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.