Radar 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.
Margaret Cheney is a Professor of Mathematics at Rensselaer Polytechnic Institute. Most of her work has been in inverse problems, including those that arise in quantum mechanics, acoustics, and electromagnetic theory. She has been working specifically in radar imaging since 2001. Brett Borden spent most of his career working on radar at the Naval Air Warfare Center Weapons Division in China Lake, California. He is currently a Professor of Physics at the Naval Postgraduate School.
List of figures; List of tables; Preface; Part I. Radar Basic: 1. Introduction; 2. Radar systems; 3. Introduction to scattering; 4. Detection of signals in noise; 5. The radar ambiguity function; Part II. Radar Imaging: 6. Wave propagation in two and three dimensions; 7. Inverse synthetic-aperture radar; 8. Antennas; 9. Synthetic-aperture radar; 10. Related techniques; 11. Open problems; Bibliography; Index.