A statistical method for fringe intensity-correlated error in phase-shifting measurement: The effect of quantization error on the N-bucket algorithm

The effect of the quantization of the fringe intensity on the phase error for the general N-bucket algorithm of phase-shifting measurement is formulated. An expression for the statistical relationship between the measured phase error and the fringe intensity error is presented. The expansion of the intensity quantization error in Fourier series allows one to obtain an analytical expression for the variance of the phase given by a general N-bucket algorithm. A numerical simulation was performed and its result is in good agreement with the analytical one. Several factors influencing the quantization effects are discussed.