Absolute interferometric testing of an ultra-precise flat substrate with a liquid mirror

The precise characterization of flat substrates is quite challenging for X-ray optics in synchrotron and free electron lasers. The surface requirements for the substrates are on the order of magnitude of few nanometers and sub-nanometers, which is also a great challenge for optical fabrication and testing. As for precise metrology, the core problem is to characterize the surface figure with high accuracy. And the key is to separate the errors of the measurement instrument from the intrinsic figure error of the surface under test. In addition, the surface figure of thin optics is largely affected by surface deformations due to gravity. In the paper, we presented an approach to achieve absolute planarity measurement of a thin x-ray mirror substrate through an interferometric method. With a liquid-flat reference using dimethyl silicone oil, the power term of the surface flatness of the interferometer transmission flat is retrieved. By floating the mirror on a heavy, high density liquid, deflections introduced by gravity are essentially eliminated. The unconstrained, floated x-ray mirror is tested through several rotational and translational shears. The absolute figure error is then calculated by iterative algorithm with pixel-level spatial resolution. By the proposed approach, both the interferometer transmission flat error and gravity-induced error are calibrated. Thus the unconstrained flatness of the x-ray mirror can be obtained. The method is described in detail and a measurement example of an x-ray mirror is provided in the paper.