用干涉条纹图像重建反射镜的三维面形

给出了用干涉条纹图像重建反射镜三维面形的方法,用泰曼-格林干涉仪采集被测镜面的干涉条纹图像,通过对干涉条纹图像进行处理得到镜面高度采样,采用泽尼克多项式拟合镜面的曲面函数,测量到了镜面的三维高度数据。干涉条纹图像上相邻条纹与参考面之间的距离相差一个标准光源波长,因而该测量方法的关键是得到条纹波峰或波谷的精确位置,从而达到了镜面相对高度的采样的目的。采用巴特沃斯低通滤波对条纹图像进行滤波,去掉噪声的影响,然后对图像二值化分割出亮条纹,用数学形态法对二值条纹图像细化得到条纹的中心线,结果表明,低通滤波方法能有效地减少细化条纹的分支和断裂。最后定义每条条纹中心线的相对高度,利用前39项泽尼克多项式对镜面高度进行最小二乘法拟合,计算了镜面被测区域的曲面高度数据。该方法可以用来测量强激光引起的镜面热变形。

Reconstruction of 3-D surface of mirror by processing fringe pattern

The fringe patterns of a measured mirror are captured by Twyman-Green interferometer, the sampling height of the mirror surface is obtained by image processing of fringe patterns, Zernike polynomial is adopted to fit the function of the mirror curved surface and get the 3D measurement of the mirror surface height. The distances between two adjacent fringes to reference mirror space is a standard light source wavelength apart, so the key of this measurement method is to locate the wave crest or wave hollow of fringe pattern accurately, thus the task of sampling height of mirror surface is completed. A Butterworth low-pass filter is used to remove the noise of fringe image, then the bright fringe is segmented by binary conversion and is thinned into its centerline by morphologic method. The thinning result indicates that low-pass filter could reduce the amount of branches and breaks of center lines. Finally, giving the relevant height of every center lines and using the pre-39 items of Zernike polynomial to fit the mirror surface height by least square solution, the 3D data of sample surface of mirror is calcalated. This method can be use to measure the laser-induced deformation of mirror.