应用频率积分相位解调测量径向畸变

为了测量光学成像系统的径向畸变，采用载频条纹模板，应用瞬时频率积分法提取因径向畸变而产生的径向调制相位；推导了条纹径向调制相位与瞬时频率的关系式，并导出径向调制相位和径向畸变位移关系；采用小波频率估计提取畸变条纹径向瞬时频率，并对其进行积分获得畸变条纹的径向调制相位；应用径向调制相位和立方卷积插值算法对畸变图像进行了校正，得出了详细的理论分析和实验结果。结果表明，上述方法是可行的。

Measurement of radial distortion based on frequency integration phase demodulation

To measure the radial distortion in optical imaging systems, adopting the straight sinusoidal carrier-fringe pattern, the radial modulated phase resulting from radial distortion was extracted by means of instantaneous frequency integration. The formula between the instantaneous frequency and the radial modulated phase was deduced, and the conversion formula between the radial modulated phase and the radial distortion displacement was obtained. The instantaneous frequency of the distorted fringe pattern in the radial direction was calculated by using frequency estimation of Gabor wavelet transform, and integrated to obtain the radial modulated phase. The radial modulated phase and the cubic convolution interpolation algorithm were used to calibrate the distorted image. Experimental results demonstrate that the method is available.