With the development of optical manufacturing and measurement methods, precision optical elements are used extensively in various fields. As the beam scattering and energy loss caused by the surface defects of optical elements will reduce the lifetime of optical elements and the performance of optical systems, it is important to detect and evaluate the surface defects. However, several technical challenges remain in the surface defect detection of spherical optical elements. In this paper, a spherical defect detection experiment based on the dark-field imaging principle is proposed. The surfaces of two convex spherical optical elements are detected. Meanwhile, the illumination module is improved through experiments. The experimental results are compared with those of a white light interferometer, thereby demonstrating the validity of the method.
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.
In order to realize large-scale absolute surface reconstruction, a generalized iterative optimization method for solving the three-flat problem is studied. First, the idea of model-based absolute surface reconstruction is proposed, which considers the problems of absolute surface reconstruction as inverse problems. Then we take the three-flat problems as an example, we introduced two generalized iterative optimization methods for three-flat model. Finally, by both simulation and experiment, it is concluded that the block SOR method with an optimal relaxation factor converges much faster and saves more computational costs and memory space without reducing accuracy. Both simulation and experimental results indicate that the proposed iterative optimization methods are effective for solving the three-flat problem with pixel-level spatial resolution and the measuring precision of two separate measurements is 0.6 nm rms, and the cross-check test result is 0.8 nm rms. It is concluded that the proposed method can correctly reconstruct absolute figures with high efficiency and pixel-level spatial resolution.
The result of an interferometric surface figure measurement is a height map, from which single parametric descriptors (for example the RMS) or residual maps are the most commonly used methods for determining the measurement repeatability. An alternate technique based on a standard deviation matrix is used to better describe the variation among successive measurements. A standard deviation matrix is acquired by computing standard deviation of the height map pixel by pixel. Only one standard deviation matrix can provide a spatial description of the repeatability as well as parametric descriptors (for example the mean) of the standard deviation matrix. Comparative study on the evaluation of measurement repeatability among different methods is shown by both simulation and experiment. It seems that the standard deviation matrix method is more valid to detect the variation than other techniques in the measurement of surface figure.
New method for reconstructing rotationally asymmetric surface deviation with pixel-level spatial resolution is proposed. It is based on basic iterative scheme and accelerates the Gauss-Seidel method by introducing an acceleration parameter. This modified Successive Over-relaxation (SOR) is effective for solving the rotationally asymmetric components with pixel-level spatial resolution, without the usage of a fitting procedure. Compared to the Jacobi and Gauss-Seidel method, the modified SOR method with an optimal relaxation factor converges much faster and saves more computational costs and memory space without reducing accuracy. It has been proved by real experimental results.
A convenient method to study the influence of error sources in Fizeau is to build a ray-tracing model to simulate the error sources. In this paper an interferometer model is presented; an extension program is called to simulate the interference; and a preliminary research of several error sources is conducted. These examples demonstrate error analysis based on interferometer models is feasible and provide some guidance for optimizing our interferometer design.