In an optical synthetic aperture imaging system, it is necessary to extract edge information of subapertures with complex shape and large gaps, aiming at cophasing of segmented mirrors ultimately. As a measure of image surface irregularities, fractal dimension (FD) was calculated for edge extraction and surface complexity evaluation. The modified differential box-counting (DBC) method was adopted to calculate FD, specifically the window merge replication method was presented to achieve FD estimation with a relatively small scanning window. The subaperture region and interference fringe edge were extracted by using a two-step strategy of preprocessing and postprocessing. Simulations and experiments are conducted to verify the feasibility and accuracy for edge extraction. As well, the capabilities of the proposed method are demonstrated with the results of numerical calculation.
Optical synthetic aperture imaging technology is an effective approach to increase the aperture diameter of optical system for purpose of improving resolution. In optical synthetic aperture imaging system, the edge is more complex than that of traditional optical imaging system, and the relatively large size of the gaps between the subapertures makes cophasing a difficult problem. So it is significant to extract edge phase of each subaperture for achieving phase stitching and avoiding the loss of effective frequency. Fractal dimension as a measure feature of image surface irregularities can statistically evaluate the complexity which is consistent with human visual image perception of rough surface texture. Therefore, fractal dimension provides a powerful tool to describe surface characteristics of image and can be applied to edge extraction. In our research, the box-counting dimension was used to calculate fractal dimension of the whole image. Then the calculated fractal dimension is mapped to grayscale image. The region with large fractal dimension represents a sharper change of the gray scale in original image, which was accurately extracted as the edge region. Subaperture region and interference fringe edge was extracted from interference pattern of optical subaperture, which has laid the foundation for the subaperture edge phase detection in the future work.
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