Abstract: The sub-system composed of an element of the receiver array and the transmitter in Synthetic Aperture Sonar (SAS) is studied. Due to the double square rooted terms in the slant range history of the sub-system, the fourth-order Taylor expansion is used to approximate the slant range. Then, the system transfer function in two-dimensional frequency domain is derived via series reversion and the method of stationary phase. Based on that, a new Range-Doppler (R-D) imaging algorithm applied to long receiver array and wide beam cases is proposed. With the presented method, the echo signals corresponding to each sub-system are processed firstly. Next, a high resolution SAS complex image can be obtained by coherently superposing each individual image. The simulation and real datasets demonstrate the validity of the proposed method.