| Spotlight-mode synthetic aperture radar (SAR) produces complex Fourier data points on a polar grid which is offset from dc in the frequency domain. To produce an image in the spatial domain, it is necessary to invest this sampled Fourier data prior to extracting magnitude information. However, the polar format of the data makes this difficult, since there is no known polar FFT. An alternative is to interpolate the complex polar data to a Cartesian grid and then perform the two-dimensional FFT. The magnitude of the resulting data array represents the magnitude of the complex ground reflectivity of the terrain under illumination. The interpolation process can be very computationally intense, with an order two to fifty times that of the FFT. Reducing the computation in the interpolation stage, while maintaining reconstruction quality is the focus of this work. Several 2D interpolation techniques are examined, including nearest neighbor, bilinear, inverse-distance to the nth power, weighted sinc, chirp z-transform, and the newest interpolation algorithm proposed for this problem--the cubic spline. It is found that separable interpolation schemes outperform the more commonly used nearest neighbor and inverse distance algorithms, and that the cubic spine is very competitive with the weighted sinc interpolator in computation requirements and reconstruction quality. The chirp z-transform is determined to be a good alternative to the classical interpolation-DFT approach. |
