Synthetic Aperture Radar - Algorithm

Algorithm

The SAR algorithm, as given here, applies to phased arrays generally.

A three-dimensional array (a volume) of scene elements is defined which will represent the volume of space within which targets exist. Each element of the array is a cubical voxel representing the probability (a "density") of a reflective surface being at that location in space. (Note that two-dimensional SARs are also possible—showing only a top-down view of the target area).

Initially, the SAR algorithm gives each voxel a density of zero.

Then, for each captured waveform, the entire volume is iterated. For a given waveform and voxel, the distance from the position represented by that voxel to the antenna(e) used to capture that waveform is calculated. That distance represents a time delay into the waveform. The sample value at that position in the waveform is then added to the voxel's density value. This represents a possible echo from a target at that position. Note that there are several optional approaches here, depending on the precision of the waveform timing, among other things. For example, if phase cannot be accurately known, then only the envelope magnitude (with the help of a Hilbert transform) of the waveform sample might be added to the voxel. If polarization and phase are known in the waveform, and are accurate enough, then these values might be added to a more complex voxel that holds such measurements separately.

After all waveforms have been iterated over all voxels, the basic SAR processing is complete.

What remains, in the simplest approach, is to decide what voxel density value represents a solid object. Voxels whose density is below that threshold are ignored. Note that the threshold level chosen must at least be higher than the peak energy of any single wave—otherwise that wave peak would appear as a sphere (or ellipse, in the case of multistatic operation) of false "density" across the entire volume. Thus to detect a point on a target, there must be at least two different antenna echoes from that point. Consequently, there is a need for large numbers of antenna positions to properly characterize a target.

The voxels that passed the threshold criteria are visualized in 2D or 3D. Optionally, added visual quality can sometimes be had by use of a surface detection algorithm like marching cubes.