In this research, the susceptibility of the phase-shifting algorithms to the random intensity error is formulated and estimated. The susceptibility of the random intensity error of conventional windowed phase-shifting algorithms is discussed, and the 7N - 6 phase-shifting algorithm is developed to minimize the random intensity error using the characteristic polynomial theory. Finally, the surface shape of the transparent wedge plate is measured using a wavelength-tuning Fizeau interferometer and the 7N - 6 algorithm. The experimental results indicate that the surface shape measurement accuracy for the transparent plate is 2.5 nm. (C) 2016 Optical Society of America.
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