Holographic approach to radiation pattern measurement—I general theory

Abstract The term “Fraunhofer hologram” is used to denote a record of the square of the modulus of a far-field radiation pattern due to a mixture of known and unknown source distributions. Provided the known and unknown sources are sufficiently separated, the unknown sources can be reconstructed from the hologram, irrespective of the relative magnitudes of the two sources. When the known source is much stronger than the unknown source, the unknown source can be reconstructed from the hologram, even when the two sources overlap. This paper gives the theory of holography for known (reference) sources of arbitrary form. Consequently, it is only feasible to apply the results in practice to acoustic and radio frequency, as opposed to optical, radiation patterns because the reconstruction procedure in general requires a digital computer. The theory recognizes that a practical hologram is necessarily imperfect and incomplete, which blurs the image but does not prevent its reconstruction, as is demonstrated in a companion paper.