Design Method of the Telescope with Freeform Surfaces Based on Optical Ellipticity Criterion

The aberration of the telescope system itself can easily lead to the change of its optical ellipticity, which interferes with the detection of dark matter. To ensure the accuracy of dark matter detection,the ellipticity of the telescope system must be precisely controlled. In this paper,an optical design method for telescope with freeform surfaces incorporating optical ellipticity criterion is proposed. It addresses the challenge of traditional optical design methods in which optical design software is unable to directly take the ellipticity in the merit function. Implementing the numerical interaction between optical design software Zemax and numerical calculation software Matlab through MZDDE. Extract point spread function data from Zemax,calculate the ellipticity value using Matlab algorithm, and then import it into the merit function editor of Zemax to assign weights for optimization. In this way,the astronomical ellipticity is included throughout the optical design procedure. A complete evaluation function system integrating wavefront aberration and ellipticity has been constructed. Based on the relationship between ellipticity and non-rotationally symmetric aberrations such as coma and astigmatism,we put forward the principle of preferentially correcting the aberration components which exhibit stronger correlation with ellipticity. With the help of the full-field aberration map in the optical design software,we analyze the correlation between the aberration nodal distributions and ellipticity node distributions. And the specific freeform surface items to be modified and the surfaces of the freeform items to be added in each step are determined based on the aberration theory. The aberration components with strong ellipticity correlation are taken as the priority correction parameters for iteration,which contributes the design idea of incorporating the ellipticity criterion into the main off-axis aberration correction. Based on the evolution law of aberration nodes and ellipticity nodes in the optimization process of the off-axis three-mirror system, an optimization strategy for the Zernike term of the freeform surface type is established. Accordingly,an off-axis three-mirror freeform surface astronomical telescope is designed,with an effective focal length of 600 mm, an aperture of 200 mm,and a field of view of 4 degrees x4 degrees. Through the joint optimization of wave aberration and ellipticity, the imaging quality and optical ellipticity are synchronously and effectively controlled. The wave aberration is close to the diffraction limit,with the maximum ellipticity value of 0.030 3,and the average value of 0.015 6. It meets the requirements of the dark matter detection with the maximum ellipticity value of less than 0.15 and the average value of less than 0.05. The traditional optimization design method adopts a gradual upgrade of surface shape,gradually adding freeform terms in order from low order to high order, and continuously maintaining the variability of system structural variables during the addition process. This method lacks optimization targeting for the current aberration of the system,and blindly using freeform terms on multiple surfaces will lead to aberration correction degradation and unnecessary freeform surface deviation. Compared with the traditional aberration correction optimization method from low-order terms to high-order terms, the application of the proposed method adopts relatively small freeform surface deviation. By adjusting the aberration nodes,the imaging quality and ellipticity performance of the designed freeform surface telescope are controlled synchronously. The maximum value of ellipticity is further compressed,and the ellipticity distribution is more evenly distributed. The design freedom of the freeform surface is fully leveraged.