Two-dimensional interferogram extrapolation method using linear carrier-frequency

Fast Fourier Transform (FFT) is one of the most important interferogram analysis methods. FFT arithmetic requires that the pixels number of sampling length of interferogram must be 2ⁿ to avoid the frequency spectrum leakage phenomenon. However, the usually captured interferogram regions are circular or annular, it is necessary to spread the interferogram region to rectangular region to satisfy with the above condition. In this paper, a simple two-dimensional interferogram extrapolation method using linear carrier-frequency is studied. First, we process the original two-dimensional interferogram by FFT and get the linear carrier-frequency (f_x1, f _y1) and (f_x2,- f_y2) in orthogonal directions. Using linear carrier-frequency (f_x1, f _y1) and (f _x2,- f _y2), we can first obtain two two-dimensional carrier interferograms. To guarantee that the two carrier interferograms are continuous with the original interferogram in orthogonal directions, the least square fitting is used. Then an ultimate two-dimensional carrier interferogram is acquired. At last, the valid-region inside the two-dimensional carrier interferogram is replaced by the original interferogram region and the filled-region is kept as it is, the extrapolated two-dimensional interferogram is obtained. Computer simulation of the two-dimensional interferogram extrapolation method is carried out. The result shows that the studied method can spread the two-dimensional region with or without obscurations to rectangular region perfectly and is effective in restraining frequency spectrum leakage and improving the interferogram process accuracy.