An algorithm that processes bursts of data generated by scan-mode synthetic-aperture radar (scanSAR) offers some advantages over older scanSAR algorithms. With relatively high computational efficiency, the algorithm can shift and scale the position along the flight track, preserve the phase of the radar signal, and provide for immediate formation of interferograms from two radar images.

Conventional practice in synthetic-aperture radar (SAR) involves the use of either the scan mode or the strip mode. The most commonly used mode is the strip mode, in which the radar antenna is pointed in a fixed direction with respect to the flight track and the illumination footprint covers a strip on the ground as the radar system moves along the flight track. The mapping swath is arbitrarily long in the azimuth (along-track) direction; as a result, the finest achievable resolution in azimuth (the along-track coordinate) is independent of range (radar/target distance) and equals half the along-track dimension of the antenna. High range resolution is obtained by use of either very short pulses or properly coded signals. The length of the range swath is limited by the pulse-repetition interval; in some applications, this can be undesirable.

In the scan mode, the radar beam is periodically stepped in range to neighboring swaths, which are denoted subswaths for scanSAR purposes. This stepping increases the length of the range swath, but exerts the undesirable effect of decreasing along-track resolution because the stepping prevents the collection of the return from a target along the full along-track synthetic antenna aperture length dimension of the synthetic aperture. The term "burst" is used to characterize both (1) the interval during which the radar beam illuminates a given subswath and (2) the data obtained from the subswath.

ScanSAR data could be processed following a standard range/Doppler approach that includes, among other things, the use of Fourier transforms for efficient frequency-domain implementation of convolutions. However, for reasons too complex to discuss within the limits of this article, this approach entails large zero-padding of burst data in preparation for azimuth compression, and this padding makes for computational inefficiency. An alternative approach is implemented by a very efficient algorithm called "SPECAN," in which azimuth focusing is accomplished in a process that involves a phase-multiplication operation called "deramping,"followed by a Fourier-transform step. This process involves the original burst data with either no zero padding or very limited padding to the nearest power of 2 for a typical discrete-Fourier-transform code. Strictly speaking, the SPECAN algorithm does not compensate for range migration, but partly as a consequence of the shortness of bursts, the range-migration effects in most scanSAR applications are small enough that one can ignore them for practical purposes.

The present algorithm is an extended version of the SPECAN algorithm (see figure). One relevant characteristic of the SPECAN algorithm is the need for range-dependent scaling of the along-track pixel dimension. This scaling is accomplished in a post-processing interpolation step that can degrade either computational efficiency or accuracy, depending on the length of the interpolation kernel. In the present algorithm, the need for the scaling and post-processing interpolation is eliminated by replacing the standard Fourier transform of the SPECAN algorithm with a chirp *z*-transform, the kernel of which includes a range-dependent correction (scaling) factor. The chirp *z-*transform can be computed by use of fast-Fourier-transform software, without need for zero-padding; however, the present algorithm is somewhat less efficient than the SPECAN algorithm is because the chirp *z*-transform involves a convolution rather than a simple Fourier transform.

The present algorithm is fully phase-preserving and retains the relative simplicity and most of the computational efficiency of the SPECAN algorithm. However, unlike the SPECAN algorithm, the present algorithm automatically generates images with constant azimuthal pixel length, without interpolation; moreover, the azimuthal pixel length can be chosen to suit the application at hand.

*This work was done by Riccardo Lanari, Scott Hensley, and Paul Rosen of Caltech for *NASA's Jet Propulsion Laboratory*. For further information, access the Technical Support Package (TSP) free on-line at www.techbriefs.com under the Information Sciences category*

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This article first appeared in the January, 1999 issue of *NASA Tech Briefs* Magazine.

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