Transparent parallel flat optical components are found everywhere and used in a wide range of applications. Surface topography and inhomogeneity distribution are important physical parameters for the components. In order to improve the performance and reliability of components, topography should be measured with high accuracy. The weighted multi-step sampling algorithm based on wavelength-shifting interferometry is an effective method for multi-surface topography recovery, which is often based on the three-surface measurement and has poor accuracy for rear-surface measurement. The four-surface measurement can compensate for this drawback, but the system and the solving process are more complex. There are fewer studies on the analysis of algorithm effectiveness. In this paper, through theoretical derivation, it is proved that the validity of the four-surface measurement algorithm is only related to the recovery of three sets of interference signals. The distribution of the wavefront residuals RMS values under different combinations of phase shift coefficients and cavity length coefficients are used to summarize the algorithm error distribution law and the best matching database of phase shift parameters under four-surface measurement is established. The effective cavity length coefficients and phase shift coefficients are selected to compare the wavefront recovery under three-surface and four-surface, and it is verified that the measurement accuracy of the four-surface is better when effective parameters are selected.
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