Research On Aspheric Surface Measurement Technology With Multi-Azimuth Shearing Phase-Shifting Interferometry

With the rapid development of optical precision manufacturing technology and the widespread application of non-spherical optical components in optical systems,there are increasing demands for the surface shape measurement of non-spherical optical elements.Lateral shear interferometry is an effective method for detecting non-spherical surfaces without the need for a reference mirror.However,existing lateral shear interferometers typically only obtain two sets of wavefront data in orthogonal directions,resulting in low phase reconstruction accuracy due to the small number of sampling points used for phase reconstruction.In order to achieve higher accuracy wavefront reconstruction,research on absolute common-path multi-directional synchronous phase-shifting shear interferometry technology has been conducted to avoid nonlinear problems and environmental effects during the phase-shifting process.This approach can obtain shear wavefront information in multiple directions,solve the coefficients of the tested wavefront by differential wavefront information in multiple directions,and recover the final surface shape by coefficient fusion,while effectively eliminating the impact of system random errors and improving the surface shape reconstruction accuracy.This dissertation systematically studies the multi-directional shear phase-shift interference detection method based on birefringent crystals and conducts simulation and experimental research.The main contents of this study are as follows:Propose an absolute common-path synchronous phase-shifting multi-directional shear interferometry measurement path for aspherical surface shape measurement.The polarization state model of the system is constructed using the Jones matrix method,and the intensity distribution of the interference fringes on the detector’s image plane is obtained.The feasibility of the theoretical verification method is demonstrated.Furthermore,the integration of a polarizer,a birefringent crystal,and a quarter-wave plate as a single unit is accomplished.Through rotational manipulation,combined with the different phase shifts experienced by left-and rightcircularly polarized light under the action of different polarization analyzers,multi-view shear and synchronous phase shifting are achieved.Study the specific implementation method of multi-directional shear and synchronous phase-shifting.The research focuses on the modulation of the birefringent crystal beam,the diffraction characteristics of the phase grating,the polarization orientation of the lens array,and other aspects.Multi-directional shear cutters,phase gratings,pinhole apertures,and polarizer arrays are designed and manufactured.The relevant parameters of the devices are calculated to complete the selection,and the azimuth of the quarter-wave plate and polarizer array that affect the phase shift accuracy are calibrated,and the system is precisely debugged.Build an experimental measurement system.To test the feasibility and correctness of the system,a spherical sample is measured for verification.The results of measuring a 50 mm diameter,400 mm radius of curvature spherical reflection mirror using multi-directional lateral shear interferometry are consistent with the results obtained by a ZYGO interferometer.The PV detection accuracy error is better than λ/20,and the RMS detection accuracy error is better thanλ/100 compared to the ZYGO interferometer.This verifies the correctness of the multi-directional shear interferometry system.Non-spherical surface measurement experiments are conducted.The non-spherical sample with a diameter of 90 mm,a vertex curvature radius of 606 mm,and a second-order conic coefficient of-1 was measured for its surface shape.The measured deviation of the non-spherical surface relative to the best-fit sphere was obtained.Additionally,the ideal deviation of the nonspherical surface relative to the best-fit sphere was calculated using ray tracing.The results of the two comparisons were found to be consistent with each other and in agreement with the results obtained from the ZYGO interferometer’s self-collimation method.The root mean square(RMS)value of the measurement deviation was better than λ/100.These experiments validate the effectiveness of the multi-view transverse shear system for measuring non-spherical surfaces...