Polar Reformatting for ISAR Imaging

R. Lipps and M. Bottoms
Radar Division

Introduction: The Navy's increased interest in operations in littoral environments requires reliable identification of a vast number of small targets. Inverse synthetic aperture radar (ISAR) is a radar imaging technique that uses target motion to achieve the Doppler discrimination that is needed to form a 2-D image. The key to using radar imaging for small-target identification is the production of high-resolution, well-focused imagery. Acceptable imagery can be produced using traditional range-Doppler processing through the utilization of modern motion-compensation techniques. While motion compensation can provide good focus for a limited number of scatterers on the target, a different approach to ISAR imaging is required to achieve a fully focused ISAR image. The problems that need to be addressed deal with target rotation that is not linear and with scatterers that migrate through range cells during the image formation period. These problems are amplified because of the need for fine range and Doppler resolution in the imagery. Polar reformatting is a technique that has been developed to address these problems in spotlight synthetic aperture radar (SAR) imaging and has been adapted by NRL for use in ISAR imaging.

Background: Polar reformatting is an image formation technique based on tomographic reconstruction techniques originally developed for medical imaging.¹ Tomographic image formation involves reconstructing the spatial representation of an object using the Fourier transform of a set of observations, each being a projection of the object onto a line, taken over a series of aspect angles. This series of observations populates a region of Fourier space and can be used to reconstruct an image of the object using inverse Fourier transform methods. A received radar pulse is the projection of the electromagnetic scattering from the target onto the radar line of sight and can be used for this technique. The difference between tomographic reconstruction using radar signals and traditional tomographic reconstruction is that the radar's signal is modulated by the carrier frequency of the radar. As a result, the Fourier transform of the radar's pulse produces a line segment in 3-D Fourier space that is offset from the origin by the carrier frequency at an angle determined by the angle of the radar line of sight. As successive pulses are received and the aspect between the radar and the target changes, the line segment sweeps out a data surface in 3-D Fourier space (Fig. 7). Once the data surface is formed, an image is reconstructed by transforming the surface into the spatial domain using a variety of techniques developed for SAR.²

FIGURE 7
Representation of the received radar pulses for a rotating target in the spatial and Fourier domains.

ISAR Imaging Using Polar Reformatting: Processing for ISAR image formation is similar to processing for spotlight SAR imaging. In ISAR processing, the main difference is that the motion of the target provides the change in aspect necessary for Doppler processing; in spotlight SAR, the change in aspect comes from the motion of the radar. As a result of this difference, the aspect change, over time, between the radar and the target is both unknown and uncontrollable in the ISAR imaging case. Because the aspect change defines the shape of the data surface, the rotation of the target must be determined before polar reformatting can process the data into imagery. Initial efforts concentrated on developing a model for and estimating the parameters of the target rotational motion and using these estimates to form the data surface. Because this approach did not yield a closed-form solution to the target motion parameters, we decided to try an approach in which we modeled the data surface directly and used measurable motion quantities to estimate the data surface model parameters. We chose a quadratic data surface model because it was as simple as possible (fewest model parameters) but still allowed us to compensate for most of the nonlinear rotational motion in the target. Also within the surface, the spacing between the data line segments was also modeled as a quadratic function. Using this model, we have two parameters of interest: the quadratic term representing the curvature of the data surface (called the outof- plane acceleration) and the quadratic term representing the line segment spacing (called the in-plane acceleration).

FIGURE 8
Block diagram of the procedure for performing polar reformatting for ISAR.
Fig9 Image

FIGURE 9
Example ISAR imagery showing the improvement in image quality using polar reformatting.

Polar Reformatting System: The implementation of this technique involves taking motion measurements from the data, estimating the data surface model parameters, projecting the data surface onto a planar surface, re-interpolating the data into equally spaced samples, and performing the inverse Fourier transform (IFFT). Figure 8 shows this process. The motion measurements are taken from three locations on a preformed image, where one location is used as a reference point and the other two are used to estimate the surface parameters. Each location provides us with a range, velocity (Doppler), and translational acceleration and a set of simultaneous equations relating these values to the quadratic terms in the model that are used for estimating the model parameters. The projection and re-interpolation steps are done simultaneously for each point on a rectangular grid by back-projecting the grid onto the data surface and performing the interpolation on the data surface. A 2-D Fourier transform of the interpolated data produces the final image. Figure 9 compares imagery produced by using range-Doppler and polar reformatting methods. The improvement in the image quality is clearly shown.

Summary: Polar reformatting is a technique that has been in use for SAR processing for many years and has been shown to produce high-quality imagery. We have successfully adapted this technique to ISAR image formation in which the rotational motion of the target is not known beforehand. This provides NRL with an imaging technique that can produce high-quality imagery in conditions with significantly complex target motion. Past work on polar reformatted ISAR has been for imaging small craft targets, but this technique is currently being applied to imaging ground targets.

[Sponsored by ONR]

References
¹ R.M. Mersereau and A.V. Oppenheim, "Digital Reconstruction of Multidimensional Signals from Their Projections," Proc. IEEE 62(10), 1319-1338 (1974).
² D.A. Ausherman, A. Kozma, J.L. Walker, H.M. Jones, and E.C. Poggio, "Developments in Radar Imaging," IEEE Trans. Aerosp. Electron. Syst. AES-20(4), 363-400 (1984).