Probe-corrected planar near-field formulas in the time domain are derived for both acoustic and electromagnetic fields, so that a single set of near-field measurement in the time domain yields the fields of the test antenna directly in the time domain. The time-domain probe-corrected formulas are first derived by taking the inverse Fourier transform of the corresponding frequency- domain formulas, and then by using a time-domain expansion for the fields of the test antenna and a time-domain receiving characteristic of the probe. Because these general formulas, which involve a double integral over the scan plane and an infinite time-convolution integral, are rather complicated, we consider a special probe whose output due to an incoming time-domain plane wave is proportional to the time derivative of the field of that plane wave. For this special D-dot probe, the probe-corrected formulas simplify to give the time- domain far-field pattern as a double spatial integral of the time-domain output of the prove over the scan plane multiplied by the angular dependence of the receiving characteristic of the probe. Time-domain reciprocity relations are derived for reciprocal probes, and their time-domain receiving characteristics are related their far fields. Finally, a time-domain sampling theorem is derived and a numerical example illustrates the use of the time-domain probe-corrected formulas. Near-field measurements, Planar scanning, Time domain, Probe correction.

This report addresses the problem of formulating planar near-field antenna measurements in the time domain, so that a single set of time-domain near-field measurements yields the far-field pattern in the time domain or over a wide range of frequencies. The time-domain planar near-field techniques are developed for both acoustic and electromagnetic fields and the space outside the region occupied by the antenna is assumed to be isotropic and homogeneous. Probe correction is ignored, that is, it is assumed that the probe is ideal so that the exact values of the field on the measurement plane are known. Two fundamentally different approaches are used in deriving time-domain formulas which give the fields in the half space z> z sub 0, in terms of their values on the plane z = z sub 0. In the first approach the time-domain formulas are obtained by inverse Fourier transforming the corresponding frequency-domain formulas. Since this approach requires extensive use of the frequency domain near-field formulas, we start by giving a rigorous derivation and review of the frequency-domain formulation that addresses a number of subtleties that have not been dealt with adequately in the literature. As part of this review, planar near-field formulas for the static electric and magnetic fields are derived for the first time. In the second approach the time-domain near-field formulas are derived directly in the time domain. The equivalence of the resulting time- domain formulas obtained by the two different approaches demonstrates the validity of the formulas and the utility of both approaches. Near-field measurements, Planar scanning, Time-domain.

"This invaluable book provides a comprehensive framework for the formulation and solution ofnumerous problems involving the radiation, reception, propagation, and scattering of electromagnetic and acoustic waves. Filled with original derivations and theorems, it includes the first rigorous development of plane-wave expansions for time-domain electromagnetic and acoustic fields. For the past 35 years, near-field measurement techniques have been confined to the frequency domain. Now, with the publication of this book, probe-corrected near-field measurement techniques have been extended to ultra-wide-band, short-pulse transmitting and receiving antennas and transducers. By combining unencumbered straightforward derivations with in-depth expositions of prerequisite material, the authors have created an invaluable resource for research scientists and engineers in electromagnetics and acoustics, and a definitive reference on plane-wave expansions and near-field measurements. Featured topics include: * An introduction to the basic electromagnetic and acoustic field equations * A rigorous development of time-domain and frequency-domain plane-wave representations * The formulation of time-domain, frequency-domain, and static planar near-field measurement techniques with and without probe-correction * Sampling theorems and computation schemes for time-domain and frequency-domain fields * Analytic-signal formulas that simplify the formulation and analysis of transient fields * Wave phenomena, such as ``electromagnetic missiles"" encountered only in the time domain * Definitive force and power relations for electromagnetic and acoustic fields and sources." Sponsored by: IEEE Antennas and Propagation Society.

This IMA Volume in Mathematics and its Applications COMPUTATIONAL WAVE PROPAGATION is based on the workshop with the same title and was an integral part of the 1994-1995 IMA program on "Waves and Scattering." We would like to thank Bjorn Engquist and Gregory A. Kriegsmann for their hard work in organizing this meeting and in editing the proceedings. We also take this opportunity to thank the National Science Foundation, the Army Research Office, and the Office of Naval Research, whose financial support made this workshop possible. A vner Friedman Robert Gulliver v PREFACE Although the field of wave propagation and scattering has its classical roots in the last century, it has enjoyed a rich and vibrant life over the past 50 odd years. Scientists, engineers, and mathematicians have devel oped sophisticated asymptotic and numerical tools to solve problems of ever increasing complexity. Their work has been spurred on by emerging and maturing technologies, primarily concerned with the propagation and reception of information, and the efficient transmission of energy. The vitality of this scientific field is not waning. Increased demands to precisely quantify, measure, and control the propagation and scattering of waves in increasingly complex settings pose challenging scientific and mathematical problems. These push the envelope of analysis and comput ing, just as their forerunners did 50 years ago. These modern technological problems range from using underwater sound to monitor and predict global warming, to periodically embedding phase-sensitive amplifiers in optical fibers to insure long range digital communication.