the widely used PSI technique. By applying the radon transform as a profile measurement, our algorithm first estimates the deviations in the phase steps, then these calculations are used to obtain the wrapped phase using the Hough transform as an estimation of coefficients in sinusoidal patterns. Simulation and experimental results have shown good performance. The results reveal that this algorithm is able to detect and decrease the phase error due to miscalibrations.