Distance deviation sensitivity on null test of convex hyperboloid mirrors with large relative aperture

In the shape measurement of convex hyperboloid mirrors with large relative apertures, alignment deviations can significantly affect the accuracy of null test results owing to their sensitivity, resulting in inaccurate results. This paper introduces autocollimation and compensation methods. Subsequently, a shape detection experiment of a large relative aperture convex hyperboloid mirror with a diameter of 15 mm was conducted using the aforementioned methods. Further, a detailed simulation analysis was performed to address the inconsistencies between the two test results. The results suggested that the Hindle sphere method was highly sensitive to distance deviation. Furthermore, the distances in the optical path exerted a complementary effect, which easily obscured the true surface shape of the measured part. The computer-generated hologram (CGH) method could accurately determine the true surface shape deviation based on the alignment judgment provided by the aligned CGH part. These studies provide scientific guidance for more accurately obtaining the true surface shape error of the hyperboloid mirror under test, and have significant engineering application value.