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E-grāmata: Understanding Earth Observation: The Electromagnetic Foundation of Remote Sensing

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Understanding Earth Observation: The Electromagnetic Foundation of Remote SensingPalielināt
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This volume addresses the electromagnetic foundation of remote sensing. The basic grounds are presented in close association with the kinds of environmental targets to monitor and with the observing techniques. The book aims at plugging the quite large gap between the thorough and quantitative description of electromagnetic waves interacting with the Earth's environment and the user applications of Earth observation (EO). It is intended for scientifically literate students and professionals who plan to gain a first understanding of remote sensing data and of their information content.

Recenzijas

The book Understanding Earth Observation - The Electromagnetic Foundation of Remote Sensing is a very comprehensive presentation about earth observation sensor types, techniques and calculations. presents a complete summary that leads to a comprehensive understanding of the elements and factors involved in using and applying earth observation remote sensing to acquire accurate, reliable and useful data. This text is a good candidate as a reference text due to the comprehensive presentation and up-to-date material and should be considered. (Jeff Thurston, 3D Visualization World Magazine, 3dvisworld.com, November, 2016)

1 The Electromagnetic Field 1(30)
1.1 Basic Definitions and Relations
1(6)
1.1.1 Maxwell's Equations
2(1)
1.1.2 Electromagnetic Constitutive Relations
2(1)
1.1.3 Electromagnetic Sources
3(2)
1.1.3.1 Electromagnetic Duality
4(1)
1.1.4 Boundary Conditions
5(2)
1.1.4.1 Normal Field Components
6(1)
1.1.4.2 Tangential Field Components
6(1)
1.2 Electromagnetic Power Budget
7(8)
1.2.1 The Electromagnetic Source
8(1)
1.2.2 Dissipated Power
9(1)
1.2.3 Stored Energy
10(1)
1.2.4 Electromagnetic Radiation
10(1)
1.2.5 Power Budget for Time-Harmonic Fields
11(4)
1.2.5.1 Power Balance for Non-dissipative Materials
11(3)
1.2.5.2 Power Balance with Lossy Materials
14(1)
1.3 Polarization and Coherence
15(12)
1.3.1 Monochromatic Fields
16(4)
1.3.1.1 Polarization of the Electromagnetic Field
17(2)
1.3.1.1.1 Modulus, "Versor" and Orthogonality of Complex Vectors
18(1)
1.3.1.2 Polarization Parameters
19(1)
1.3.2 Quasi-monochromatic Fields
20(2)
1.3.3 Spectral Maxwell's Equations
22(1)
1.3.4 Random Electromagnetic Fields
23(9)
1.3.4.1 Polarization Matrix
24(1)
1.3.4.2 Coherency Matrix
25(2)
What We Learned on the Electromagnetic Field
27(1)
References
28(3)
2 Dielectric Behavior of Terrestrial Materials 31(42)
2.1 Permittivity in the Spectral Domain
32(15)
2.1.1 Non-polar Non-conducting Materials
34(4)
2.1.1.1 Low-Frequency Dielectric Behavior
36(1)
2.1.1.2 High-Frequency Dielectric Behavior
36(1)
2.1.1.3 Dielectric Behavior About Resonance
37(1)
2.1.1.4 Permittivity of Composite Materials
