基于等光程性的光学自由曲面构造方法研究
Research of the construction method for optical free form surfaces based on aplanatismYE Jingfei, GA
Research of the construction method for optical free form surfaces based on aplanatism YE Jingfei, GAO Zhishan, LIU Xiaoli, YANG Zhongming Abstract: (Institute of Electrical Engineering&Photoelectric Technology, Nanjing, 210094,China) The representation and design of the optical free form surfaces(OFFS) is anotably topic in the modem optical system design. In this paper, despite the challenges in manufacture and metrology of optical free form surfaces, an computing algorithm for constructing the OFFS based on the aplanatism in geometrical optics is presented conceived by Winston. Equations for getting the surface data are derived by geometric optics and ray vectors. The treatment of equivalent abbe sphere is proposed in the algorithm to make it more straightforward than Wassermann-Wolf differential equations. Meanwhile, the treatment is an improvement relating to Winston's method. Some considerations and restrictions that validate the algorithm are discussed. According to the algorithm, tabular data shape is derived and sampled data points are well fitted by Chebyshev polynomials, thereby gaining the great approximate optical surfaces. Key words: geometric optics, free form surface, representation, aplanatism 0Introduction 7, Recently optical free form surface((9/MS) has been widely discussed and investigated in terms of its representation, design, metrology, manufacture and application. Optical free form surfaces play akey role in the design of modern optical systems, especially in ofT-axis systems. They can reduce the count of optical components and make the structure of the system compactness, most importantly help to control high order OFFS aberrations that can improve optical performance substantially. For optical designers, provide more degrees of freedom than using conventional rotationally symmetric optical surfaces such as spherical and aspherical surfaces. OFFS As we know, the representation of is afundamental and key problem. There are afew OFFS, understandings on the design of (l)start from the spherical surface and gradually aspherize it until the desired imagery performance is obtained, (2)begin with quadric surface added by power series that is a combination of base functions and thereafter introduce tilts, displacement, and deformation, (3)design the surface from the optical axis to the off axis, and then choose the required portion for the specific application OFFS). such as off^axis ellipsoid surface(also can be regarded as Ozanti] presented the use of radial basis OFFS. ftmctions(7?BF) for describing Forbes[2j proposed anew set of orthogonal functions to represent surface shape which is feasible to manufacture with asmall number of coefficients. Yabeq introduced anew OFFS representation of shape by modifying orthogonal functions for the simple and efficient optimization. Forbes and Yabe's viewpoints are based on the standard way of representing ageneral aspheric which is a OFFS. power series added to abase conic and then by means of modifying it to obtain Wasserman and Wolffs derived two simultaneous differential equations to devising aspheric surfaces for given centered system, W- W)OFFS Dewen Cheng[5] improved the Wassermann-Wolf( differential equations to design off-axis prism which is applied in head mounted display(MWD) system. These Foundations: the National Natural Science Foundation of China(NSFC, No: 6067804& 60977008), the Doctoral Foundation of Ministry of Education(No: 20103219110014) and Open Foundation of Chinese Academy of Science(CAS) Key Laboratory(No: 2008DP173445) Brief author introduction: Ye Jingfei(1988-), male, PhD candidate, optical design Correspondance author: Gao Zhishan(1966-), male, Professor, optical design and optical measurement. E-mail: OFFS representations or design methods of sometimes seem to be very zhishgao@mail.njust.edu.cn cumbersome. OFFS The finial goal applying into the imaging optics is to achieve better imaging quality than conventional optical surfaces, as mentioned above. In geometrical optics, perfect imaging is approached by satisfying the rigorous aplanatism, although it is sometimes difficult to realize in the practical optical devices.
