Phase-shifting algorithm inside an optical cavity for absolute length measurement

Phase-shifting interferometry inside an optical cavity is useful for measuring the length of a cubic object and the diameter of a metal sphere. A new error-compensating phase-shifting algorithm is proposed, with which a spatially uniform phase error caused by nonlinear phase modulation can be eliminated. It is shown that the conventional algorithm design for harmonic analysis cannot compensate for this dc error unless the sampling weight definition is extended to a complex number. Specifically, a 3% quadratic nonlinearity in the phase modulation is found to yield a systematic error of 1.5 nm in the object length in many conventional algorithms. A new 13-frame algorithm is described that applies a modified discrete Fourier window and can reduce the dc error to less than 0.5 nm.