Formulation of probe-corrected planar near-field scanning in the time domain

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 measurements 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-held pattern as a double spatial integral of the time-domain output of the probe over the scan plane multiplied by the angular dependence of the inverse receiving characteristic of the probe. Time-domain reciprocity relations are derived for reciprocal probes, and their time-domain receiving characteristics are related to 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