Since holography was first described by D. Gabor--A New Microscope Principle, Nature, V.161 (1948), p. 777--the development within this field has proceeded quickly, in particular following the introduction of the laser for reconstruction, see E. N. Leith and J. Upatnieks: Reconstructed Wavefronts and Communication Theory, J. Optical Society of America, V. 53 (1963), p. 1377. This development from what may be called classical holography to digital holography for producing synthetic holograms--T. S. Huang: Digital Holography, Proc. of the IEEE, V. 59 (1971) no. 9--has made it possible to look at three-dimensional representations of objects which have been described mathematically, but which do not exist.
Within classical holography a wave coming from a real object is combined with a reference wave, and the sum of these waves is recorded on a modulator for a reconstruction wave. By directing the reconstruction wave against the hologram thus produced, the object is reconstructed. In the computer generation of holograms the combination of an imaginary wave from the mathematically described object and an imaginary reference wave is calculated mathematically, such that the imaginary total wavefront is calculated in quantized areas in the plane in which the hologram is located during reconstruction. This involves the calculation of amplitude and phase for the total wave field. In optical holography a calculated wave information is usually recorded by plotting the interference pattern between the two light waves at a practical scale as an artwork which is then scaled down photographically. The present invention comprises the direct generation of quantized hologram areas, for instance by means of a scanning electron microscope.
Several methods have been developed for recording amplitude and phase information for a light wave front. In the Lohmann's technique the hologram generated is binary, thus it consists of opaque and transparent windows. The size of a transparent window is then proportional to the desired amplitude, and its position is related to the desired phase. In Lee's technique the complex wave information is decomposed into four real parts displaced from each other, so that both the real and the imaginary parts of the desired information are recorded. In both these techniques the object points considered to be emitting light against the hologram plane, must be on a plane or a collection of planes located in the Fraunhofer region, so that the fast fourier transform (FFT) can be used to calculate the light wave amplitude and phase at quantized apertures in the hologram plane. In Waters' technique the individual object points as well as the hologram due to each of these points are considered separately. In other words the zone plate pattern is recorded. In such case the object points can be in the Fresnel region. In the kinoform technique the amplitude of the light wave is assumed to be constant, and only the phase is recorded, which will be approximately correct for objects giving diffuse reflection. The phase information can be recorded by means of binary selection, such that when the phase is between 0 and .pi. radians, a window is made on the hologram, and when the phase is between .pi. and 2.pi. radians, no record is made.
Generally one of the big problems in connection with computer generation of holograms is that the time for computing the interference pattern between the object wave and the reference wave may be so long that the generation excludes itself. Even the simplified methods used are complicated and time consuming. With respect to the kinoform technique in particular there must be used a gray scale in order to simulate the actual phase angle. In a sampled representation of the object and binary quantization also conjugate and higher order images are created.