Research On The Application Of Freeform Surface In Off-axis Reflective Optical System

With the development of advanced technology,higher requirements are put forward for optical imaging system,such as higher imaging quality,larger relative aperture,wider spectral imaging range,smaller volume,and lighter weight.All these high-performance indices have brought great challenges to the design of modern imaging optical systems.Traditionally,rotationally symmetric optical systems often leverage spherical or aspherical surfaces to correct optical aberrations.However,spherical,or aspherical surfaces just own few degrees of freedom,and the structure of the design is monotonous,which is difficult to meet the application requirements of modern optical imaging.Therefore,it is necessary to adopt new design forms to improve the comprehensive performance of optical imaging systems.Compared with the refractive and catadioptric designs,the off-axis reflective optical system designs own the advantages of no chromatic aberration,insensitivity to temperature change,foldable optical path,easy to lightweight design.However,aberration correction for off-axis reflective systems is also more difficult.Optical freeform surface is defined as an optical surface with no rotational symmetry axis and arbitrary surface shape.Compared with spherical or conic surfaces,freeform surfaces own more degrees of freedom and stronger aberration correction ability,so it is very suitable for aberration correction of off-axis reflective imaging optical system.At present,the off-axis reflective imaging system with freeform surface have been successfully applied in many fields,such as space remote sensing,head-mounted displayer,heads-up displays,extreme ultraviolet lithography objective lens,and will have a significant impact on future development.Although off-axis reflective systems with freeform surfaces have many obvious advantages,the design and optimization of such optical systems are more difficult.How to take the advantages of freeform surfaces to design off-axis reflective systems with excellent overall performance is a problem for optical designers to solve.This thesis focuses on the design method of off-axis reflective optical imaging systems with freeform surface,including the design and optimization methods,the direct design methods,the manufacturing and testing of offaxis aspheric mirror,and specific examples are given in this dissertation.The main research contents can be summarized as follows:(1)Research on aberration theory for off-axis optical systems.The nodal aberration characteristics of the systems with tilted and decentered surfaces,with pupil decentration and with freeform surfaces were analyzed respectively by using nodal aberration theory.For the system with tilted and decentered surfaces,the relationship between the number and position of the third-order aberration nodes and the field decentration vector is analyzed.For the system with pupil decentration,the coupling between different types of aberrations caused by the pupil decentration and the influence on the aberration node are analyzed.For the system with freeform surface,the influence of the Zernike polynomial term of freeform surface on the position and number of aberration nodes is analyzed.The above analysis plays an important guiding role in the design of off-axis reflective system with freeform surface.(2)Research on the design and optimization method of off-axis reflective optical system with freeform surface based on nodal aberration theory.First of all,two methods for solving the initial structure of the coaxial reflective system based on the third-order aberration theory method and based on the optical matrix method are analyzed and compared,and the relationship between the coaxial reflective structure form,the obscure ratio and the transversal magnification is summarized.Furthermore,based on the idea of using freeform surface to adjust and control the aberration nodes,an off-axis reflective optical imaging system with 20°×6° field of view,2500 mm focal length,and F-number 10 is designed and optimized using nodal aberration theory,and the processes including determination of optical system form,calculation of coaxial initial structure parameters,obscuration elimination,selection of freeform surface optimization parameters,structure and size constraints,full-field aberration correction and balance are introduced in detail.Based on the above methods,the efficient and purposeful design and optimization of off-axis reflective system with freeform surface are realized.(3)Research on the design of off-axis reflective system with freeform surface based on direct iterative design method.Given the ideal object-image relationship and the initial structure of the plane,this method first calculates the ideal normal at the sampling point of the surface to be designed based on Fermat’s principle and the vector form reflection law,and then combines the ideal normal and coordinate points to fit the surface to be solved into a freeform.Furthermore,based on the system with freeform surface that has been solved,the imaging quality of the system is improved through multiple iterations,so that an initial structure of off-axis reflective system with good imaging quality can be obtained.Based on this method,a XY Polynomial freeform surface single mirror and an off-axis three-mirror system with focal length of 700 mm and field of view of 14°×5° were designed respectively.The above design process demonstrates the efficiency of the direct iterative design method in the design of offaxis systems with complex structures.(4)Research on mapping distortion correction in off-axis aspheric mirror testing with a null compensator.To solve the problem that the mapping distortion in the offaxis aspheric mirror testing with null compensation lens limits the precision of optical deterministic machining,a fast and efficient mapping distortion correction method is proposed.This method first uses the imaging distortion data of the null lens to determine the law of mapping distortion,and then uses an iterative algorithm to solve the coordinate of the null distortion point and the rotation angle of the testing results and realizes high-precision mapping distortion correction through the algorithm iteration process.Based on this method,the mapping distortion correction is performed on the testing results of the primary mirror and the tertiary mirrors of an off-axis three-mirror system,and the distortion-corrected data is used to guide the deterministic polishing of magnetorheological machine to improve the surface shape accuracy.After no more than6 times of polishing,the surface RMS of the primary mirror and the tertiary mirror is better than λ/50,which shows the effectiveness and high efficiency of this mapping distortion correction method.