The inverse source problem for monochromatic sources Re[ρ(<b>r</b>, ω)<i>e</i><sup><i>-iωt</i></sup>] to the scalar-wave equation is investigated. It is shown that a unique solution to the inverse source problem can be obtained by imposing the constraint that the solution minimize the source energy <i>E</i> = ∫ d<sup>3</sup><i>r</i>|ρ(<b>r</b>, ω)|<sup>2</sup>. For certain recording geometries the time derivative of the real image produced by a point-reference hologram is shown to be directly proportional to the time-reversed minimum energy source Re[ρ*<i>ME</i>(<b>r</b>, ω)<i>e</i><sup><i>-iωt</i></sup>] in the short-wavelength limit.
© 1982 Optical Society of America
R. P. Porter and A. J. Devaney, "Holography and the inverse source problem," J. Opt. Soc. Am. 72, 327-330 (1982)