The quantum mechanical theory of the formation of an emission hologram with gamma radiation is developed. Radiation, produced by a radioactive source nucleus, can go directly to a detector or can be resonantly scattered by neighboring resonant nuclei before going to the detector. The interference between these two precesses gives rise to fluctuations in the radiated intensity as a function of the emission angle. These fluctuations contain information about the surrounding of the emitting nucleus. The coupled system of equations describing the scattering amplitudes has been solved in the single scattering approximation. [S0163-1829(99)02733-2].