Extending the Measurement Range of Interferometers Through the Use of a Priori Information

Abstract

The primary limitation of conventional phase-shifting interferometry (PSI) is its inability to measure the shapes of surfaces or wavefronts with large departures from a best-fit reference sphere. The surface must have limited asphericity. The reason for this limitation is that the current phase-shifting algorithms will correctly reconstruct the wavefront only if the change of the wavefront between adjacent measurement points is less than a half wave. This requirement arises from the need to remove the 2π phase discontinuities that result from an inverse tangent in the data reduction algorithm for PSI. These statements are equivalent to saying that the maximum permissible fringe frequency in the interferogram is the Nyquist frequency of the sensor (there must be two samples per fringe). Fringes at higher spatial frequencies are aliased by the sensor.