一维倾斜载频条纹测量径向畸变

Radial Distortion Measurement Using One Dimensional Inclined Fringe Pattern and Gabor Transform

摘要: 为了测量光学成像系统的径向畸变并校正畸变图像，提出基于一维任意方向(倾斜)载频条纹相位分析联合伸缩Gabor变换的测量方法，通过测量径向畸变调制相位获得径向位置畸变分布。首先，利用一维任意方向正弦载频条纹作为测量模板，通过成像系统采集的畸变图像就是变形光栅条纹；接着考虑径向畸变的中心对称性，为了获得径向位置畸变分布，经畸变条纹中心点沿某个方向提取一行像素，采用伸缩Gabor窗口傅立叶变换直接从中心零畸变点提取并重构出理想光栅条纹像基频信息，应用Gabor窗口傅立叶变换对该方向的变形光栅条纹和理想光栅条纹进行相位分析，获得该方向的径向畸变调制相位分布并换算为径向位置畸变位置分布规律。最后采用双线性插值灰度重建对畸变图像进行校正。给出详细的理论分析过程，实验结果表明该方法是可行的。

Abstract: For the purpose of measuring the radial distortion in optical imaging systems and correcting distorted images, based on phase analysis of fringe pattern, a new method using one dimensional inclined carrier-fringe pattern and Dilating Gabor transform is proposed, and the radial distortion distribution is obtained from the radial modulated phase distribution. Firstly, one dimensional inclined sinusoidal carrier-fringe pattern in arbitrary direction is used as measuring template, and a deformed grating pattern regarded as a distorted image is obtained by the optical imaging system. Then, considering the radial symmetry of radial distortion, one row of pixels along a certain direction is extracted from deformed fringe pattern; since there is no distortion at the center of the row, from which the fundamental frequency information including instantaneous frequency and phase, of the ideal pattern image, is extracted using Dilating Gabor transform, and the ideal image of fringe pattern along the above direction is constructed by use of an inverse Fourier Transform to measure the radial distortion. Phase analysis of the above row of deformed fringe pattern and its ideal fringe pattern is carried out using Dilating Gabor transform. The radial modulated phase distribution is converted the radial distortion distribution. Finally, by use of bilinearity interpolation, the calibrated image is reconstructed. Theoretical analysis and experimental results are presented to demonstrate the validity of the above method.