Fourier Transform in Synthetic Aperture Radar Systems

Synthetic Aperture Radar

A synthetic aperture radar (or simply SAR) is an imaging radar system that uses the recorded echoes of electromagnetic waves transmitted by an antenna to produce images. As an example, shown below is an image of Mount Teide in Spain, synthesized by a SAR system installed on the now-retired space shuttle Endeavour [1].

1200px-TEIDE.JPG

What role does Fourier Transform play in SAR systems?

First, we have to establish that for many applications, the measurements of a SAR system (relevant to the echoes recorded by the antenna) are taken along a more-or-less linear path, as in a case where the SAR is mounted or installed on an airplane. This way, A SAR antenna is at different points at different times during the measurement process.

It is easy to imagine that generating an image by simply collating individual antenna measurements would result in one in which the same images are overlapping. This is where Fourier transform comes into play. ” In order to efficiently convert these measurements into a SAR image, the data are first [re-sampled] onto an equally spaced rectangular grid and then transformed into the image domain by a fast Fourier transform.” [2] This Fourier method allows the SAR system to synthesize, using the recorded information, an image that approximates what the object looks like in reality.

References:

  1. https://en.wikipedia.org/wiki/Synthetic_aperture_radar
  2. bshttp://www.maths.lth.se/~fa/preprints/SAR_andersson_moses_natterer.pdf, (Fast Fourier Methods for Synthetic Aperture Radar Imaging, Andersson et al.)
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