The theory developed in the preceding paper1 is applied to a number of questions about timelimited and bandlimited signals. In particular, if a finite-energy signal is given, the possible proportions of its energy in a finite time interval and a finite frequency band are found, as well as the signals which do the best job of simultaneous time and frequency concentration.

Prolate spheroidal wave functions, fourier analysis and uncertainty — II

Phased Arrays in Radar and Communication Systems. Pattern Characteristics and Synthesis of Linear and Planar Arrays. Patterns of Nonplanar Arrays. Elements, Transmission Lines, and Feed Architectures for Phased Arrays. Summary of Element Pattern and Mutual Impedance Effects. Array Error Effects. Special Array Feeds for Limited Field of View and Wideband Arrays.

Phased Array Antenna Handbook

It is well known that the phenomenon of radiation from line-source antennas is very similar to that of the diffraction of light from narrow apertures. Unlike the optical situation, however, antenna design technique permits the use of other-than-uniform distributions of field across the antenna aperture. Line source synthesis is the science of choosing this distribution function to give a radiation pattern with prescribed properties such as, for example, narrow angular width of the main lobe and low side lobes. In the present article the mathematical relationships involved in the radiation calculation are studied from the point of view of function theory. Some conclusions are drawn which outline the major aspects of synthesis technique very clearly. In particular, the problem of constructing a line source with an optimum compromise between beamwidth and side-lobe level (analogous to the Dolph - Tchebycheff problem in linear array theory) is considered. The ideal pattern is cos π √ {u /sup 2/ - A/sup 2/} , where u = (2a/λ) cos θ, a is the half-length of the source, and cosh π A is the side-lobe ratio. Because of theoretical limitations, this pattern cannot be obtained from a physically realizable antenna; nevertheless its ideal characteristics can be approached arbitrarily closely. The procedure for doing this is given in detail.

Design of line-source antennas for narrow beamwidth and low side lobes

Design of line source antennas for narrow beamwidth and low sidelobes

The past decade has seen numerous efforts to achieve imaging resolution beyond that of the Abbe-Rayleigh diffraction limit. The main direction of research aiming to break this limit seeks to exploit the evanescent components containing fine detail of the electromagnetic field distribution at the immediate proximity of the object. Here, we propose a solution that removes the need for evanescent fields. The object being imaged or stimulated with subwavelength accuracy does not need to be in the immediate proximity of the superlens or field concentrator: an optical mask can be designed that creates constructive interference of waves known as superoscillation, leading to a subwavelength focus of prescribed size and shape in a field of view beyond the evanescent fields, when illuminated by a monochromatic wave. Moreover, we demonstrate that such a mask may be used not only as a focusing device but also as a super-resolution imaging device.

Super-Resolution without Evanescent Waves

It appears that it is possible to approximate as closely as desired to a specified radiation-pattern by a suitable distribution of field over an aperture of given size, though the necessary currents in the conducting elements of the source would in general be prohibitively large in comparison with the power radiated. The difficulty of obtaining a high degree of approximation, and in particular a power gain very much greater than that of a uniformly illuminated aperture, is thus a practical rather than a theoretical one. The same is true for the linear array of given length as for the continuous aperture if no limit is set to the number of elements. Even when this number is limited by the adoption of half-wavelength spacing, the broadside power gain is not a maximum when the amplitudes and phases of the elements are equal, unless the elements are ideal isotropic point-sources.

J.D. Lawson

Papers

The Theoretical Precision with which an Arbitrary Radiation-Pattern may be Obtained from a Source of Finite Size