A fast algorithm for signature prediction and image formation using the shooting and bouncing ray technique

In radar signature applications it is often desirable to generate the range profiles and inverse synthetic aperture radar (ISAR) images of a target. The simulation of synthetic range profiles and ISAR images is usually a time intensive task and computation time is of prime importance. We present a fast algorithm to generate range profiles and ISAR images using the shooting and bouncing ray (SBR) technique. A closed form time-domain ray-spread function was derived by Jeng, Bhalla, Lee, Ling and Andersh (see IEEE Trans. Antennas Propagat., Sept. 1993) for the direct computation of the time-domain response (or range profile) of a conducting target without resorting to multi-frequency calculations. This formula gives the explicit contribution of each exit ray in the time domain. We have also extended this formula to the two-dimensional ISAR plane under the small-angle approximation. We cast these previously derived formulas into a convolution form. The convolution consists of a non-uniformly sampled signal and a closed form time-domain or image-domain ray-spread function. Using a fast scheme proposed by Sullivan (1990), the non-uniformly sampled function is first interpolated onto a uniform grid before the convolution is performed by the fast Fourier transform (FFT) algorithm. Results for several complex targets are presented to demonstrate the computation time savings and fidelity of the scheme.