Spherical Harmonic-Based Spectral Projection Model for Holographic SAR Imaging

A spectral projection model which is based on spherical harmonics is developed for three-dimensional holographic SAR imaging. The addition theorem for spherical harmonics is used for describing the SAR measurement process as a projection of a source spectral vector onto an observation spectral vector. The source vector for a particular scatterer is determined by the spherical coordinates of that scatterer. The dimension of the source vector is determined by the largest dimension of the SAR viewing area. The observation vectors are similarly defined in terms of the spherical coordinates of each measurement point along the SAR flight path. By separating the source and observation terms in the addition theorem, the contribution from each scatterer to each specific SAR measurement is described as the projection of the source spectral vector onto the observation spectral vector. Simulations are used to investigate the spectral properties of a variety of source distributions and SAR flight paths. Sample holographic images are simulated using this spectral projection model.