| Aspheric surfaces have more degrees of freedom than traditional spherical surfaces,allowing for precise correction of aberrations during the imaging process without increasing the number of components.This reduces the complexity of the system structure and improves the imaging quality,making them widely used in fields such as astronomy,medical machinery,and industrial testing.With the rapid progress of astronomical optical technology,the demand for higher resolution of optical systems and energy harvesting techniques has increased.Moreover,due to the envelope limitation of satellite fairing,a lightweight,foldable,and easy to carry large aperture space-based telescope is required.Therefore,the use of splicing telescopes instead of full mirror telescopes makes the concept of ultra large aperture telescopes possible.In order to achieve the surface shape accuracy of the entire mirror surface for largeaperture segmented aspherical mirrors,it is necessary to ensure that the position of each lens can meet the requirements,achieving the alignment of the overall surface shape.This requires each segmented mirror to have high surface shape accuracy and geometric parameter accuracy.Therefore,one of the key challenges for large aperture segmented aspherical mirrors to be equivalent to the same mirror surface is high-precision detection of both surface shape and geometric parameters.This thesis focuses on the challenge of high-precision test of large aperture segmented aspherical mirrors,and mainly completes the following work:1.Research on the imaging theory of segmented aspherical mirrorsBased on the wavefront aberration theory of optical components and Strehl Ratio(SR)theory,the imaging aberration theory of large aperture segmented aspherical mirrors is analyzed.An analysis was conducted on the impact of the shape,position,and geometric parameters of the assembled aspheric mirror on the overall surface accuracy.Provide the index requirements for each parameter of the spliced aspherical mirror with N=36,diameter of 320mm,and radius of curvature of 2000mm,when the Strehl ratio is greater than 0.8.2.Theoretical study of wavefront optical spacingUnder the conditions of interferometric compensation testing,the characteristics of each degree of freedom of segmented mirrors are analyzed,and the eigenvalue of geometric parameters along the wavefront propagation direction of segmented mirrors are defined.The spacing between the wavefront at the ideal design position and the wavefront at the actual detection position is defined as the wavefront optical spacing(WOS).The effect of the equal wavefront optical spacing on the test of aspheric and free-form surface shapes is theoretically derived.Quantitative simulation analysis is performed on a freeform mirror with a radius of curvature of-2139mm,and the influence of wavefront optical spacing of d=-0.44mm on surface error is simulated and analyzed.3.Research of cat-eye CGH test methodFor the test problems of wavefront optical spacing of large-aperture segmented aspheric off-axis sub-mirrors,the test method of cat-eye CGH is proposed based on the theory of cat-eye method combined with computer generated hologram(CGH)test technology.A test model for cat-eye CGH was established,and the optical path design and pattern layout design for cat-eye CGH were carried out.In addition,the contrast of interferometric fringes,carrier frequency,and fringe density were analyzed,and the encoding method for making cat-eye CGH was studied.The solution method of wavefront optical spacing is derived,and the feasibility analysis of wavefront optical spacing for cat-eye CGH test is carried out,including the method accuracy analysis and simulation.The contribution rate of each optical path was calculated for a large-aperture segmented off-axis mirror with a diameter of ?320mm and radius of-2139mm,and the method test accuracy was analyzed,and the accuracy was 8.5μm.4.Research on generalized cat-eye CGH test methodIn order to solve the problem of testing wavefront optical spacing in large-aperture segment aspheric center mirrors,the concept of a generalized cat-eye was proposed,and a test model for generalized cat-eye CGH was established.Research was conducted on the test method of generalized cat-eye CGH,including optical path and pattern layout design,cat-eye point calculation,phase function calculation,interference fringe contrast analysis,etching depth calculation,carrier frequency analysis,and line density analysis.The encoding method for making cat-eye CGH was also studied.The method sensitivity was analyzed,and the calculation formula for testing wavefront optical spacing using generalized cat-eye CGH was derived.The precision of the method was analyzed and verified through simulation.The analysis showed that for aspheric center mirror with a diameter of ?650mm,radius of 1968.08mm,and conic constant of-0.9986,the method accuracy was 9.0μm.5、Large-aperture segmented aspheric mirror test experimentExperimental verification of the cat-eye CGH theoretical method and the generalized cat-eye CGH theoretical method proposed in this paper were carried out.First,a adjustment experiment were performed to address the problem of non-coinciding focal points in the optical path.Then,the theoretical method of cat-eye CGH for ?320mm,R-2139mm mirror was verified through methodological experiment and repeatability experiment.The absolute test accuracy of the method was obtained as 10.2±4.3μm(P=95%),the repeatability as 4.5μm,and the relative accuracy as 2.1 ppm.For the proposed theoretical method of generalized cat-eye CGH,a mirror with a diameter of 650 mm and R-1968.08 mm was used to construct the optical path for repeatability experimental verification and test accuracy experimental verification.The experimental results showed that the test accuracy of this method is 11.4μm,the repeatability of 12.9μm,and the relative test accuracy is 6.5ppm.Finally,the co-focal experiment was conducted to verify the correctness of the method proposed in this thesis.In this paper,research work is carried out around the curvature consistency test problem of high-precision test of large aperture segmented aspheric mirrors.According to the aberration theory,the test accuracy requirement for degrees of freedom along the propagation direction of light waves is tens of microns.The concept of wavefront optical spacing is proposed,and the influence of wavefront optical spacing on the front surface test is quantitatively analyzed.The test method of cat-eye CGH is proposed for the test of segmented aspheric off-axis sub-mirror with the accuracy of 10.2μm ± 4.3μm(P=95%),repetitive test accuracy of 4.5μm,relative test accuracy of 2.1 ppm.The test method of generalized cat-eye CGH is proposed for the test of wavefront optical spacing such as segmented aspheric central mirror,and the test model of generalized cat-eye CGH is established,and the test accuracy of mirrors with a curvature radius of 2 meters is verified to be 11.4μm,repeatability of 12.9μm,and the relative test accuracy is 6.5ppm through experiments.Through the research on the key technology of highprecision test of large-aperture separated aspheric mirrors,it is possible to develop super-large aperture astronomical telescopes,which is of great significance for the development of astronomical optics and space. |
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