A two-step imaging process discovered by Gabor involves photographing the Fresnel diffraction pattern of an object and using this recorded pattern, called a hologram, to construct an image of this object. Here, the process is described from a communication-theory viewpoint. It is shown that construction of the hologram constitutes a sequence of three well-known operations: a modulation, a frequency dispersion, and a square-law detection. In the reconstruction process, the inverse-frequency-dispersion operation is carried out. The process as normally carried out results in a reconstruction in which the signal-to-noise ratio is unity. Techniques which correct this shortcoming are described and experimentally tested. Generalized holograms are discussed, in which the hologram is other than a Fresnel diffraction pattern.

1. D. Gabor, Nature 161, 777 (1948); Proc. Roy. Soc. (London) A197, 454 (1949).
2. L. J. Cutrona, E. N. Leith, C. J. Palermo, L. J. Porcello, Trans. IRE IT-6, 386 (1960).
3. A discussion of various similar techniques for eliminating the twin image is given by Lohmann, Optica Acta (Paris) 3, 97 (1956). These are likewise developed by use of a communication theory approach.
4. See reference 2, p. 391.
5. See reference 3.
6. The impulse response of the half-plane filter is derived from Hilbert transform relations. For a discussion of Hilbert transforms, see, for example, W. Brown, Analysis of Linear Time-Invariant Systems McGraw-Hill Book Company, Inc., New York, 1962). As given by Brown, the Hilbert transform of a function s(t) is represented in the frequency domain by a filter which phase-shifts the positive frequencies by, and in the time domain by the convolution integral 1/π∫^∞_∞s(τ)t-τ)^-1dτ.

Other

• D. Gabor, Nature 161, 777 (1948); Proc. Roy. Soc. (London) A197, 454 (1949).
• L. J. Cutrona, E. N. Leith, C. J. Palermo, L. J. Porcello, Trans. IRE IT-6, 386 (1960).
• A discussion of various similar techniques for eliminating the twin image is given by Lohmann, Optica Acta (Paris) 3, 97 (1956). These are likewise developed by use of a communication theory approach.
• See reference 2, p. 391.
• See reference 3.
• The impulse response of the half-plane filter is derived from Hilbert transform relations. For a discussion of Hilbert transforms, see, for example, W. Brown, Analysis of Linear Time-Invariant Systems McGraw-Hill Book Company, Inc., New York, 1962). As given by Brown, the Hilbert transform of a function s(t) is represented in the frequency domain by a filter which phase-shifts the positive frequencies by, and in the time domain by the convolution integral 1/π∫^∞_∞s(τ)t-τ)^-1dτ.

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