  We summarise the mathematical foundation of the holographic method of
measuring the reflector profile of an antenna or radio telescope. In
particular, we treat the case, where the signal source is located at a finite
distance from the antenna under test, necessitating the inclusion of the
so-called Fresnel field terms in the radiation integrals. We assume a ``full
phase'' system with reference receiver to provide the reference phase. We
describe in some detail the hardware and software implementation of the system
used for the holographic measurement of the 12m ALMA prototype submillimeter
antennas. We include a description of the practicalities of a measurement and
surface setting. The results for both the VertexRSI and AEC
(Alcatel-EIE-Consortium) prototype ALMA antennas are presented.
