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Complex image registration is a crucial step in interferometric synthetic aperture sonar (InSAS) signal processing. The registration quality directly influences the generation of interferogram and subsequent reconstruction of digital elevation model (DEM). Utilizing the geometric model of imaging, the rational function relationship between offset and slant range is deduced, thus this paper propose a new InSAS complex image registration method based on second order rational function surface fitting. Compared with the traditional polynomial surface fitting method, the proposed method in this paper has the advantages of higher precision and smaller calculation cost. The evaluation has been carried out using the root mean squared error(RMSE), correlation coefficient,residue numbers and computing time as the criteria. Simulation and real data experiments results indicate the validity of the proposed method. [ABSTRACT FROM AUTHOR]