38(1)
2.1.2 Polar Materials
38(4)
2.1.3 Conducting Materials
42(2)
2.1.3.1 Conductivity
43(1)
2.1.3.2 Permittivity vs. Conductivity
43(1)
2.1.4 Complex Permittivity and Power Budget
44(3)
2.1.4.1 Complex Source Term
45(1)
2.1.4.2 Term with Conductivity
45(1)
2.1.4.3 Term with Permittivity
45(1)
2.1.4.4 The Radiation Term
46(1)
2.2 Permittivity of Relevant Terrestrial Materials
47(19)
2.2.1 The Atmosphere
47(4)
2.2.1.1 Microwave Permittivity of Air
48(2)
2.2.1.2 Optical Permittivity of Air
50(1)
2.2.2 Water and Ice
51(6)
2.2.2.1 Liquid Water
52(2)
2.2.2.2 Ice
54(1)
2.2.2.3 Sea Water
55(2)
2.2.3 Vegetal Tissues
57(5)
2.2.3.1 Green Matter
57(3)
2.2.3.1.1 Microwave Permittivity
57(1)
2.2.3.1.2 Optical Permittivity
58(2)
2.2.3.2 Ligneous Matter
60(1)
2.2.3.3 Effect of Temperature
61(1)
2.2.4 Soil
62(3)
2.2.5 The Ionosphere
65(1)
What We Learned About Dielectric Properties
66(1)
References
67(6)
3 Electromagnetic Sources and Radiation 73(30)
3.1 The Radiated Field
73(21)
3.1.1 Impulse Response of Free Space
75(7)
3.1.1.1 The Scalar Green's Function
76(1)
3.1.1.2 The Wave
77(4)
3.1.1.3 Doppler Effect
81(1)
3.1.2 Wave Interference
82(2)
3.1.3 Field of Point Source
84(4)
3.1.4 Field of Finite-Dimension Sources
88(6)
3.1.4.1 The Far Field
89(2)
3.1.4.2 Properties of Field and Power at Far Distance
91(1)
3.1.4.3 Radiation Parameters
92(2)
3.2 Reciprocity and Equivalence
94(6)
3.2.1 Reciprocity
94(3)
3.2.1.1 The Reaction Integrals
95(1)
3.2.1.2 Test Source
96(1)
3.2.2 Equivalence
97(7)
3.2.2.1 Field of Equivalent Sources
99(1)
We Meet the Electromagnetic Radiation
100(1)
References
101(2)
4 Waves and Fields 103(32)
4.1 Plane Wave Approximation
104(14)
4.1.1 The Propagation Vector
105(1)
4.1.2 Phase and Amplitude
105(13)
4.1.2.1 Wavelength
111(1)
4.1.2.2 Velocity of Propagation
112(1)
4.1.2.3 Interrelation Among Fields and Propagation Vector
112(2)
4.1.2.4 Power Density
114(1)
4.1.2.5 Refraction and Absorption in the Atmosphere
115(3)
4.1.2.5.1 Atmospheric Refractivity
115(1)
4.1.2.5.2 Atmospheric Absorption
116(2)
4.2 Vector-Field Representations of Plane Waves
118(4)
4.2.1 Jones Representation
118(3)
4.2.2 Stokes Representation
120(1)
4.2.2.1 The Poincare Sphere
121(1)
4.3 Interference of Plane Waves
122(9)
4.3.1 Effect of Height
125(2)
4.3.1.1 Interference Fringes on a Slant Plane
126(1)
4.3.2 Interference and Coherence
127(4)
Surfing Fields and Waves
131(1)
References
132(3)
5 Propagation 135(30)
5.1 Field in Weakly Inhomogeneous Materials
136(7)
5.1.1 The Geometrical Optics Model
136(7)
5.1.1.1 Dielectric Structure and Propagation Features
138(3)
5.1.1.2 The Direction of Propagation
141(2)
5.2 Electromagnetic Rays
143(12)
5.2.1 Rays in Layered Media
145(4)
5.2.1.1 Spherical Layering
145(3)
5.2.1.1.1 Reference Refractivity
147(1)
5.2.1.2 Plane Layering
148(1)
5.2.2 Rays and Path Length
149(4)
5.2.2.1 Ray Tracing
149(1)
5.2.2.2 Fermat Principle
150(1)
5.2.2.3 Electromagnetic Path Length and Distance
151(4)
5.2.2.3.1 The GPS
152(1)
5.2.2.3.2 The Radar
152(1)
5.2.2.3.3 Radar Interferometry
153(1)
