Recent reports on the effects of vibrating targets on synthetic-aperture radar (SAR) imagery and the potential of SAR to extract non-stationary signatures have drawn significant interest from the remote-sensing community. SAR returned signals are the superposition of the transmitted pulses modulated by both static and non-static targets in both amplitude and phase. More precisely, the vibration of a target causes a small sinusoid-like frequency modulation along the synthetic aperture (slow time), whereby the phase deviation is proportional to the displacement of the vibrating object. By looking at successive small segments in slow time, each frequency modulated pulse can be tracked and further approximated as a piecewise-linear frequency-modulated signal. The discrete-time fractional Fourier transform (DFRFT) is an analysis tool geared toward such signals containing linear frequency modulated components. Within each segment, the DFRFT transforms each frequency-modulated component into a peak in the DFRFT plane, and the peak position corresponds to the frequency modulation rate. A series of such measurements provides the instantaneous-acceleration history and its spectrum bears the vibrating signature of the target. Additionally, when the chirp z-transform (CZT) is incorporated into the DFRFT, vibration-induced modulations can be identified with high resolution. In this work, the interplay amongst SAR system parameters, vibration parameters, the DFRFT's window size, and the CZT's zoom-in factor is characterized analytically for the proposed SAR-vibrometry approach. Simulations verify the analysis showing that the detection of vibration using the slow-time approach has significantly higher fidelity than that of the previously reported fast-time approach.

Date Published: 27 April 2010
PDF: 10 pages
Proc. SPIE 7669, Radar Sensor Technology XIV, 766911 (27 April 2010); doi: 10.1117/12.849671

Published in SPIE Proceedings Vol. 7669:
Radar Sensor Technology XIV
Kenneth I. Ranney; Armin W. Doerry, Editor(s)