Many optical designs are constrained by the physical size and weight of the refractive elements –lenses and prisms - involved. In many cases these limitations can be reduced or eliminated by the use of diffractive optical elements. In the simplest case, a diffractive element might be a surface grating that directs light as a function of the wavelength and the pitch of the grating. In more complex designs, a diffractive element can be a volume hologram, or a collection of multiplexed holograms in a relatively thin layer.

Holographic elements are particularly useful for combining many optical functions into a single optical element. In principle, any complex waveform may be converted into another complex waveform with a hologram as long as the required hologram can be recorded with coherent light into an appropriate medium. In practice, the design of useful holograms is a combination of optical science and art. The design of the hologram dictates a recording geometry that must also account for “non-ideal” behavior of the recording media, as well as any other differences in environment between hologram recording and use.

A hologram is a record of an object wavefront, formed from the interference of the wavefront with a suitable reference wave. Since the hologram is a record of an interference pattern, the reference wave must be coherent with the object wave. The most convenient method to generate mutually coherent waves is to generate both waves from a source with a long coherence length, such as a laser.

After recording, the original wavefront can be generated by illuminating the hologram with a wavefront corresponding to the reference wave. Since the object wavefront can be the result of the product of many optical functions, several components may be replaced by a single holographic element. This type of compression of optical functions formed the basis of Aprilis biometric imager technology.

If the holographic medium is sufficiently thick, then any variation from the original reference wavefront will result in a failure to reconstruct the original wave. This selectivity is the basis for multiplexing, where a number of holograms with different reconstruction characteristics may be recorded into a single layer. Holographic multiplexing is a key feature that is the basis for high-density optical data storage.

Another important feature of holograms is that the reconstruction can be performed equally with either the original reference or object waves. As a result, a hologram containing recorded information can reconstruct the original reference wave when interrogated with a wave containing some of the information. The efficiency of the reconstruction will be a direct measure of the correlation strength of the information used for the interrogation with the information recorded in the hologram. This feature is the basis for content addressable memory based on optical correlation.