Distortion mapping correction in the AIMS primary mirror testing by a computer-generated hologram

The National Solar Observatory is currently developing the Accurate Infrared Magnetic Field Measurements of the Sun (AIMS). The primary mirror of the AIMS solar telescope is an off-axis parabolic with a diameter of 1 m and with a large off-axis amount of 1 m. Due to the surface figure of the primary mirror under the used state is directly related to image quality of the whole system, a computer-generated hologram (CGH) is carried out to test the primary mirror, and the test results are used to polish the mirror to a higher surface accuracy. However, the fact that the distortion exists in the testing results leads to the failure of a further guide to deterministic optical processing. In this paper, a distortion correction method is proposed, which uses an orthogonal set of vector polynomials to mapping the coordinates of the mirror and the pixels of fringes, and then an interpolation method is adopted to obtain the corrected results. The testing accuracy by using CGH is also verified by an auto-collimate test experiment. According to the distorted corrected results, the root-mean-square of the surface figure is about 1/50 lambda (lambda = 632.8 nm) after polishing.