Research On Aspheric Surface Detection And Algorithm Based On Sub-aperture Splicing And Transverse Shear Interference Technology

Aspheric optical elements have excellent optical properties,but owing to its complex surface shape,it is difficult to test the surface shape.In order to solve this problem,the relevant research is carried out,including the sub-aperture stitching methods and the lateral shearing interferometry.For the sub-aperture stitching method,according to the characteristics of the aspheric surface,the model of the annular sub-aperture division based on the principle of fringe resolution is established,and then a specific aspheric surface is divided as an example.After that the principle and mathematical formula of sub-aperture phase extraction method,real-time domain phase-shifting method is given,meanwhile the actual phase extraction simulation is carried out.Finally,the sub-aperture stitching algorithm: successive stitching methods and global-error equalization methods are introduced,and the corresponding mathematical derivation is given.In order to verify the feasibility of the stitching algorithm,the global-error equalization algorithm is used to simulate the stitching and reconstruction of the above partition examples,and good stitching results are obtained.For the lateral shearing interferometry technology,the principle was studied in detail firstly.According to the principle,the mathematical model of the four-wave lateral shearing interferometry is given,and the mathematical expression of the interferogram is deduced.Then,the actual simulation of the wave-front to be measured of an aspheric surface is carried out,and the four-wave lateral shearing interferogram of the wave-front is obtained.According to the characteristics of the four-wave lateral shear interferogram,the Fourier transform space-carrier method is proposed to extract the differential phase.Finally,the wave-front reconstruction is realized by using the Difference-Zernike polynomials to fit the wave-front.The results show that the reconstruction precision of the annular sub-aperture stitching is higher than four-wave lateral shearing interferometry,but the testing range of the four-wave lateral shearing interferometry technology is larger than the annular sub-aperture stitching.Theoretically,if the two methods can be integrated organically,maybe achieve a large range of high-precision testing of aspheric surface,which is also the future research of this subject.