Деннис Габор

Hitherto communication theory was based on two alternative methods of signal analysis. One is the description of the signal as a function of time; the other is Fourier analysis. Both are idealizations, as the first method operates with sharply defined instants of time, the second with infinite wave-trains of rigorously defined frequencies. But our everyday experiences—especially our auditory sensations—insist on a description in terms of both time and frequency. In the present paper this point of view is developed in quantitative language. Signals are represented in two dimensions, with time and frequency as co-ordinates. Such two-dimensional representations can be called “information diagrams,” as areas in them are proportional to the number of independent data which they can convey. This is a consequence of the fact that the frequency of a signal which is not of infinite duration can be defined only with a certain inaccuracy, which is inversely proportional to the duration, and vice versa. This “uncertainty relation” suggests a new method of description, intermediate between the two extremes of time analysis and spectral analysis. There are certain “elementary signals” which occupy the smallest possible area in the information diagram. They are harmonic oscillations modulated by a “probability pulse.” Each elementary signal can be considered as conveying exactly one datum, or one “quantum of information.” Any signal can be expanded in terms of these by a process which includes time analysis and Fourier analysis as extreme cases.These new methods of analysis, which involve some of the mathematical apparatus of quantum theory, are illustrated by application to some problems of transmission theory, such as direct generation of single sidebands, signals transmitted in minimum time through limited frequency channels, frequency modulation and time-division multiplex telephony.

Abstract The subject of this paper is a new two-step method of optical imagery. In a first step the object is illuminated with a coherent monochromatic wave, and the diffraction pattern resulting from the interference of the coherent secondary wave issuing from the object with the strong, coherent background is recorded on a photographic plate. If the photographic plate, suitably processed, is replaced in the original position and illuminated with the coherent background alone, an image of the object will appear behind it, in the original position. It is shown that this process reconstructs the coherent secondary wave, together with an equally strong ‘twin wave’ which has the same amplitude, but opposite phase shifts relative to the background. The illuminating wave itself can be used for producing the coherent background. The simplest case is illumination by a point source. In this case the two twin waves are shown to correspond to two ‘twin objects’, one of which is the original, while the other is its mirror image with respect to the illuminating centre. A physical aperture can be used as a point source, or the image of an aperture produced by a condenser system . If this system has aberrations, such as astigmatism or spherical aberration, the twin image will be no longer sharp but will appear blurred, as if viewed through a system with twice the aberrations of the condenser. In either case the correct image of the object can be effectively isolated from its twin, and separately observed. Three-dimensional objects can be reconstructed, as well as two-dimensional. The wave used in the reconstruction need not be the original, it can be, for example, a light-optical imitation of the electron wave with which the diffraction diagram was taken. Thus it becomes possible to extend the idea of Sir Lawrence Bragg’s ‘X -ray microscope’ to arbitrary objects, and use the new method for improvements in electron microscopy. The apparatus will consist of two parts, an electronic device in which a diffraction pattern is taken with electrons diverging from a fine focus, and an optical synthetizer, which imitates the essential data of the electronic device on a much enlarged scale. The theory of the analysis-synthesis cycle is developed, with a discussion of the impurities arising in the reconstruction, and their avoidance. The limitations of the new method are due chiefly to the small intensities which are available in coherent beams, but it appears perfectly feasible to achieve a resolution limit of 1 Å, ultimately perhaps even better.

The theory of diffraction microscopy is completed and extended in different directions. In this two-step method of image formation the object is reconstructed by optical means from a diffraction diagram, taken in coherent illumination with light or with electrons. The `projection method', originally described, and the `transmission method', recently proposed by Haine and Dyson, are two variants which can be treated by one theory. The Proc.ess of image formation, the coherence requirements, and the conditions for a good reconstruction are discussed in detail It is shown that the reconstructed image of extended objects suffers from some spurious detail, but this can be largely suppressed in the `dark-field' method of reconstruction, in which the illuminating wave is cut out after it has passed through the diffraction diagram.