Research On The Modeling And Application Of Aspheric Interferometry,based On Ray Tracing And Characteristic Function

With the development of advanced optical manufacturing and metrology,aspheric part is widely used in large optical systems(astronomical telescope and laser fusion,et al),integrated circuit industry(lithography),consumer optics,et al.The manufacturing of aspheric part is based on aspheric metrology.C urrently,the fulfillment of high-performance optical systems is limited by high-accuracy aspheric metrology while the popularization of aspheric parts in regular optics is limited by flexible and low-cost aspheric metrology.Fizeau interferometer,using transmission sphere,can be directly used to test sphere,while aspheric testing needs special compensation system to transform spheric wavefront to aspheric one,making interference fringes detectable.Computer-generated hologram(C GH)and deformable mirror(DM)are two kinds of typical compensation parts and they meet the requirements of high-accuracy and flexible aspheric metrology,respectively.Modeling Fizeau interferometer and its compensation systems(computer-generated hologram and deformable mirror)is an important method to discern and quantify error sources to improve the accuracy of aspheric metrology.Ray tracing and characteristic function are widely used in modeling optical system.Ray tracing is divided into sequential,non-sequential,polarized and non-polarized one;characteristic function is divided into low-order and high-order one.The task of this thesis is to provide basic modeling principles and procedures for discerning and quantifying error sources in Fizeau interferometer and its compensation systems of computer-generated hologram and deformable mirror,and verify the effectiveness of these modeling principles and procedures.The main content of this thesis is to use sequential non-polarized ray tracing,non-sequential polarized one,low-order characteristic function and high-order one to model some error sources in Fizeau interferometer and its compensation systems.The comparison of the results from different modeling methods or from simulation and experiment is provided to verify the effectiveness of basic modeling methods.The content is divided into:(1)Presenting the inherent relationship among Maxwell's equations,Kirchhoff diffraction theory and geometric optics and its feasible scope;introducing the principles of sequential non-polarized ray tracing,non-sequential polarized one,low-order characteristic function and high-order one,and showing the pros and cons of these tools;analyzing the equivalent ray model of computer-generated hologram in series expansion.(2)In sequential non-polarized ray tracing,Fizeau interferometer model,CGH distortion model and deformable mirror model are built.By Fizeau interferometer model,the accuracy of the designed Fizeau interferometer in ideal condition,the impact of spectrum broadening and environmental stability are discussed,which guide an better design of Fizeau interferometer and help rationally selecting laser source and testing environment.By CGH distortion model,the simulated and measured distortion curves are compared.The small difference between these two curves demonstrates our model can correctly calculate the distortion in C GH aspheric testing.By deformable mirror model,these key factors impacting on the performance of DM system and the measurable range and tolerance of DM are analyzed.(3)In non-sequential polarized ray tracing,the model of figure error of stray light in CGH system is built.The model analyzes the area disturbed by stray light,quantifies the figure error induced by stray light,and lists the main error source of stray light.The simulated and measured figure errors from stray light are compared.The model preliminarily demonstrates the feasibility of using non-sequential polarized ray tracing to model coherent metrology system.(4)In low-order characteristic function,the model of ray error of stray light in CGH system is built.The model analyzes the ray error of stray light on cat-eye plane and compares the ray error with the one from real ray tracing.The basic guiding principles of C GH system design are provided.With these guiding principles,four CGH systems with different structures are designed.The model provides insight into the relationship between CGH stray light and CGH structure parameter s and is useful in designing a preliminary C GH system.(5)In high-order characteristic function,the retrace error model of Fizeau interferometer is built.The reference and testing wavefronts are constructed,the retrace error induced by tilted testing plat is analyzed and compared with the one directly calculated by the sequential non-polarized ray-tracing model of Fizeau interferometer.The comparison shows the high-order characteristic function has the same modeling accuracy as the sequential non-polarized ray-tracing.O ur work is the foundation of retrace error calibration,based on reversely optimizing characteristic function.