5.2.3 Atmospheric Path Delay
153(2)
5.3 Properties of the Field
155(6)
5.3.1 Field in Lossless Media
155(2)
5.3.1.1 Flux Tubes and Field Amplitude
155(1)
5.3.1.2 Phase
156(1)
5.3.1.3 Polarization
157(1)
5.3.2 Field in Lossy Media
157(9)
5.3.2.1 Weakly Lossy Materials
158(1)
5.3.2.2 The Attenuated Field
159(2)
Waves in a Smooth Environment
161(1)
References
161(4)
6 Reflection 165(44)
6.1 Reflection for Normal Incidence
166(6)
6.1.1 Field Reflection and Transmission
167(2)
6.1.2 Power Reflection and Transmission
169(1)
6.1.2.1 Lossy Materials
169(1)
6.1.2.2 Power Absorption
170(1)
6.1.3 The Stationary Field
170(2)
6.2 Oblique Incidence, Lossless Materials
172(7)
6.2.1 Angles of Reflection and Refraction
173(1)
6.2.2 Reflection Coefficients and Wave Polarization
174(5)
6.3 Oblique Incidence, Lossy Materials
179(8)
6.3.1 The Refracted Wave
180(3)
6.3.1.1 Penetration Depth
182(1)
6.3.2 Reflection Coefficient of Lossy Media
183(7)
6.3.2.1 Power Absorption
186(1)
6.4 Total Reflection
187(3)
6.5 Reflection from Layered Materials
190(10)
6.5.1 Lossless Materials
191(4)
6.5.1.1 The Reflection Coefficient
192(3)
6.5.2 Lossy Materials
195(5)
6.5.2.1 The Reflection Coefficient
196(2)
6.5.2.2 The Transmission Coefficient
198(2)
6.6 Reflection from Composite Planar Structures
200(5)
6.6.1 Reflection from Dihedrons
200(3)
6.6.1.1 Phase Shift Between Polarizations
201(2)
6.6.2 Reflection from Trihedrons
203(2)
Bounced Waves
205(1)
References
206(3)
7 Scattering 209(78)
7.1 Scatter Modeling
210(10)
7.1.1 Scattering Source
210(2)
7.1.2 Scattered Field
212(5)
7.1.2.1 Scattering Matrix
215(1)
7.1.2.2 Muller Matrix
216(1)
7.1.3 Scattered Power
217(3)
7.1.3.1 Transverse Sections
218(1)
7.1.3.2 The Backscattering Coefficient
219(1)
7.2 Coherent and Incoherent Scattering
220(6)
7.2.1 General Features of Scattering
223(3)
7.2.1.1 Intensity
223(1)
7.2.1.2 Angular Dependence
224(1)
7.2.1.3 Polarization
225(1)
7.3 Coherent Scattering
226(21)
7.3.1 Scattering from Plane Homogeneous Targets
226(4)
7.3.1.1 Coherently Scattered Field
227(1)
7.3.1.2 Angular Dependence of Coherent Scattering
228(2)
7.3.2 Scattering from Curved Homogeneous Targets
230(4)
7.3.3 Coherent Scattering from Rough Targets
234(3)
7.3.4 Scattering from Small Bodies
237(10)
7.3.4.1 Scattering from Disks
242(2)
7.3.4.2 Scattering from Needles
244(3)
7.4 Incoherent Scattering
247(33)
7.4.1 Scattering from Ensembles of Discrete Elements
248(5)
7.4.1.1 Scattering from a Canopy of Random Disks
248(2)
7.4.1.2 Scattering from a Canopy of Random Needles
250(3)
7.4.2 Continuous Approach to Incoherent Scattering
253(2)
7.4.3 Incoherent Scattering from Inhomogeneous Targets
255(4)
7.4.4 Dependence of Scattering on Target Structure
259(8)
7.4.5 Scattering from Periodic Structures
267(3)
7.4.6 Effect of Sub-surface Structure
270(3)
7.4.7 Surface and Volume Scattering
273(14)
7.4.7.1 Modeling the Backscattering Coefficient
277(1)
7.4.7.2 Effect of Polarization
277(3)
Scattered Waves
280(1)
References
281(6)
8 Thermal Emission 287(26)
8.1 Spontaneous Radiation
287(20)
