A simple theory of three forms of holographic interferometry “time‐average,” multiple‐exposure, and “real‐time” (live) interferometry is presented, based on a new development in holographic “image synthesis” (complex amplitude addition and subtraction), introduced in 1965 by D. Gabor and G. W. Strokeet al.They demonstrated the remarkable property of holography: Interference can occur between two or more light beams that are not superimposed either in time or in space, if the holographic intensities corresponding to the beams are obtained with the aid of a coherent reference‐background beam of the same spatial shape and if these intensities are successively added in the same hologram. Following the independent discovery of holographic interferometry, in 1965, by J. M. Burch; by R. L. Powell and K. A. Stetson; and by L. O. Heflinger, R. F. Wuerker, and R. E. Brooks, among others, it was found that two or more successive photographic additions of the hologram intensities (corresponding to two or moresequentialpositions or shapes of a given object) would thus indeed permit one to “synthesize,” in the form of an interferogram, the complex sum of the spatial‐electric‐field vectors, corresponding to each object‐point position, as if the different object‐point positions had all existedsimultaneouslyrather than sequentially, as they do during the hologram recording (for instance in the case of multiple holographic‐image recording of a vibrating object). The rigorous equations we present, notably in vector form, for the general cases of practical interest bear out the equations previously derived by a number of authors, for some special cases, frequently in heuristic form.