High-precision reconstruction of second- and high-order reference errors based on sub-aperture stitching interferometry

Abstract The reference mirror error in an interferometer is a crucial factor affecting the accuracy of x-ray mirror metrology. In this study, a reference surface (RS) reconstruction method based on redundant data from sub-aperture stitching interferometry (SSI) and the attitudes of each sub-aperture is developed to obtain both second- and high-order surface errors. Theoretical simulations show that the errors of the fitted angle attitudes of sub-apertures and the reconstructed reference increase with the second-order term of the surface under test (SUT). Decreasing the second-order term of the SUT to below 2.5 nm (RMS) can improve the accuracy of the fitted sub-aperture attitudes to below 100 nrad and the reconstructed RS to below 1 nm (RMS). This was experimentally demonstrated using mirrors with different second-order terms in SSI measurements and the accuracy of reconstructed references was verified based on different calibration methods. The accuracy of the overall reconstructed RS reached 0.78 nm RMS and the high-order terms reached 0.37 nm.