Self-calibrating algorithm for three-sample phase-shift interferometry by contrast levelling

Abstract

A new statistical self-calibrating algorithm for phase-shift interferometry is presented. The algorithm can be applied to the case of three phase-shifted interferograms for which the assumption of a constant fringe contrast over the viewing field can be made. Self-calibration is achieved by minimizing the non-uniformity that appears in the map of the calculated contrast when incorrect phase shifts are supposed. No information on the actual phase shifts has to be supplied, the only input needed is the set of three interferograms. The residual errors of the algorithm are as low as in usual conditions.

Statistical processing of Newton’s rings using discrete Fourier analysis

“…5,[8][9][10][11] A very important application would be to determine the carrier fringe pattern ͑straight equispaced fringe patterns or Newton's rings͒ used to reconstruct the optical phase map, as described in Ref. 9.…”

Statistical self-calibrating algorithm for phase-shift interferometry based on a smoothness assessment of the intensity offset map

“…(2) which can be derived from the system (1) by multiplying the three equations with coefficients chosen so that the influence of ϕ and V will be eliminated after the equations are summed. The non-symmetrical formula given in [7] (equation (A11) there) can be used as well, with identical results.…”

“…As we announced in [5], we continue our series of statistical self-calibrating algorithms [6,7], belonging to this category, by presenting here another method of retrieving the values of the phase steps that generate a set of three phase-shifted interferograms. The principle of this algorithm, as with the preceding ones, consists of defining and calculating a feedback quantity which allows an estimation of how well the supposed values of the phase shifts match the actual ones.…”

“…The second statistical algorithm [7] is based on the assumption that the fringe contrast is constant and has the same value in all three interferograms. An initial set of supposed phase steps is taken and the feedback quantity is calculated as the uniformity of the resulting contrast map.…”

Phase-shifting method contrast calculations in time-averaged interferometry: error analysis

“…[9][10][11] In that application, the interferogram contrast or modulation analyses using TPS-relevant algorithms are limited. 12 A different situation is encountered in the spatial carrier phase-shifting ͑SCPS͒ method used to obtain the envelope of interferogram modulation in the object surface microprofilometry 13 ͑white light interferometry͒ and optical coherence tomography ͑OCT͒ for biotissue investigations. 14 Later we present an error analysis of the TPS method applied to the interferogram contrast.…”