基于小波变换的拼接重叠区域融合方法

为了解决大口径光学元件面形高精度测量问题，建立了拼接测量系统，通过测量得到整体表面面形。在拼接测量过程中，需要将待测面形进行划分，按着一定的顺序进行测量，再根据各个子口径之间的相对位置进行拼接。各个子口径存在重叠部分，采用均化的处理方法会导致高频面形数据的丢失。采用小波变换的拼接重叠区域融合方法可以减少高频数据的丢失。首先，对各个子口径的重叠区域分别进行小波变换得到低频和高频系数矩阵；然后，根据不同的方法对低频和高频系数矩阵进行融合得到新的系数矩阵；最后，通过小波逆变换得到整体面形。对尺寸为120 mm×40 mm的长方形反射镜面形进行拼接干涉测量，并用功率谱密度对本文方法和平均融合结果进行客观比较。实验结果表明，该方法可以保留更多的高频面形数据。

Abstract

In order to achieve the measurement of large-aperture mirrors with high precision, the stitching interferometer system is established, the whole surface is obtained. The basic theory of stitching measurement technology is to divide the whole test mirror into several parts, and then measure the surface of each part respectively, and finally stitch these surfaces of different parts together. In the process of stitching measurement, overlapping areas between different local surface shapes use mean method of fusing overlapping areas would reduce the high-frequency components. First of all, the original overlapping areas surface shape goes through the wavelet transformation, resulting in low frequency coefficients and high frequency coefficients; Then, low frequency coefficients and high frequency coefficients is determined by different fusion rules; in the end, Finally, overlapping area surface shape is obtained by wavelet inverse transformation. This paper discusses the stitching interferometer test on a 120 mm×40 mm rectangular reflection mirror, in which fusion of overlapping areas has average method as well as the proposed algorithm, and also uses power spectral density conduct an objective comparison on the fusion results. The result of this experiment shows that the proposed algorithm fusion has better effects to improves the retention of high-frequency than the conventional methods.

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刘丁枭, 盛伟繁. 基于小波变换的拼接重叠区域融合方法[J]. 强激光与粒子束, 2018, 30(8): 081001. Liu Dingxiao, Sheng Weifan. Fusion of the stitching interferometer overlapping areas[J]. High Power Laser and Particle Beams, 2018, 30(8): 081001.

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