Radio Occultations Using Earth Satellites: A Wave Theory Treatment

Preface.

Acknowledgments.

Chapter 1. Radio Occultation Using Earth Satellites Background and Overview.

1.1 Introduction.

1.2 Information Content in GPS Occultation.

1.3 Scientific Applications of GPS Occultation Observations.

1.4 Problems from Multipath and Some Remedies.

1.5 Overview.

1.6 Limitations and Simplifications.

1.7 Recommendations for the Next Chapters.

Chapter 2. Scattering of Electromagnetic Waves from a Spherical Boundary Using a Thin Phase Screen Model and Scalar Diffraction Theory.

2.1 Introduction.

2.2 Geometric Optics in a Spherical Medium.

2.3 Thin Phase Screen Models.

2.4 Multipath Using a Thin Phase Screen Model.

2.5 Scalar Diffraction: The Rayleigh-Sommerfeld Integral.

2.6 The Stationary-Phase Technique.

2.7 Numerical Results Using Thin Screen/Scalar Diffraction.

2.8 Sensing Boundary in the Ionosphere.

2.9 The Error in the Recovered Refractivity Resulting from Fresnel Phase Perturbations.

2.10 Fresnel Transform Techniques.

Chapter 3. Scattering from a Large Transparent Sphere Based on Maxwell’s Equations: Mie Scattering Theory.

3.1 Introduction.

3.2 Scalar Potentials.

3.3 Multiple Internal Reflections.

3.4 Fresnel Formulas for Reflection and Transmission Amplitudes.

3.5 Mie Scattering Theory: Obtaining the Scattering Coefficients at a Boundary.

3.6 The Problem of Slow Convergence.

3.7 The Sommerfeld-Watson Transformation.

3.8 Evaluating Scattering Coefficients with Asymptotic Expansions.

3.9 Expressing Scattering Coefficients in Terms of Phasors.

3.10 Asymptotic Forms for the Hankel and Legendre Functions Evaluated at the LEO.

3.11 Geometric Optics Interpretation of Mie Scattering Theory.

3.12 Evaluating Mie Scattering by Integration of the Scattering Phasor.

3.13 Interpreting Scattering Using the Stationary-Phase Technique.

3.14 Duality Between Stationary-Phase Concepts in Electrodynamics and in Geometric Optics.

3.15 Diffraction from a Large, Transparent, Refracting Sphere Using Mie Scattering Theory.

3.16 Looking for Rainbows.

3.17 Limiting Cases.

Chapter 4. Wave Propagation in a Stratified Medium: The Thin-Film Approach.

4.1 Introduction.

4.2 Thin-Film Concepts.

4.3 The Characteristic Matrix.

4.4 The Stratified Medium as a Stack of Discrete Layers.

4.5 The Characteristic Matrix for an Airy Layer.

4.6 Incoming and Outgoing Waves and Their Turning Points.

4.7 Concatenated Airy Layers.

4.8 Osculating Parameters.

4.9 Airy Functions as Basis Functions.

4.10 Wave Propagation in a Cylindrical Stratified Medium.

4.11 Wave Propagation in a Spherical Stratified Medium.

4.12 Correspondence Between Characteristic Matrices for Cartesian and Spherical Stratified Airy Layers.

Chapter 5. Propagation and Scattering in a Spherical-Stratifield Refracting Medium.

5.1 Introduction.

5.2 Maxwell’s Equations in a Stratified Linear Medium.

5.3 Modified Spherical Bessel Functions.

5.4 Asymptotic Forms.

5.5 Modified Mie Scattering in a Spherical Stratified Medium.

5.6 More Geometric Optics: Cumulative Bending Angle, Bouguer’s Law, and Defocusing.

5.7 More Asymptotic Forms.

5.8 Spectral Representation of an Electromagnetic Wave in a Spherical Stratified Medium.

5.9 Interpreting Wave Theory in a Refracting Medium Using the Stationary Phase Technique.

5.10 Comparison of Geometric Optics and Wave Theory.

5.11 The Electric Field at a Turning Point.

5.12 Caustics and Multipath.

5.13 Spectral Coefficients in a Spherical Refracting Medium with an Embedded Discontinuity.

5.14 The Scattered Field from a Perfectly Reflecting Sphere Embedded in a Refracting Medium.

Chapter 6. The Inverse Problem: Using Spectral Theory to Recover the Atmospheric Refractivity Profile.

6.1 Introduction.

6.2 GPS Receiver Operations.

6.3 Spectral Representation of the Field of the LEO.

6.4 Refractivity Recovery.

6.5 Summary.

Appendix A: Miscellaneous Derivations.

Appendix B: Caustic Surfaces.

Appendix C: Multiple Ray Path Separation Altitudes.

Appendix D: Third-Order Stationary Phase Theory.

Appendix E: Bending by a Gaussian Electron Density Distribution.

Appendix F: The Effect of Cycle Slips on Recovered Refractivity.

Appendix G: Using the Sommerfeld–Watson Transformation.

Appendix H: Characteristic Matrix in a Stack of  Airy Layers.

Appendix I: Field Equations in a Stratified Medium.

Appendix J: Conditions for Near-Equivalence Between dG^† (v)/dv and ã(v,v), and Between d²G^† (v)/ dv² and dã(v,v)/dv.

Glossary of Terms.

Acronyms.