8.1.1 The Thermal-Emission Field
289(3)
8.1.2 Thermal Emission at Far Distance
292(3)
8.1.3 Thermal Emission from Body with Plane Boundary
295(3)
8.1.4 Thermal Emission from Plane-Layered Body
298(4)
8.1.5 Thermal Emission from Randomly Inhomogeneous Bodies
302(5)
8.1.5.1 Connection of Emission with Reflection
305(1)
8.1.5.2 Effect of Structure
305(1)
8.1.5.3 Effect of Absorption
306(1)
8.2 Features of Thermal Radiation
307(4)
8.2.1 Thermal Radiation Parameters
307(2)
8.2.2 Black-Body Radiation
309(5)
8.2.2.1 Black-Body Radiation at Microwave Frequencies
310(1)
Emitted Waves Carry Information
311(1)
References
312(1)
9 Radiative Transfer and Passive Sensing 313(42)
9.1 Radiation in Random Medium
314(8)
9.1.1 Radiation from Extended Sources
321(1)
9.2 Radiative Transfer
322(9)
9.2.1 Incoherent Radiation
323(1)
9.2.2 The Radiative Transfer Equation
324(7)
9.3 Passive Sensing of the Earth's Surface
331(12)
9.3.1 Optical Sensing of the Surface and Atmospheric Correction
332(7)
9.3.1.1 Optical Sensing from Space Platforms
335(3)
9.3.1.2 Optical Sensing from Aerial Platforms
338(1)
9.3.2 Sensing the Surface in the Thermal Infrared
339(2)
9.3.2.1 TIR Sensing from Space Platforms
340(1)
9.3.2.2 TIR Sensing from Aerial Platforms
341(1)
9.3.3 Passive Sensing of the Surface at Microwaves
341(2)
9.4 Passive Sensing of the Earth's Atmosphere
343(5)
9.4.1 Thermal Sensing of the Non-scattering Atmosphere
344(11)
9.4.1.1 Satellite-Based Sounding of the Atmosphere
344(2)
9.4.1.2 Ground-Based Sounding of the Atmosphere
346(2)
Managing Multiple Scattering and Radiation Transfer
348(1)
References
349(6)
10 Electromagnetic Spectrum and Remote Information 355(46)
10.1 Selection of Frequency/Wavelength
355(15)
10.1.1 The Electromagnetic Spectrum
356(1)
10.1.2 Role of the Atmosphere in Surface Observation from Space
357(10)
10.1.2.1 Air Transmissivity
358(13)
10.1.2.1.1 Absorption by the Gaseous Atmosphere
358(5)
10.1.2.1.2 Extinction by Aerosols
363(2)
10.1.2.1.3 Extinction by Hydrometeors
365(2)
10.1.3 Wavelength and Information
367(3)
10.2 Basic Measurements
370(19)
10.2.1 Passive Measurements in Ultraviolet, Visible, Near Infrared
371(2)
10.2.1.1 Optical Observation of the Surface
372(1)
10.2.2 Measurements in the Thermal Infrared
373(5)
10.2.2.1 TIR Observation of the Surface
375(2)
10.2.2.2 TIR Observation of the Atmosphere
377(1)
10.2.3 Passive Measurements at Microwaves
378(4)
10.2.3.1 Microwave Observation of the Surface
378(3)
10.2.3.2 Microwave Observation of the Atmosphere
381(1)
10.2.3.3 Radiometric Measurements and Polarimetry
381(1)
10.2.4 Radar Measurements
382(7)
10.2.4.1 Radar Images of the Earth's Surface
382(6)
10.2.4.1.1 Multi-temporal Imaging
385(1)
10.2.4.1.2 Multi-polarization Imaging
385(3)
10.2.4.2 Microwave Backscattering vs. Emission
388(1)
10.2.5 Lidar Measurements
389(1)
10.3 Interpreting Observations of the Earth's Surface
389(4)
10.3.1 Interpreting Microwave Data
390(1)
10.3.2 Interpreting Optical Data
391(1)
10.3.3 Interpreting Thermal Emission Data
392(1)
A Panorama on Spectral Bands and Techniques for EO
