Wavelength-tuning phase-shifting interferometry has advantages over conventional hardware phase-shifting for the simultaneous detection of all surfaces of the transparent parallel flats. The Fourier transform and its derivative methods can be used to characterize the signal based on the optical path difference and the phase-shifting value of the corresponding interferometric harmonic signals on each measured surface and to solve for the phase accordingly. Therefore, considering the influence of the sampling length and the choice of the window function in the Fourier transform on the measurement results, based on the established multi-surface interference model, an adequate simulation analysis is carried out, and the corresponding explanations and discussions are given subsequently. In practical measurements, the appropriate window function and sampling length should be selected according to the corresponding measurement conditions, so that reliable measurements can be guaranteed.
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.
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.
Wavelength tuning laser interferometry can measure the front and rear surface profile and thickness variation of transparent plate at one time. Separating the collected aliasing fringe patterns containing multi-surface interference information can obtain the surface shape information of each surface of the transparent plate. However, in the process of image acquisition and transmission, it will inevitably be affected by noise, and the existence of noise will affect the separation of multi surface shape information, and further affect the recovery of each surface phase and the accurate acquisition of three-dimensional shape. In this paper, a noise reduction method of aliasing fringe pattern based on convolutional neural network is proposed. The simulation data and experimental fringe patterns show that the network can effectively improve the quality of fringe patterns, has faster calculation speed.
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