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# Fresnel zone

About: Fresnel zone is a research topic. Over the lifetime, 2337 publications have been published within this topic receiving 37650 citations.

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TL;DR: Laser beams that contain phase singularities can be generated with computer-generated holograms, which in the simplest case have the form of spiral Fresnel zone plates.

Abstract: Laser beams that contain phase singularities can be generated with computer-generated holograms, which in the simplest case have the form of spiral Fresnel zone plates.

1,251 citations

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TL;DR: In this article, the spatial bandwidth of an optical system can be increased over the classical limit by reducing one of the other constituent factors of N. This invariance theorem was established in Part I of this series [J. Opt. Soc. Am.56, 1463].

Abstract: The fundamental invariant of an optical system is the number N of degrees of freedom of the message it can transmit. The spatial bandwidth of the system can be increased over the classical limit by reducing one of the other constituent factors of N. As examples of this invariance theorem N=const. established in Part I of this series [ J. Opt. Soc. Am.56, 1463 ( 1966)], we discuss (a) a system whose spatial-bandwidth increase is achieved by a proportional reduction of its temporal bandwidth, and (b) the airborne synthetic-aperture, terrain-mapping radar, whose spatial resolution comes from exploitation of the temporal degrees of freedom of the received signal. The increase of the spatial bandwidth beyond the classical limit is, however, limited by the appearance of evanescent waves.The number of degrees of freedom of the object wave field stored in a hologram is discussed. The storage capacity of the photographic plate, which is proportional to its size times its spatial cutoff frequency, is fully exploited only by single-sideband Fraunhofer but not by single-sideband Fresnel holograms.

430 citations

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TL;DR: In this article, phase reversal zone plates are designed for regions of the electromagnetic spectrum where the index of refraction is complex, with a real part close to 1.0, and materials with suitable optical and mechanical properties exist throughout most of the 1-800-A wavelength range for their construction.

Abstract: Phase-reversal zone plates can be designed even for regions of the electromagnetic spectrum where the index of refraction is complex, with a real part close to 1.0. These devices are superior to Fresnel zone plates both in their light collection, and in their signal-to-noise characteristics. Materials with suitable optical and mechanical properties exist throughout most of the 1–800-A wavelength range for their construction. Imperfections in fabrication, such as incorrect plate thickness, sloping zone edges, or an error in the width of alternate zones result in only moderate deterioration in optical performance.

403 citations

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TL;DR: It is shown that a large number of pinholes distributed appropriately over the Fresnel zones make it possible to focus soft X-rays to spot sizes smaller than the diameter of the smallest pinhole.

Abstract: Fresnel zone plates consisting of alternating transmissive and opaque circular rings can be used to focus X-rays1. The spatial resolution that can be achieved with these devices is of the order of the width of the outermost zone and is therefore limited by the smallest structure (20–40 nm) that can be fabricated by lithography today2. Here we show that a large number of pinholes distributed appropriately over the Fresnel zones make it possible to focus soft X-rays to spot sizes smaller than the diameter of the smallest pinhole. In addition, higher orders of diffraction and secondary maxima can be suppressed by several orders of magnitude. In combination with the next generation of synchrotron light sources (free-electron lasers) these ‘photon sieves’ offer new opportunities for high-resolution X-ray microscopy and spectroscopy in physical and life sciences.

362 citations

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TL;DR: In this article, the necessary and sufficient conditions for self-imaging were derived in order that an infinite plane object, illuminated by a plane monochromatic wave of normal incidence, images itself without the aid of lenses or other optical accessories.

Abstract: The necessary and sufficient conditions are derived in order that an infinite plane object, illuminated by a plane monochromatic wave of normal incidence, images itself without the aid of lenses or other optical accessories. This involves a solution of the reduced wave equation which does not satisfy the Sommerfeld radiation condition. The solution is obtained by requiring a geometrical-optics limiting condition as the wavelength λ goes to zero. Two cases of self-imaging are considered. The first case, called weak, deals with the faithful imaging of objects whose spatial frequencies are all much smaller than the (1/λ) value of the illuminating source. The conditions for this case demand that the two-dimensional Fourier spectrum of the object lies on the circles of a Fresnel zone plate. The second case, called strong, deals with the faithful imaging of objects for spatial frequencies up to the natural cutoff of 1/λ. Both doubly- and singly-periodic and nonperiodic objects are considered. For periodic objects the results are shown to agree well with the experimental and theoretical work to date, the latter of which has always employed the Fresnel–Kirchhoff diffraction integral with the parabolic approximation appropriate to Fresnel diffraction.

347 citations