Apodization of generalized axicons to produce uniform axial line images
01 May 1998-Pure and Applied Optics: Journal of The European Optical Society Part A (IOP Publishing)-Vol. 7, Iss: 3, pp 537-548
TL;DR: In this paper, the effects of apodization of a generalized holographic axicon that produces a uniform axial line intensity distribution are considered, both by simulations and experimentally, and it is shown that the apoization considerably improves the image line quality within the extended focal region, especially near the image end points.
Abstract: The effects of apodization of a generalized holographic axicon that produces a uniform axial line intensity distribution are considered. It is shown, both by simulations and experimentally, that the apodization considerably improves the image line quality within the extended focal region, especially near the image end points. A simple method of implementing the apodization by a binary-amplitude encoding of the generalized axicon is assessed in detail. Fabrication of the axicon by photoreduction and experimental results on the intensity variations of the line image, which are in substantial agreement with the theoretical considerations, are presented and analysed. On apodization the axial intensity becomes nearly uniform, while transversely the line image retains its high definition.
Citations
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TL;DR: In this article, a beam former and an aberration corrector combined with a nonlinear axicon are designed for the transformation of Gaussian beams into Bessel fields with uniform axial intensity over a specified line segment.
40 citations
TL;DR: A novel method of designing diffractive axicons for use in spatially partially coherent illumination by leading to a coherence-dependent differential equation with appropriate boundary conditions for the axicon phase function is proposed.
Abstract: We propose a novel method of designing diffractive axicons for use in spatially partially coherent illumination. The design procedure is based on the results obtained by the stationary-phase method. The technique leads to a coherence-dependent differential equation with appropriate boundary conditions for the axicon phase function. We demonstrate the method with annular-aperture axicons generating extended focal line segments of uniform on-axis intensity.
36 citations
TL;DR: In this paper, a binary diffractive axicon is fabricated by electron beam lithography to generate a uniform axial line focus over a specified interval, and a split-groove apodization method is introduced to suppress second-order interference.
34 citations
TL;DR: In this paper, a lens axicon (a converging lens with spherical aberration) illuminated by a Gaussian beam is studied, and it is shown that, with an appropriate beam radius of the incident Gaussian beacon, one can achieve a focal segment with uniform axial intensity, which is similar to that generated by the logarithmic axicon.
Abstract: A lens axicon (a converging lens with spherical aberration) illuminated by a Gaussian beam is studied. It is demonstrated that, when a backward-type lens axicon is illuminated with an appropriate beam radius of the incident Gaussian beam, one can achieve a focal segment with uniform axial intensity, which is similar to that generated by the logarithmic axicon. It is shown that this approach is very simple and efficient. A forward-type lens axicon illuminated by a Gaussian beam is also investigated.
33 citations
TL;DR: A novel design method for a circularly symmetric phase mask using the free-form rational function as the solution space is proposed, which proves the resulting rational phase mask's superiority to the existing quartic phase mask in intensity distribution and imaging performance.
Abstract: We propose a novel design method for a circularly symmetric phase mask to extend the depth of focus. Using the free-form rational function as the solution space, we optimize the profile of the phase mask by analysis of the axial intensity distribution, which can be calculated efficiently by employing the fast Fourier transform algorithm. Numerical comparisons prove the resulting rational phase mask's superiority to the existing quartic phase mask in intensity distribution and imaging performance.
31 citations
References
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TL;DR: The axicon autocollimator as discussed by the authors is a projector which projects a straight line of images into space, and it can be used to determine the perpendicularity of a mirror.
Abstract: A search for a universal-focus lens has led to a new class of optical elements. These are called axicons. There are many different kinds of axicons but probably the most important one is a glass cone. It may be either transmitting or reflecting. Axicons form a continuous straight line of images from small sources.One application is in a telescope. The usual spherical objective is replaced by a cone. This axicon telescope is in focus for targets from a foot or so to infinity without the necessity of moving any parts. It can be used to view simultaneously two or more small sources placed along the line of sight.If a source of light is suitably added to the telescope it becomes an autocollimator. Like ordinary autocollimators it can be used to determine the perpendicularity of a mirror. In addition, it can simultaneously act as a telescope for a point target which may be an illuminated pinhole in the mirror.The axicon autocollimator is also a projector which projects a straight line of images into space.
956 citations
TL;DR: This work shows by the method of stationary phase that any of these wave fields can be realized approximately with a laser and a single computer-generated hologram, and demonstrates experimentally the formation of arbitrary-order Bessel beams and rotationally nonsymmetric beams.
Abstract: A new class of solutions to the scalar wave equation was introduced recently that represents transversely localized but totally nondiffracting fields. We show by the method of stationary phase that any of these wave fields can be realized approximately with a laser and a single computer-generated hologram. We briefly discuss various techniques for coding and fabrication of the required hologram and the associated diffraction efficiencies. Using both binary-amplitude and four-level phase holograms, we demonstrate experimentally the formation of arbitrary-order Bessel beams and rotationally nonsymmetric beams.
668 citations
TL;DR: A novel aspheric holographic optical element, the holographic axilens, is reported for achieving extended focal depth while keeping high lateral resolution.
Abstract: We report a novel aspheric holographic optical element, the holographic axilens, for achieving extended focal depth while keeping high lateral resolution. The element is designed according to special optimization techniques and recorded as a computer-generated hologram. The results for a specific element, which has a depth of focus of 30 mm, a lateral resolution of 80 microm, a focal length of 1250 mm, and a diameter of 12.5 mm at a wavelength of 633 nm, are presented.
220 citations
TL;DR: The geometric law of energy conservation is utilized in evaluating the phase transmittance function for axicons with arbitrary distribution of the on-axis intensity.
Abstract: The geometric law of energy conservation is utilized in evaluating the phase transmittance function for axicons with arbitrary distribution of the on-axis intensity. Several simple analytical solutions are presented, and a computer-generated holographic version of the uniform-intensity axicon is examined.
157 citations
TL;DR: A method for determining the phase-retardation function of the uniform-intensity axilens is discussed and compared with that of an earlier publication.
Abstract: A method for determining the phase-retardation function of the uniform-intensity axilens is discussed and compared with that of an earlier publication [Opt. Lett. 16, 523 (1991)]. Within the presented formulation good agreement is achieved between the geometrical-optics prediction and the numerically evaluated diffraction integral.
101 citations