F/0.78 High Order Aspheric Surface Testing with Null Compensator and Mapping Distortion Correction

Compared with traditional spherical surfaces, aspheric surfaces own more degrees of freedom, which is beneficial to the light weight, integration and aberration correction of an optical system. In recent years, with the development and progress of high-precision optical manufacturing technology, aspheric surfaces have been widely used in the optical systems design in aerospace, space telephoto and other fields. Meanwhile, the testing of aspheric surfaces, especially high-order aspheric surfaces, is more difficult and is a prerequisite for guiding optical deterministic manufacturing. That is to say, it is not only necessary to realize the testing of aspheric surfaces, but also to be able to give correct guidance for manufacturing based on the testing results. At present, aspheric surfaces testing can he achieved with null lens compensator, but for high-order aspheric surfaces with a small F-number, traditional two-piece tens compensator cannot meet the testing accuracy requirements, and the structure of null lens needs to be further optimized. What's more, the shape of interfermetric image obtained with null lens compensator is inconsistent with that of the mirror under test, that is, mapping distortion. It is worth noting that deterministic manufacturing techniques such as Computer Controlled Optical Surfacing (CCOS), Magnetorheological Finishing (MRF), and Ion Beam Figuring (IBF) all require accurate guidance and feedback from interfermetric image, position errors caused by mapping distortion will seriously affect manufacturing efficiency, and even lead to a failure. Therefore, the mapping distortion correction is crucial for the interferometric image to correctly guide deterministic manufacturing. In this paper, not only the design method of high-order aspheric null lens compensator is discussed, but also the mapping distortion correction of interferometric image. Firstly, based on third-order aberration theory and PW method, the initial structure calculation formula of the high-order aspheric three-piece tens compensator is deduced, and the above formula is programmed, which facilitates the null lens compensator design. For an 8th-order even-order aspheric surface with an effective diameter of 311 mm and F/0.78, the initial structural parameters of null tens compensator were obtained by using the calculation formula. Then, it is substituted into the optical design software for scaling and optimization, and finally the design result with PV=0.0096 lambda, RMS=0.0012 lambda (lambda=632.8 mm) can be obtained, which can meet the high-precision testing requirements. Furthermore, a correction method is proposed to solve the problem of mapping distortion in the interferometric image obtained with null tens compensator. This method combines imaging distortion of null lens and an algorithm for solving null distortion point coordinates, which can conveniently realize the rapid mapping distortion correction. On the one hand, null lens imaging system with high-order aspheric surfaces as object can he obtained by reversing the testing light path, and the imaging distortion is consistent with the mapping distortion, which can he used for mapping distortion correction. On the other hand, since the mitt distortion point is also the geometric center of the interfermetric image, the least squares method is used to fit the circle boundary in combination with the boundary data of interfermetric image, and then the null distortion point can be obtained. Then, The correction method is used to correct the mapping distortion of the interferometeric image obtained by null tens compensator. After 6 times of magnetorheological finishing based correction results, the surface RMS reduced from 0.270 lambda to 0.019 lambda, which verifies the validity and efficiency of this correction method.