闭合条纹图的傅立叶分析方法

Closed-fringe analysis based on Fourier-transform Method

在基于条纹投影的傅里叶变换轮廓术(FTP)方法中,相位信息叠加在载波条纹中,即必须存在载波条纹。当干涉图中条纹以闭合形式存在,由于没有载频存在,不能直接采用傅立叶条纹分析方法恢复物光波的相位信息。本文采用极坐标的坐标变换方法,将封闭条纹展开,用传统傅立叶滤波方法进行处理,再将得到的信息反变换到原坐标中,得到测量物体的三维分布。文中用二维FFT的迭代算法对条纹进行解析延拓可明显减小由于坐标变换引入的条纹锐截止误差,从而提高测量精度。计算机模拟证实了所提方法的有效性。

A coordinate - transform technique is proposed that enables the Fourier - transform method to analyze an interferogram that includes a closed - fringe pattern. First, the closed - fringe pattern is converted to an open - fringe pattern by transformation of the Cartesian coordinate system to a polar coordinate system. Then the phase distribution for the open fringe interferogram is determined by the conventional Fourier transform methed. The phase distribution for the original closed - fringe pattern is obtained by inverse coordinate transformation from the polar coordinate system back to the Cartesian coordinate system. The measuring accuracy can be improved through the use of an iterated region spreading arithmetic for interforogram with 2 - D FFT. The computer simulation demonstrates the effectiveness of this method.