A diffraction-limited, electromagnetic theory of image formation is presented for a point-reference hologram whose recording arrangement consists of a surface of arbitrary shape, a point-reference source, and the object. The hologram is illuminated by a spherical electromagnetic wave during reconstruction. The electromagnetic hologram is assumed to have recorded two components of the field scattered from the object so that the vector field is completely reconstructed. The vector hologram is modeled by electric and magnetic surface currents determined from the irradiance of each of two orthogonal components of the object field on the film. The image field is described by a dyadic kernel, the system response to a point object, which is related to the scalar kernel by Π (r,r′) = DK (r,r′), where D is the dyadic operator D =(I+k-2∇∇). It is shown that the conjugate-image field produced by a point-reference electromagnetic hologram approximates the field produced by the ideal system, which forms the image of a point object by launching a spherically converging wave.
ROBERT P. PORTER and WALTER C. SCHWAB, "Electromagnetic Image Formation with Holograms of Arbitrary Shape," J. Opt. Soc. Am. 61, 789-796 (1971)