I started this book roughly 20 years ago with the intention of producing a finished product within a year or so. But reality in the form of government research grants and “publish or perish” soon set in and so now, at long last, I have finally finished. The final product has of course changed significantly over these intervening years, both in content and in breadth. My original plan was to put together a six- or seven-chapter treatise on basic “Fourier-based” coherent imaging and diffraction tomography complete with Matlab codes implementing the imaging and inversion algorithms presented in the text. The current book certainly includes this material, but also includes a host of other material such as the chapter on time-reversal imaging and the four chapters on the propagation and scattering of waves in homogeneous and inhomogeneous backgrounds. More importantly, the “Fourier-based” inversion schemes originally used to develop much of coherent imaging and linearized inverse scattering (diffraction tomography) have been replaced by the much more powerful singular value decomposition (SVD). This approach allows virtually all of the linearized inverse problems associated with the wave and Helmholtz equation both in homogeneous and in inhomogeneous backgrounds to be treated in a uniform “turn the crank” manner.

My work on imaging and wavefield inversion began as a graduate student under Professor Emil Wolf at the University of Rochester. Originally I had intended to pursue my Ph.D. in quantum optics, but had my plans changed significantly by an off-hand remark by Professor Wolf during one of our meetings.