Error-compensating phase-shifting algorithm for surface shape measurement of transparent plate using wavelength-tuning Fizeau interferometer

•New 13-sample phase-shifting algorithm is proposed.•The characteristics of 13-sample algorithm is estimated in the frequency domain.•The phase error of 13-sample algorithm is compared with those of other algorithms.•Surface shape is measured by wavelength tuning and 13-sample algorithm.

When measuring the surface shape of a transparent sample using wavelength-tuning Fizeau interferometry, the calculated phase is critically determined by not only phase-shift errors, but also by coupling errors between higher harmonics and phase-shift errors. This paper presents the derivation of a 13-sample phase-shifting algorithm that can compensate for miscalibration and first-order nonlinearity of phase shift, coupling errors, and bias modulation of the intensity, and has strong suppression of the second reflective harmonic effect. The characteristics of the 13-sample algorithm are estimated with respect to Fourier representation in the frequency domain. The phase error of measurement performed using the 13-sample algorithm is discussed and compared with those of measurements obtained using other conventional phase-shifting algorithms. Finally, the surface shape of a fused silica wedge plate obtained using a wavelength tuning Fizeau interferometer and the 13-sample algorithm are presented. The experimental results indicate that the surface shape measurement accuracy for a transparent fused silica plate is 3 nm. The accuracy of the measurement is discussed by comparing the amplitudes of the crosstalk noise calculated using other conventional algorithms.