Mathematical theory of holographic memory

Light waves are theoretically capable of recording octal information, based on the dimensionality of the set of bicharacteristic equations of Maxwell and their invariant vector measures. However, the impossibility of recording the amplitudes and phases of wave trains from actual light sources reduces this number to six. Holography allows all six signal parameters to be recorded on a two-dimensional surface and later reproduced. This statement is refined and is demonstrated mathematically. At points greater than a certain minimum distance from the surface of the hologram, the initial signal can be restored with accuracy equivalent to a certain complex factor and separated from the background for all orders of the short wave approximation. The amplitude, phase and polarization structure of the signal can take on any values. The reference wave is fixed, however. Complete restoration of signal polarization requires a known reference wave structure.