Steps length error detector algorithm in phase-shifting interferometry using Radon transform as a profile measurement

Abstract

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.

Fast measurement of wavefront aberration in double-grating Ronchi lateral shearing interferometry

“…Using sinusoidal or quasi-sinusoidal Ronchi gratings is another alternative method that could eliminate the higher diffractions 16 – 20 The impact of high diffraction orders can also be reduced using appropriate phase-retrieval algorithms, such as arbitrary phase shifts 21 and the calibration of relative errors in phase-shifting 22 . From this perspective, the 8-frame, 10-frame, and 13-frame algorithms 23 were designed to extract the shear phase between the +1st and zeroth orders in double-grating Ronchi LSI.…”

“…[16][17][18][19][20] The impact of high diffraction orders can also be reduced using appropriate phase-retrieval algorithms, such as arbitrary phase shifts 21 and the calibration of relative errors in phase-shifting. 22 From this perspective, the 8-frame, 10-frame, and 13-frame algorithms 23 were designed to extract the shear phase between the +1st and zeroth orders in double-grating Ronchi LSI. However, they are still influenced by the interference between the −1st and higher orders (≥ AE9 orders).…”

A high-accuracy phase shifting retrieval approach based on phase shifts search

“…Phase retrieval refers to recovering the phase information from the interferogram of recorded light intensity. Among the methods of phase extraction, phase shifting interferometry (PSI) is widely used in refractive index measurement, three-dimensional (3D) morphology measurement, 3D imaging and other fields due to its advantages of high precision, full-field and nondestructive [1][2][3][4][5][6]. In standard PSI, it is usually necessary to know the phase shifts in advance, and the phase shifts is equal or fixed step length [7][8][9][10].…”

Nanoscale surface characterization using laser interference microscopy

“…This class brings together methods of white light interferometry [1,2], phase shift interferometry [3][4][5], digital holographic microscopy [6,7], laser interference microscopy [8,9], coherent phase microscopy [10], coherent correlation interferometry [11,12], etc.…”