No abstract

A new self-calibrating algorithm is described that succeeds in reconstructing an almost error-free wavefront from only three interferograms. The algorithm is based on the assumption that the optical phase, taken modulo 2π , is quasi-uniformly distributed in the range [0, 2π) over the field of the interferograms. When the actual reference phases differ from those considered in the phase computation program a non-uniform histogram of the computed phase results. An analysis of this histogram allows a fitting procedure to find the actual phase shifts. Eventually an accurate shape of the wavefront can be calculated or a corrected signal can be sent to the phase-shifting device.

A self-calibrating algorithm for phase-shift interferometry is described that is able to cancel the effect of accidental relative tilts that may occur during phase stepping. The algorithm is able to retrieve both the phase steps and the tilts that accompany them. Only three phase-shifted interferograms are needed, and no other information about the intentional phase shifts or possible tilts has to be supplied. This purpose is achieved by division of the interferogram space into blocks on which a previously reported self-calibrating algorithm is applied and the actual values of the local phase shifts are calculated. The information thus obtained is used for extracting the global shift and tilt values. Further improvement in the results is achieved by means of a fitting routine.

Our paper provides analytical expressions for the statistical errors related to statistical processing of digitally recorded Newton's rings interference patterns by least squares fitting. These results completes some of our previous papers concerned with Newton's rings fringe patterns processing, which well describe an iterative numerical algorithm that we commonly use for fringe processing3'4.

We present a practical numerical method for processing the fringes obtained when two waves, with a quadratic phase difference function, interfere. This kind of fringe includes straight equispaced fringes and Newton's rings as particular cases. The numerical method we present is based on the discrete Fresnel ͑Fourier͒ transform of the data and has the same precision as least square fitting ͑LSF͒. Compared to the LSF method, this new method is better, as it is more efficient and does not require initial approximations for the fringe parameters to be determined.