In conventional procedures for image acquisition (photography, TV recording, etc.) the intensity distribution is recorded and the phase information is lost. Since the phase distribution carries a significant part of the propagation information, such as the propagation direction represented by linear phase factors, this information is lost as well. Part of the lost information contains data about the 3D character of the light field leaving only a 2D distribution which is recorded. Modern technology provides means to fabricate phase functions artificially (the lens and prism are just two examples) as well as amplitude functions. However, one cannot directly record the phase information in a light field unless it is compared to some reference phase like in an interferometer. To overcome the difficulty in recording the complete information, amplitude as well as phase, a fundamentally different approach must be employed. Such a new approach was suggested by Dennis Gabor  in 1948 and, independently, a little later by Yuri Denisyuk  from a different point of view. Both procedures are now called holography. While a special case of holography was already encountered in section 5.6.2, this chapter is devoted to a detailed discussion of this subject. Most of this chapter is rather descriptive and a generalized mathematical description is left for the last section 11.12 which provides an operator description of the whole process. More detailed analysis of the holographic process can be found in the literature (see, for example, Refs. [89, 91]).
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