Measurement of highly reflective surface shape using wavelength tuning Fizeau interferometer and polynomial window function

• 5N − 4 algorithm comprising the polynomial window and discrete Fourier transform was developed based on the characteristic polynomial theory.
• The characteristics of 5N − 4 algorithm were discussed and compared with other conventional algorithms with respect to Fourier representation.
• The phase error calculated by 5N − 4 algorithm was estimated considering not only the phase shift error but also the coupling error.
• The surface shape of the highly reflective silicon wafer was measured by using wavelength tuning interferometer and 5N − 4 algorithm.

In this study, a 5N − 4 phase shifting algorithm comprising a polynomial window function and a discrete Fourier transform is developed to measure interferometrically the surface shape of a silicon wafer, with suppression of the coupling errors between the higher harmonics and the phase shift error. A new polynomial window function is derived on the basis of the characteristic polynomial theory by locating five multiple roots on the characteristic diagram. The characteristics of the 5N − 4 algorithm are estimated with respect to the Fourier representation in the frequency domain. The phase error of the measurements performed using the 5N − 4 algorithm is discussed and compared with those of measurements obtained using other conventional phase shifting algorithms. Finally, the surface shape of a 4-in. silicon wafer is measured using the 5N − 4 algorithm and a wavelength tuning Fizeau interferometer. The accuracy of the measurement is discussed by comparing the amplitudes of the crosstalk noise calculated by other algorithms. The uncertainty of the entire measurement was 34 nm, better than that of any other conventional phase shifting algorithms.