The conjugate shift differential method, based on Fourier transforms, is critical for surface error testing of high-precision optical elements. However, this common approach is also prone to periodic spectrum loss. As such, this paper proposes conjugate double shift differential (CDSD) absolute testing, which can effectively compensate for spectrum loss and achieve accurate wavefront reconstructions. Spectrum loss in the single shift differential method is analyzed through a study of the Fourier reconstruction process. A calculation model for the proposed CDSD method is then established and constraint conditions for shift quantities are provided by analyzing double shear effects observed in transverse shear interference. Finally, the reconstruction accuracies of various spectrum compensation methods are compared. Results showed that spectrum loss became more evident with increasing shift amounts. However, the CDSD method produced the smallest measurement error compared with conventional direct zero filling and adjacent point averaging, suggesting our approach could effectively improve absolute shape measurement accuracy for planar optical elements.
The aspheric surface testing system based on the shearing interference principle is used to better analyze how the installation and fabrication errors of linear polarizer affects the precision of the aspheric surface. The effects of the angle error of the linear polarizer and the phase-shifting error of the wave plate on the reconstruction of the aspheric surface are studied. Constructing the model of the Jones matrix with the error term system, the reconstruction surface and residual after the corresponding error system are obtained using the four-step phaseshifting and differential Zernike method. The polarizer array of an angle of θ was varied from ðθ − 1 degÞ to ðθ þ 2 degÞ every 0.2 deg, and the changes of the fitting surface and the residual surface were simulated. The phase-shifting error of the simulated one-fourth wave plate was <λ∕300. Then, the change of the fitting surface and residual surface when these two errors exist at the same time were simulated. The simulation results show that the influence of the phaseshifting error of the wave plate on the fitting surface is much greater than the angle error of the polarizer array. When assembling the interference system, the phase-shifting error of the wave plate should be <λ∕300 when the light transmission angle error of the polarizer array is between −0.2 deg and 0.2 deg, which will ensure the testing precision of the aspheric surface testing system.
For identifying the surface features of ultra-smooth optical or non-optical surfaces, light scattering analysis and measurement is a very useful method. Aiming at the requirement of detecting depth information of surface defects on ultra-smooth surfaces, the author propose a method of measuring the depth information about the surface defects of optical elements by using a relationship model between surface roughness and surface defects. The relationship between surface roughness and surface scratches is analyzed, and the relationship model is established. Then, by simulating the surface roughness with scratches and without scratches, according to the relationship model, the depth information of the surface of the optical component is calculated and the correctness of the model is verified. Finally, the length and width information of the surface scratches are measured according to the microscopic scattering dark field imaging method, the surface roughness is measured by white light interferometry, and the depth information of the surface scratches is calculated according to the above relationship model. The results are compared with the conclusion of the white light interferometer. The depth calculated by the roughness is basically consistent with the measured scratch depth, and the error is between 0.205 nm and 4.246 nm. Therefore, the experimental results demonstrate the effectiveness and feasibility of this proposed method.
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