The influence of phase-shifting algorithms on the instrument transfer function in a Fizeau interferometer

The phase-shifting algorithms are essential for a Fizeau interferometer to reconstruct the topography of the optical element's surface or wavefront. There are differences between different algorithms for reconstruction results, especially for the suppression of noise. To acquire a more accurate instrument transfer function (ITF) which reflects the axial spatial frequency response of a Fizeau interferometer, the algorithm transfer function (ATF) which represents the characteristics of the calculation process in spatial frequency is proposed here. In this paper, numerical simulations were calculated and analyzed several instrument transfer functions of the well-known phase-shifting algorithms (3- frame, 4-frame, 5-frame and 13-frame algorithms). Then, the ITFs of a step plate with a height of 118 nm were measured with different algorithms by experiments and the results were analyzed. The simulations and experimental results indicate that the phase-shifting algorithm has an effect on the ITF measurement and is related to the number of interferograms. When interferograms with a similar number are selected, the ITF values calculated by different phase-shifting algorithms do not differ significantly. Therefore, the phase-shifting algorithm is not a key factor affecting the ITF measurement.