393(1)
References
394(7)
11 Antennas and Apertures in Earth Observation 401(58)
11.1 Radiating Antennas
402(8)
11.1.1 Directivity and Reaction
409(1)
11.2 Receiving Antennas
410(9)
11.2.1 Reception and Reaction
411(2)
11.2.2 Polarization-Selective Antennas
413(3)
11.2.2.1 Optical Systems
415(1)
11.2.3 Aperture Efficiency and Effective Area
416(1)
11.2.4 Reception vs. Transmission
417(2)
11.3 Directional Properties of Apertures
419(13)
11.3.1 Radiating/Receiving Angular Pattern
421(11)
11.3.1.1 Angular Pattern of Circular Apertures
422(5)
11.3.1.1.1 Angular Pattern of Elliptic Apertures
426(1)
11.3.1.2 Angular Pattern of Rectangular Apertures
427(5)
11.4 The Role of Antennas and Apertures in Earth Observation
432(20)
11.4.1 Antennas and Surface Spatial Resolution
432(2)
11.4.2 The Received Signal
434(7)
11.4.2.1 Signal in Passive Microwave Observation of the Surface
435(3)
11.4.2.2 Signal in Passive Optical Observation
438(3)
11.4.2.2.1 Observation in the Visible/NIR
440(1)
11.4.2.2.2 Observation in the TIR
440(1)
11.4.3 Radar Observation
441(10)
11.4.3.1 Basic Radar Operation
441(2)
11.4.3.2 Radar Mapping
443(2)
11.4.3.3 Radar Observation of Earth
445(2)
11.4.3.4 SAR Observation of the Surface
447(13)
11.4.3.4.1 Antenna Elevation Synthesis
450(1)
11.4.4 Lidar Observation
451(1)
Getting to the Heart of Observing Systems
452(1)
References
453(6)
12 Earth Surface Rendering from Images 459(60)
12.1 Range Positioning in Images of the Earth's Surface
460(16)
12.1.1 Range Positioning by Passive Systems
460(2)
12.1.1.1 Flat Surface
460(1)
12.1.1.2 Surface with Elevation
460(2)
12.1.2 Range Positioning by Active Systems
462(14)
12.1.2.1 Flat Surface
463(1)
12.1.2.2 Surface with Elevation
464(2)
12.1.2.3 Lay-Over
466(1)
12.1.2.4 Images of Vertical Objects
467(4)
12.1.2.4.1 Images of Trees
467(2)
12.1.2.4.2 Images of Buildings
469(2)
12.1.2.5 The Double Bounce Effect
471(5)
12.1.2.5.1 Double Bounce from Individual Trees
472(1)
12.1.2.5.2 Double Bounce from Individual Building Walls
473(3)
12.2 3-D Information in EO Images
476(8)
12.2.1 3-D Rendering from Passive Images
476(1)
12.2.2 3-D Rendering from Radar Images
476(8)
12.2.2.1 Height-Ground Range Ambiguity
477(3)
12.2.2.2 Disentangling Height from Ground Range
480(4)
12.3 SAR Interferometry
484(30)
12.3.1 The Interferogram
484(3)
12.3.2 Accuracy of Interferometric Measurements
487(17)
12.3.2.1 Effect of the Atmosphere
487(5)
12.3.2.2 Effect of the Structure of the Target
492(12)
12.3.2.2.1 Effect of Permanent Structure
495(4)
12.3.2.2.2 Effect of Temporal Changes
499(5)
12.3.3 Coherence of the Scattered Field
504(5)
12.3.3.1 Effect of Changes and Temporal Coherence
506(1)
12.3.3.2 Effect of Baseline
507(2)
12.3.3.3 Permanent Scatterers
509(1)
12.3.4 Interferometric Coherence
509(11)
12.3.4.1 Decorrelation Factors
513(1)
Retrieving Height Information is Not a Simple Task
514(1)
References
515(4)
13 Sensing Surface and Underneath Features 519(24)
13.1 Macroscopic Scattering Mechanisms
520(19)
13.1.1 Surface Scattering
521(10)
13.1.1.1 Reflection from the Surface Layer
