Abstract

The primary limitation of conventional phase-shifting or heterodyne interferometry (PSI) is its inability to measure the profile 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 only correctly reconstruct the wavefront if the change of the wavefront between adjacent measurement points is less than a half wave. This requirement arises from the need to remove 2π phase discontinuities that result from the 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. Attempts by others to overcome this limitation, which restricts the degree of asphericity permitted on the measured surface, have included using detector arrays with more elements, longer wavelengths, computer-generated holograms and null lenses, or two-wavelength techniques.

© 1986 Optical Society of America