Phase-shifting is one of the most useful methods of phase recovery in digital interferometry in the estimation of small displacements, but miscalibration errors of the phase shifters are very common. In practice, the main problem associated with such errors is related to the response of the phase shifter devices, since they are dependent on mechanical and/or electrical parts. In this work, a novel technique to detect and measure calibration errors in phase-shifting interferometry, when an unexpected phase shift arises, is proposed. The described method uses the Radon transform, first as an automatic-calibrating technique, and then as a profile measuring procedure when analyzing a specific zone of an interferogram. After, once maximum and minimum value parameters have been registered, these can be used to measure calibration errors. Synthetic and real interferograms are included in the testing, which has thrown good approximations for both cases, notwithstanding the interferogram fringe distribution or its phase-shifting steps. Tests have shown that this algorithm is able to measure the deviations of the steps in phase-shifting interferometry. The developed algorithm can also be used as an alternative in the calibration of phase shifter devices.
We describe a new algorithm for phase determination from a single interferogram with closed fringes based on an unwrapping procedure. Here we use bandpass filtering in the Fourier domain, obtaining two wrapped phases with sign changes corresponding to the orientation of the applied filters. An unwrapping scheme that corrects the sign ambiguities by comparing the local derivatives is then proposed. This can be done, assuming that the phase derivatives do not change abruptly among adjacent areas as occurs with smooth continuous phase maps. The proposed algorithm works fast and is robust against noise, as demonstrated in experimental and simulated data.
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