## Fundamentals of Radar ImagingRadar imaging is a mathematically rich subject with many interesting applications and a large variety of challenging, mathematical open problems. The goal of this book is to provide mathematicians with the background they need to work in the field, building on the foundation of the underlying partial differential equations. The focus is on showing the connection between the physics and the mathematics and on supplying an intuitive mathematical understanding of basic concepts. The book includes a description of how a radar system works, together with the relevant mathematics; theory that guides the choice of radar waveforms; derivation of the fundamentals of scattering theory; derivation and discussion of the image formation process; and a long list of current open problems. Readers are assumed to be familiar with the Fourier transform. Other assumed background material includes certain basic facts from vector calculus, complex variables, linear algebra and physics. |

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### Contents

CB79_ch1 | 3 |

CB79_ch2 | 15 |

CB79_ch3 | 21 |

CB79_ch4 | 25 |

CB79_ch5 | 35 |

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CB79_ch7 | 59 |

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CB79_ch9 | 91 |

CB79_ch10 | 113 |

CB79_ch11 | 121 |

CB79_bm | 127 |

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Air Force Research algorithms ambiguity function ambiguity surface angular aperture antenna beam pattern antenna courtesy antenna position approximation array backprojection Barker codes chirp corresponding courtesy of Air courtesy of NASA/JPL-Caltech courtesy of Sandia courtesy of U.S. current density CW pulse data collection manifold denotes determine direction Doppler resolution Doppler shift down-range electric field equation example far-field expansion flight path Force Research Laboratory frequency bands frequency domain Glenn Research Center ISAR L-band Laboratory Sensors Directorate matched filter mathematical measure Microstrip antennas microwave moving target multiple scattering objects obtain operator phase point-like target polarization radar imaging radar system Radon transform range resolution range-Doppler image received signal Research Laboratory Sensors rotation Sandia National Laboratories SAR images SAR systems scattered field shown in Figure shows sinc function slotted waveguide ſº stepped-frequency theory typically U.S. Department velocity waveform wavelength zero