Using Derivatives of an Implicit Function to Obtain the Stationary Phase of the Two-Dimensional Spectrum for Bistatic SAR Imaging

There are two square-root terms in the range history of a return signal from a bistatic synthetic aperture radar (BiSAR). The transfer function for imaging in the 2-D frequency or range Doppler domain using the principle of stationary phase cannot be analytically derived. To address this problem, we approximated the stationary phase of the 2-D spectrum with an expansion of the Taylor series on the azimuth frequency and called the approximation as the derivatives of an implicit function (DIF). After algebraic manipulation, the DIF and 2-D spectrum were obtained for a generally configured BiSAR. With the DIF method, we dissolved one square-root term out of the two for an azimuth-invariant BiSAR, which is particularly advantageous in the implementation of an imaging algorithm. Then, a modified range Doppler algorithm was developed to process the BiSAR data. Promising results were obtained.