The possibility of exploiting the dispersive properties of materials to recover medium properties from scattering measurements has long been considered by science. Since many battlefield materials (concrete, foliage, soil, human tissue, wood and plastics) exhibit widely varying dispersive properties this finding can significantly impact the ability to remotely detect and classify camouflaged targets, assess bomb damage and achieve real-time targeting. In commercial applications this capacity could be used for terrain classification, environmental planning and monitoring, and searching for downed aircraft.
A variety of passive sensors in wide-range optical bands have been investigated for the material identification problem. However, all passive sensors are limited by changes in illumination by the weather conditions and diurnal effects in some bands or spatial resolution in other bands.
The potential advantages of using SAR for remote material classification include:
• usability with a variety of existing sensor platforms independence of performance on weather conditions and time-of-day
• ability to collect data at multiple frequencies leading to a multispectral imaging model
• ability to tailor illuminating spectral bands specifically to produce unique reflection spectra
• greater signal return for improved target discrimination and classification
As part of our work, we have modeled material invariants mathematically in terms of their reflection kernels from reflected radar signals. We have formulated the relationship between the reflection kernel and matched filter computation for the case of dielectric objects whose distances from the transmitter are known. One of our fundamental results is an explicit algorithm for distinguishing between a wide variety of materials by employing a chirp waveform of duration as short as 4 nanoseconds.
Two key mathematical results are a closed form expression of the echo in the time duration of interest and a relationship between the matched filter computation of the echo and the reflectivity kernel.
For the case of multiple targets, we have developed a model to distinguish the targets and their reflectivity kernels using several strip SAR measurements. Under certain simplifying assumptions, targets are distinguished by inversion of the model geometry matrix.
We have developed the discrete Zak transform into a unifying framework for adaptive signal design. As part of this effort we have clarified the relationship between the discrete fractional Fourier transform, orthonormal eigen vector bases of the finite Fourier transform and discrete chirps. The main result establishes a Zak space condition and algorithm for exact deconvolution which explicitly brings out the distinguished role played by discrete chirp and chirp-like signals in deconvolution.
