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Microlocal analysis of Doppler Synthetic Aperture Radar

Raluca Felea, Romina Gaburro, Allan Greenleaf, Clifford Nolan

Abstract

We study the existence and suppression of artifacts for a Doppler-based Synthetic Aperture Radar (DSAR) system. The idealized air- or space-borne system transmits a continuous wave at a fixed frequency and a co-located receiver measures the resulting scattered waves; a windowed Fourier transform then converts the raw data into a function of two variables: slow time and frequency. Under simplifying assumptions, we analyze the linearized forward scattering map and the feasibility of inverting it via filtered backprojection, using techniques of microlocal analysis which robustly describe how sharp features in the target appear in the data. For DSAR with a straight flight path, there is, as with conventional SAR, a left-right ambiguity artifact in the DSAR image, which can be avoided via beam forming to the left or right. For a circular flight path, the artifact has a more complicated structure, but filtering out echoes coming from straight ahead or behind the transceiver, as well as those outside a critical range, allows one to obtain an artifact-free image. Initially derived under a start-stop approximation widely used in range-based SAR, we show that some of these results are robust and hold under a more realistic approximation.

Microlocal analysis of Doppler Synthetic Aperture Radar

Abstract

We study the existence and suppression of artifacts for a Doppler-based Synthetic Aperture Radar (DSAR) system. The idealized air- or space-borne system transmits a continuous wave at a fixed frequency and a co-located receiver measures the resulting scattered waves; a windowed Fourier transform then converts the raw data into a function of two variables: slow time and frequency. Under simplifying assumptions, we analyze the linearized forward scattering map and the feasibility of inverting it via filtered backprojection, using techniques of microlocal analysis which robustly describe how sharp features in the target appear in the data. For DSAR with a straight flight path, there is, as with conventional SAR, a left-right ambiguity artifact in the DSAR image, which can be avoided via beam forming to the left or right. For a circular flight path, the artifact has a more complicated structure, but filtering out echoes coming from straight ahead or behind the transceiver, as well as those outside a critical range, allows one to obtain an artifact-free image. Initially derived under a start-stop approximation widely used in range-based SAR, we show that some of these results are robust and hold under a more realistic approximation.

Paper Structure

This paper contains 17 sections, 8 theorems, 109 equations, 2 figures.

Table of Contents

  1. Introduction
  2. The Doppler SAR model
  3. The DSAR transform as a Fourier Integral Operator
  4. The left and right projections and the Bolker condition
  5. Contributions of this paper
  6. Notation, key properties, projections and singularities
  7. Properties of the right and left projections
  8. Singularities of smooth maps
  9. The case of a linear flight path
  10. The case of a circular flight path
  11. Preliminaries
  12. Condition for $\mathcal{C}$ to be a local canonical graph
  13. The singularity of $\pi_L$
  14. The singularity of $\pi_R$
  15. Criteria for absence of artifacts
  16. ...and 2 more sections

Key Result

Theorem 1

Under assumptions height_above and reflectivity, the mapping $\mathcal{F}$ is a Fourier integral operator of order $-1/2$ associated with the canonical relation $\mathcal{C}$ in eqn Cphi below.

Figures (2)

  • Figure 1: Schematic of a circular flight path.
  • Figure 2: The curves of constant $u$ (hyperbolas) and constant $v$ (vertical lines) for a location on the flight path in which the flight velocity vector is along the vertical axis. The coordinate system is centered directly under the antenna.

Theorems & Definitions (25)

  • Theorem 1
  • proof
  • Theorem 2
  • Theorem 3
  • Remark 1
  • Definition 1
  • Definition 2
  • Definition 3
  • proof : Proof of Theorem \ref{['thm line']}
  • Remark 2
  • ...and 15 more