Birefringence double refraction 141 941 fresnel

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Birefringence (double refraction) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 9.4.1 Fresnel equation of wave normals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 9.4.2 Astrom’s equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 9.4.3 Booker quartic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 9.4.4 Appleton-Hartree equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 9.4.5 Phase and group velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 4
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9.4.6 Index of refraction surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 9.4.7 Ionospheric sounding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 9.4.8 Generalized raytracing in inhomogeneous, anisotropic media . . . . . . . . . . . . . . . . . . 151 9.4.9 Attenuation and absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 9.4.10 Faraday rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 9.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 9.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 10 Overspread targets 155 10.1 Conventional long pulse analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 10.2 Amplitude modulation and the multipulse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 10.3 Frequency and polarization diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 10.4 Phase modulation, coded long pulse, and alternating codes . . . . . . . . . . . . . . . . . . . . . . . 160 10.5 Range-lag ambiguity functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 10.6 Error analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 10.6.1 Noise and self clutter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 10.6.2 Comparative analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 10.6.3 Normalization errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 10.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 10.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 11 Radar applications 171 11.1 Radar interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 11.1.1 Ambiguity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 11.1.2 Volume scatter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 11.2 Acoustic arrays and non-invasive medicine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 11.3 Passive radar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 11.4 Inverse problems in radar signal processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 11.5 Synthetic Aperture Radar (SAR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 11.5.1 Image resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 11.5.2 Range delay due to chirp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 11.5.3 Range migration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 11.5.4 InSAR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 11.6 Weather radar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 11.7 GPR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 5
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11.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 11.9 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 12 Appendix - review of electrodynamics 186 12.1 Coulomb’s law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 12.2 Gauss’ law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 12.3 Faraday’s law (statics) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 12.4 Biot Savart law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 12.5 Another equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 12.6 Ampere’s law (statics) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 12.7 Faraday’s law of induction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 12.8 Ampere’s law (revisited) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 12.9 Potentials and the wave equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 12.10Macroscopic equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 12.11Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 12.12Boundary value problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 12.13Green’s functions and the field equivalence principle . . . . . . . . . . . . . . . . . . . . . . . . . . 199 12.14Reciprocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 6
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Chapter 1 Introduction This text investigates how radars can be used to explore the environment and interrogate natural and manufactured objects in it remotely. Everyone is familiar with popular portrayals of radar engineers straining to see blips on old-style radar cathode ray tubes. However, the radar art has evolved beyond this cliche. Radars are now used in geology and archeology, ornithology and entomology, oceanography, meteorology, and in studies of the Earth’s upper atmosphere, ionosphere, and magnetosphere. Radars are also used routinely to construct fine-grained images of the surface of this planet and others. Astoundingly detailed information, often from otherwise inaccessible places, is being made available to wide audiences for research, exploration, commerce, security, and commercial purposes. New analysis methods are emerging all the time, and the radar art is enjoying a period of rapidly increasing sophistication. 1.1 History Marconi (December, 1901) sent radio signals from Cornwall to Newfoundland (many mishaps) H¨ulsmeyer (1904) detected ships in channels Appleton (1924) early ionospheric sounding: Kennely-Heaviside layer, Appleton layer Watson-Watt (1935) Death ray? No – but aircraft detection by radio possible Chain Home stations (1939) direction and range detection, 20–30 MHz, floodlight Tx, crossed dipole Rx Chain Home low — 200 MHz, mechanical steering Pearl Harbor (all WWII combatants had radar) Magnetron (MIT Radiation Lab)
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