A complement to the theory of Lohmann-type computer holograms

The introduction by Lohmann and co-workers of the detour phase method in realizing synthetic holograms has been an important step in the history of computer generated holography. In 1969, Brown and Lohmann proposed an improvement to their method: they used true phase and amplitude coding at the center of the diffracting aperture instead of periodically sampled phases and amplitudes. We present a mathematical analysis of this procedure and examine the approximation related to its practical realization.