522(3)
13.1.1.2 Scattering from the Surface Layer
525(6)
13.1.1.2.1 Backscattering from Rough Surfaces
527(2)
13.1.1.2.2 Backscattering from Periodic Surfaces
529(2)
13.1.2 Volume Scattering
531(5)
13.1.2.1 Volume Scattering Source Function
532(4)
13.1.3 General Features of Volume Scattering
536(1)
13.1.4 Surface and Volume Scattering in Image Features
537(1)
13.1.5 Scattering Mechanisms and Interferometric Coherence
538(6)
13.1.5.1 Coherence in Surface Scattering
538(1)
13.1.5.2 Coherence in Volume Scattering
539(1)
Further Steps Toward Interpreting Images
539(1)
References
540(3)
14 Wave Interaction with Land, Water and Air 543(104)
14.1 Interaction with Land
544(44)
14.1.1 Passive Observation of Land in the Optical Spectral Range
544(10)
14.1.1.1 Optical Observation of Bare Surfaces
545(3)
14.1.1.2 Optical Observation of Vegetation
548(5)
14.1.1.3 Optical Observation of Snow
553(1)
14.1.2 Radar Observation of Land
554(17)
14.1.2.1 Radar Observation of Bare Soil
555(3)
14.1.2.1.1 The Interferometric Coherence of Bare Soil
558(1)
14.1.2.2 Radar Observation of Urban Areas
558(3)
14.1.2.3 The Interferometric Coherence on Urban Areas
561(1)
14.1.2.4 Radar Observation of Vegetation
561(7)
14.1.2.4.1 Backscattering from Crops
562(3)
14.1.2.4.2 Backscattering from Trees
565(3)
14.1.2.5 Lidar Observation of Vegetation
568(1)
14.1.2.6 Interferometric Coherence of Vegetation
568(2)
14.1.2.7 Radar Observation of Snow
570(1)
14.1.3 Observation of Land in the Thermal Infrared
571(9)
14.1.3.1 TIR Observation of Bare Soil
573(2)
14.1.3.1.1 Emissivity vs. Observation Angle
575(1)
14.1.3.2 TIR Observation of Vegetation
575(4)
14.1.3.3 TIR Observation of Snow
579(1)
14.1.4 Microwave Passive Observation of Land
580(8)
14.1.4.1 Microwave Passive Observation of Bare Soil
580(1)
14.1.4.2 Microwave Passive Observation of Vegetation
581(5)
14.1.4.2.1 Microwave Emissivity of Crops
582(1)
14.1.4.2.2 Microwave Emissivity of Forests
583(1)
14.1.4.2.3 Effect of Polarization on Vegetation Emissivity
583(3)
14.1.4.3 Microwave Passive Observation of Snow
586(2)
14.2 Interaction with Water Bodies
588(16)
14.2.1 Passive Observation of Water Bodies in the Optical Range
588(4)
14.2.1.1 Passive Optical Observation of Oil Slicks
589(2)
14.2.1.2 Lidar Observation of Oil Slicks
591(1)
14.2.2 Radar Observation of Water Bodies
592(6)
14.2.2.1 Radar Altimetry and Lidar Bathymetry
595(2)
14.2.2.2 Radar Observation of Sea Ice
597(1)
14.2.2.3 Radar Observation of Oil Slicks
597(1)
14.2.3 Observation of Water Bodies in the Thermal Infrared
598(2)
14.2.3.1 TIR Observation of Oil Spills
600(1)
14.2.4 Microwave Passive Observation of Water Bodies
600(4)
14.2.4.1 Radiometric Observation of Ocean Salinity
600(1)
14.2.4.2 Radiometric Observation of Ocean Surface Wind
601(1)
14.2.4.3 Radiometric Observation of Sea Ice
601(1)
14.2.4.4 Radiometric Observation of Oil Slicks
602(2)
14.3 Interaction with the Atmosphere
604(19)
14.3.1 Passive Observation of the Atmosphere in the Optical Range
604(7)
14.3.1.1 Observation of Trace Gases and Atmospheric Pollution
