This book gives a very complete, authoritative and up-to-date treatment of acoustic and electromagnetic fields generated by bounded sources from several intertwined viewpoints: (a) their representations by volume sources and by "Huygens sources" distributed over a surface enclosing the source region, (b) plane-wave spectra, (c) far fields, and (d) far-field radiation patterns. When field measurements are made in a plane outside the source region, the plane-wave spectral representation lends itself naturally to correcting for the characteristics of the probe performing the measurements to compute the true fields beyond the scan plane. This explains the subtitle "Near-field Scanning Applications." Throughout the book, the scalar (acoustic) and vector (electromagnetic) cases are treated in tandem, with the acoustic case usually preceding the algebraically more complicated electromagnetic case.

Whereas the above topics have been the subject of a number of previous studies, the novelty of the present approach is in examining them thoroughly in the time domain as well as the frequency domain. The time-domain formulations are derived in two ways: by Fourier transforming the corresponding frequency-domain expressions, and then directly in the time domain from the properties of Green functions. The identity of the results, sometimes after long and difficult mathematical manipulations, helps the reader gain confidence in the final product even if she or he was unable to follow all the details of the derivation. As a mathematician, I was especially impressed by the consistently rigorous level of the treatments. Although mathematical rigor is sometimes dismissed by engineers as largely academic, the authors give ample demonstrations of its practical necessity. For example, the proof in Sections 6.1.1 (or 7.1.3) that the probe output solves the homogeneous Helmholtz equation (or wave equation) outside the region occupied by the sources and the probe is a case study of the need to justify bringing partial differential operators under an integral sign, as a sloppy treatment simply leads to the wrong conclusion that the homogeneous equation is satisfied in all of space!

The book ends with some practical considerations on sampling and numerical applications of the foregoing results.