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.
Wavelength-tuning phase-shifting interferometry (WPI) is a feasible method to measure transparent parallel plates. But the existing algorithms are effective when the measurement positions are fixed. To overcome the limitations, this paper proposes a multi-surface measurement method at arbitrary positions based on the four-surface interferometry. The proposed method consists of two parts: a multi-surface phase demodulation algorithm, and a selection technique of the optimal phase-shifting sampling parameters for the measured plates at arbitrary positions. The results of the simulations verify the effectiveness of the proposed algorithm.
The surface morphologies and thickness variation are the basic characteristics of a transparent parallel plate with multiple surfaces. Measurements of these profiles are greatly significant for the evaluation of surface quality. The measurement accuracy of phase-shifting interferometry can reach the nanometer level, which is an effective method for high-precision measurements of ultra-smooth surfaces. However, each measured surface will give its own harmonic to the captured interferograms, resulting in the information of harmonics mixed. Thus the surface topology information can not be detected directly, which can cause problems of the wavefront reconstruction of the measured surface. To solve this problem, separating the mixed harmonics is necessary. The fundamental difference in harmonics lies in their frequency. Therefore, determining these differences of harmonics by frequency is a preliminary method of phase demodulation.
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