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.