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# Fresnel number

About: Fresnel number is a research topic. Over the lifetime, 1918 publications have been published within this topic receiving 27499 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 paper, a theory of Fresnel images of plane periodic objects viewed in monochromatic light is presented, which is in agreement with the experimental and computer research available in the literature.

Abstract: A theory of Fresnel images is presented. Only the Fresnel images of plane periodic objects viewed in monochromatic light are considered. The theory is in agreement with the experimental and computer research available in the literature. Photographs of Fresnel images of gratings are shown to verify certain aspects of the theory.

444 citations

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TL;DR: In this article, a new Green-function formalism is developed for calculating fields generated by sources in the presence of a multilayer geometry, and the approach is to formulate the problem immediately in terms of s and p-polarized waves generated, so that the calculation of the effect of interfaces proceeds by the introduction of Fresnel reflection and transmission coefficients and parallels the simple physical picture of light progressing through the structure.

Abstract: A new Green-function formalism is developed for calculating fields generated by sources in the presence of a multilayer geometry. The approach is to formulate the problem immediately in terms of s- and p-polarized waves generated, so that the calculation of the effect of interfaces proceeds by the introduction of Fresnel reflection and transmission coefficients and parallels the simple physical picture of light progressing through the structure.

410 citations

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TL;DR: Simple procedures and formulas for tracing the characteristics of a spherical Gaussian beam through a train of lenses or mirrors are described which are analogous to those used in geometrical optics to trace repeated images through an optical train.

Abstract: Simple procedures and formulas for tracing the characteristics of a spherical Gaussian beam through a train of lenses or mirrors are described which are analogous to those used in geometrical optics to trace repeated images through an optical train.

339 citations

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TL;DR: In this paper, it was shown that when the incident wave is uniform and the angular semi-aperture is small, the ratio of the point of maximum intensity to the distance between the geometrical focus and the plane of the aperture depends only on the Fresnel number N of the image when viewed from the focal point.

Abstract: It is known from a number of publications that when a converging, monochromatic spherical wave is diffracted at a circular aperture, the point of maximum intensity of the diffracted wave may not be at the geometrical focus of the incident wave, but may be located closer to the aperture. In the present note we show that when the incident wave is uniform and the angular semi-aperture is small, the ratio of such a shift Δƒ of the point of maximum intensity to the distance ƒ between the geometrical focus and the plane of the aperture depends only on the Fresnel number N of the aperture when viewed from the geometrical focus. The effect becomes significant when N ≲ 5. When N = 1, for example, |Δƒ| ≈ 0.4 ƒ and the maximum intensity is approximately twice as large as the intensity at the geometrical focus.

316 citations