605(3)
14.3.1.1.1 Monitoring Space Weather
607(1)
14.3.1.2 Optical Passive Observation of Clouds and Aerosol
608(3)
14.3.1.2.1 Optical Passive Sensing of Aerosols
610(1)
14.3.2 Radar Observation of Clouds and Precipitation
611(4)
14.3.2.1 Lidar Observation of Aerosols and Clouds
615(1)
14.3.3 Observation in the Thermal Infrared
615(5)
14.3.3.1 Mapping Clouds and Water Vapor
616(3)
14.3.3.2 Atmospheric Sounding in the Thermal Infrared
619(1)
14.3.4 Passive Sounding at Microwaves
620(27)
14.3.4.1 Mapping Rain by Microwave Radiometry
621(2)
Paving the Road to Applications
623(2)
References
625(22)
A Vectors, Coordinates and Operators 647(20)
A.1 Recalling Vectors
647(2)
A.1.1 Vectors in Cartesian Coordinates
647(1)
A.1.2 Vector Multiplication
648(1)
A.1.2.1 Dot Product
648(1)
A.1.2.2 Cross Product
648(1)
A.1.2.3 Outer Product and Dyadics
648(1)
A.1.2.4 Double Products
649(1)
A.1.3 Vector Circuitation and Flux
649(1)
A.2 Recalling Curvilinear Coordinates
649(5)
A.2.1 The Metric Coefficients
650(3)
A.2.1.1 Cartesian Coordinates
651(1)
A.2.1.2 Spherical Coordinates
651(2)
A.2.1.2.1 Metric Coefficients for Spherical Coordinates
652(1)
A.2.1.3 Cylindrical Coordinates
653(1)
A.2.1.3.1 Metric Coefficients for Cylindrical Coordinates
653(1)
A.2.2 Transformation of Vector Components
653(1)
A.2.2.1 Transformation from Cartesian to Spherical
654(1)
A.2.2.2 Transformation from Cartesian to Cylindrical
654(1)
A.3 Recalling Operators
654(7)
A.3.1 Gradient
654(1)
A.3.2 Divergence
655(1)
A.3.3 Curl
656(1)
A.3.4 Operators in Orthogonal Curvilinear Coordinates
657(4)
A.3.4.1 Gradient
657(1)
A.3.4.2 Divergence
658(2)
A.3.4.3 Curl
660(1)
A.4 Recalling Nabla and Using It
661(6)
A.4.1 Operators in Terms of Nabla
662(1)
A.4.1.1 Gradient
662(1)
A.4.1.2 Divergence
662(1)
A.4.1.3 Curl
662(1)
A.4.2 Using Nabla
663(1)
A.4.3 Laplacian
664(3)
A.4.3.1 Laplacian in Cartesian Coordinates
664(1)
A.4.3.2 Laplacian in Orthogonal Curvilinear Coordinates
664(1)
A.4.3.3 The Laplacian in Some Vector Identities
665(2)
A.4.3.3.1 Green's Lemma
665(1)
A.4.3.3.2 Double Curl
665(2)
Acronyms 667(4)
Symbols 671(18)
Index 689
Domenico Solimini has obtained the tenure as assistant professor at the University of Rome, Italy, since 1966, and as full professor since 1980. In 1981 he moved to the newly established Tor Vergata University, Rome,Italy, where he acted as dean of Engineering curricula faculties, department director, and PhD coordinator. His teaching has concerned electromagnetic fields, antennas, propagation, and remote sensing. He received the 2005 IEEE Geoscience and Remote Sensing Society Education Award. His research mainly concerns passive and active remote sensing of both Earth's atmosphere and solid land surface, also within several international projects. He has authored and co-authored a few hundred publications. He is a co-founder of GEO-K, a geoinformation company spin-off of Tor Vergata University.
Biežāk uzdotie jautājumi par e-grāmatām Biežāk uzdotie jautājumi par e-grāmatām
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