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Tomographic methods in range-Doppler radar. (English) Zbl 0645.43007

The holographic transform is the coefficient function of the linear Schrödinger representation at the projection along the one-dimensional center of the real Heisenberg group. See the reviewer’s monograph entitled “Harmonic analysis on the Heisenberg nilpotent Lie group, with applications to signal theory” [Pitman Res. Notes Math. Ser. 147 (1986; Zbl 0632.43001)] and the articles “The holographic transform” [Numerical Methods and Approximation Theory III, Nis 1987, 67-91 (1988)], ”The holographic transform and the neural model” [Seminar in Complex Analysis and Geometry 1987, Univ. Calabria 107-134 (1988)]. The group of outer automorphisms of the irreducible unitary linear representations of the real Heisenberg nilpotent Lie group allows to recognize high resolution Synthetic-Aperture Imaging Radar (SAR) like Side-Looking Airborne Radar (SLAR) and spaceborne Shuttle Imaging Radar (SIR) as a special kind of holographic microwave imagery. Indeed, the motion of the radar platform and the resulting Doppler frequency shift give rise to a linear mapping of the holographic plane onto itself. They generate a chirping of the transmitted radar pulses. The chirp parameter mu depends upon various SAR parameters like the platform ground-track velocity, the film speed, the radar wavelength, and the range, all of these parameters being available at the controller of the SAR processor. Specifically, the tilted azimuth cylinder collimator placed against the signal record of the optical processor depends upon mu.
The paper under review deals with the interplay between the reconstruction performed for various values of the parameter mu according to the reciprocity theorem of the holographic transform and the tomographic reconstruction techniques. The computer simulations of extremely short Gaussian pulses illustrate the fact that the resolution of SAR depends upon the pulse duration and does not depend upon the sensor altitude. This capability allows the acquisition of high-resolution images from satellite altitude as long as the received echo has sufficient strength above the noise level. Specific SAR systems like that of SEASAT, SIR-A, SIR-B, ALSE, and VOIR are not considered in the paper.
Reviewer: W. Schempp

MSC:

43A65 Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis)
22E27 Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.)
94A12 Signal theory (characterization, reconstruction, filtering, etc.)

Citations:

Zbl 0632.43001
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