Research On Characterization Function And Application Of Free-form Surface

Free-form surface, which is non-rotational symmetric optical surface, has become a hot research area in the optical industry. The direction of research contains the free-form surface characterization function, the free-form surface optical system design, the free-form surface fabrication with testing, and the free-form surface aberration theory. At present, free-form surface is widely and gradually used in the field of optical engineering. However, with the enhancing requirement of large designing field of view (FOV), relative aperture enlargement, and imaging quality, the non-rotational high-order aberration of the free-form surface system is increased step by step. But the current characterization functions of free-form surface, such as Zernike Function, Gaussian Radial Basis Function (GRBF), and the Q-TYPE Function, cannot provide enough spatial variables to balance the gradually increased non-rotational aberration, which has limited the application of the free-form surface in the system of high-resolution reflecting telescope. Therefore, the creation of new-type characterization function has big significance on the widespread use of free-form surface.It takes a long time to construct the appropriate initial structure for the designers of the off-axis free-form surface system. Therefore, it is also greatly significant to propose an efficient approach to build initial structure of the off-axis free-form surface system for optical design.In recent years, the rectangle and hexagon surfaces, which are non-circular aperture, are widely used in the off-axis free-form surface system. The Zernike Polynomial is not orthogonal over the non-circular aperture, and which function should be utilized to analyze wave-front of the off-axis free-form surface system with non-circular aperture in alignment. All the problems mentioned above must be settled when the free-form surface is applied in the off-axis free-form surface system. This dissertation refers to the research on the free-form surface characterization function and the application of the free-form surface characterization function based on the problems mentioned above. The destination is listed as follows:solve the limitation of surface characterization ability and optimization ability by using most of the existing functions; solve the time-consuming problem when build the initial system structure; solve the non-orthogonal features of the Zernike Polynomial which is used to align off-axis free-from surface system with non-circular aperture. The research contents are mainly explained as follows:(1) By using theoretical analyzing method, firstly, the theory, the advantages and disadvantages, and the corresponding relationship with aberration items of the popularly characterization functions of free-form surface, such as Zernike Polynomial, Q-TYPE, Chebyshev Polynomial, and GRBF are researched deeply. Secondly, one new-type characterization function named New function is established on the basis of the research above. In the meantime, the non-circular orthogonal polynomial theory is proposed. At last, the reason why nodal aberration is not appropriate to guide the alignment of the free-form surface with decentration and tilt is explained.(2) The free-form surface characterization function mentioned in the Section Two is researched by using numerical analysis method. For the selected typical free-form surface, the fitting precision and the optimization ability by using the characterization function are analyzed in order to highlight the fitting precision advantage of the New function. And it is proved that the Zernike Polynomial cannot be directly used in resolving by means of numerical analysis. (3) Focusing on the time consuming problem of constructing initial free-form surface optical system structure, an efficient method for structuring the off-axis free-form surface is proposed. Then, one large field of view (60°) off-axis free-from surface system is designed by integrating New function. The imaging quality and the processing possibility of the optical system are analyzed. The result meets the requirement.(4) The rectangle aperture wave-front is analyzed by using rectangle area orthogonal polynomial named Legendre Polynomial. By integrating the sensitivity matrix method, the rectangle aperture free-form surface system with large field of view is aligned. The result shows that the alignment method is correct, which can use for reference to other non-circular aperture off-axis free-form surface system alignment.