scispace - formally typeset
Search or ask a question
Topic

Fresnel zone

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


Papers
More filters
Journal ArticleDOI
TL;DR: In this paper, the radiated far field is determined from a rapidly convergent series representation of the radiation integral, where the coefficients of the series are independent of the observation angles, and the field may be determined very rapidly at large numbers of points.
Abstract: Given the true or any approximate current on a reflector, the radiated far-field is determined from a rapidly convergent series representation of the radiation integral. The leading term is a well-shaped J_{1}(x)/x beam pointing in a desired direction. Higher order terms provide perturbations to the leading term. The coefficients of the series are independent of the observation angles. Hence, once they are computed, the field may be determined very rapidly at large numbers of points. Initially, a suitable small angle approximation is made that places the radiation integral in the form of a Fourier transform on a circular disk. The theory is then extended such that the results are valid in both the near and the wide angle regions. Application to a rotationally symmetric paraboloid is presented herein. Other applications include the offset and dual reflectors and near- to far-field integrations. A modified form of the series can also be used for Fresnel zone computations.

110 citations

Patent
01 Jul 1992
TL;DR: In this article, the alignment mechanism uses a helium-neon laser, the beam from which is projected onto a surface relief grating on the workpiece, which is filtered to create interference fringes which, when aligned, provide maximum light intensity projected through a transmission grating.
Abstract: The apparatus for machining and material processing includes an excimer laser and a Fresnel zone plate array (FZP) positioned parallel to the workpiece, with the distance between the FZP and the workpiece being the focal length of the FZP. For each hole to be formed on the workpiece a corresponding Fresnel zone is patterned onto the FZP. Each Fresnel zone may be patterned directly centered over the desired hole location or in high density patterns it may be located off-center from the hole with deflection being accomplished by the formation of finer circular arcs on the side of the Fresnel zone opposite the desired direction of deflection. A beam scanner is included to provide a more uniform illumination of the FZP by the laser beam. The scanning eliminates non-uniformity of intensity. The alignment mechanism uses a helium-neon laser, the beam from which is projected onto a surface relief grating on the workpiece. The reflected light from the surface relief grating is filtered to create interference fringes which, when aligned, provide maximum light intensity projected through a transmission grating on the Fresnel zone plate.

106 citations

Journal ArticleDOI
TL;DR: This work presents a simple yet accurate analytical model for the focusing of the pinhole photon sieve, applicable to arbitrary paraxial illumination with arbitrary complex amplitude distribution at the photon sieving plane.
Abstract: Recently, a new class of diffractive optical element called a photon sieve, which consists of a great number of pinholes, was developed for the focusing and imaging of soft x rays. In terms of the closed-form formula for the far field of individual pinholes and the linear superposition principle, we present a simple yet accurate analytical model for the focusing of the pinhole photon sieve. This model is applicable to arbitrary paraxial illumination with arbitrary complex amplitude distribution at the photon sieve plane. We check the validity range of this model by comparing it with the exact Fresnel diffraction integral. Some special problems, such as the individual quasi-far-field correction for very large pinholes and the related phase shift induced by this correction, are also discussed.

106 citations

Journal ArticleDOI
TL;DR: The concept of the Fresnel-zone effect was introduced by Hagedoorn as mentioned in this paper, who showed that a sizeable portion of a reflector is involved in causing a reflection as seen on a seismic trace, but the areal extent is usually not calculated and hence not appreciated.
Abstract: Geophysicists commonly recognize that a sizeable portion of a reflector is involved in causing a reflection as seen on a seismic trace, but the areal extent is usually not calculated and hence not appreciated. Most commonly, concepts are simply transferred from classical physical optics and called Fresnel-zone effects. Confusion sometimes results due to the failure to distinguish whether incident waves are plane or spherical. An excellent explanation (but one which does not use the term “Fresnel zone”) is given by Hagedoorn (1954), from which Figure 1 is taken.

106 citations

Journal ArticleDOI
TL;DR: In this paper, a generalization of the Fresnel approximation in diffraction theory is proposed, where the phase term in the diffraction integral is approximated by a paraboloidal variation, not by a binomial expansion but rather by a matching at the critical points in asymptotic evaluation of the integral.
Abstract: A generalization of the Fresnel approximation in diffraction theory is proposed. The phase term in the diffraction integral is approximated by a paraboloidal variation, not by a binomial expansion but rather by a matching at the critical points in asymptotic evaluation of the integral. The method provides a correction to the optical coordinates of the Fresnel diffraction theory that extends its region of validity. It is applied to diffraction by a circular aperture of a plane wave or focused beam, including effects caused by a large numerical aperture, finite Fresnel number, off-axis illumination, and the presence of aberrations. The method may also be used with other geometries: It is readily applied to cylindrical focusing.

106 citations


Network Information
Related Topics (5)
Resonator
76.5K papers, 1M citations
83% related
Wave propagation
55K papers, 1.1M citations
82% related
Polarization (waves)
65.3K papers, 984.7K citations
82% related
Optical fiber
167K papers, 1.8M citations
81% related
Diffraction
63.7K papers, 1M citations
79% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202326
202249
202137
202052
201965
201878