Fast Time Domain Synthetic Aperture Imaging by Plane Wave Migration

A new synthetic aperture imaging algorithm named plane wave migration (PWM) is presented. PWM can be described entirely in the time domain and consists of three basic steps. First, an angular spectrum of wideband plane waves is computed by far-field beamforming of the raw data in the time domain. Next, the plane waves are matched filtered by the two-way physical beampattern, viewed as a transfer function in frequency for a given beam angle, to maximize the signal-to-noise and azimuth ambiguity ratio. Finally, the filtered plane waves are migrated, i.e., backpropagated, to the image pixels. It is shown that both beamforming and migration can be done using fast transforms so that the algorithm has the same order of computational complexity as the frequency domain wavenumber algorithm. Beamforming in the time domain allows known motion errors to be corrected precisely and efficiently while also avoiding the cumbersome Stolt interpolation. PWM is shown to combine in a single algorithm the benefits of many existing algorithms, such as the range–Doppler algorithm and extensions, such as secondary range compression and chirp scaling, the wavenumber algorithm, the polar format algorithm, and fast factorized backprojection. Finally, we illustrate PWM by simulations of the theoretical point spread function of a 220–280 kHz synthetic aperture sonar and refer to existing publications for experimental results of real-time implementations of PWM.