An Ideal Focusing Lens and Its Shape
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According to Fermat tenet, this paper deduces an equation of the protruding side of flat convex lens which can focus parallel lights perfectly and trace its shape with the help of computer aids such as electronic tables.Keywords:
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Based on non-Euclidean transformation optics, we design a thin metamaterial lens that can achieve wide-beam radiation by embedding a simple source (a point source in the three-dimensional (3D) case or a line current source in the 2D case). The scheme is performed on a layer-by-layer geometry to convert curved surfaces in the virtual space into flat sheets, which pile up and form the entire lens in the physical space. Compared to previous designs, the lens does not have extreme material parameters. Simulation results confirm its functionality.
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A Zoomar is a varifocal lens system consisting of alternately fixed and movable lenses or lens groups in which all movable components are contained in one common, linearly movable barrel. The basic theory of such a Zoomar system has been illustrated in a previous paper for a three lens system.The present paper will generalize this theory to cover any Zoomar system and will also illustrate the development of the Zoomar system by selected examples of applications.
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Optical waveguide geodesic lens, which can be used as optical imagery or Fourier transform elements, is important to photon technology. Many spherical geodesic lenses with profile of revolving symmetry are designed to eliminate aberration and obtain diffraction limitation. Studies concentrated on choice of the profile are aimed-to make the design convenient and the practical fabrication possible. But the process of practical fabrication is controlled by no feedback loop. Know the ray trace out of the lens, know the lens' profile. The text wants you learn a method to display the pattern of the ray traces on CRT. Thus, you can see the reflection of the profile's actual shape by image processing. We made an optic-electronic installation with a computer participating in. The text also gives you the installation's principle and structure.
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By a single lens (two refracting surfaces, one dispersive medium) an achromatic real point image can be obtained. We show how such a lens brings a large aperture bundle of axial-parallel rays to the same sharp focus for two wavelengths, that is, for two refractive-index values. The normal of one of the two refracting surfaces is, in general, discontinuous at the axis. The numerical aperture which is practically attainable can be enhanced by off-axis steps in the refracting surfaces. The design principles for such lenses, computational formulas, and examples of results are given. Limitations and further possibilities are discussed.
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4.1 Definition of a Thin Lens
A thin lens is a theoretical lens whose thickness is assumed to be zero and, therefore, negligible during thin-lens calculations. The thin lens is a design tool used to simulate a real lens during the preliminary stages of optical system design and analysis. The concept is particularly valuable because it enables the optical engineer to quickly establish many basic characteristics of a lens or optical system design. By assuming a lens form where the thickness is zero, the formulas used to calculate object and image relationships are greatly simplified. The drawback to the thin-lens approach is that it is not possible to determine image quality without including actual lens thickness (and other lens data) in the calculations. As a result, while it is possible to establish many valuable facts about an optical system by the application of thin-lens theory and formulas, the ultimate quality of the final image can, at best, only be estimated.
4.2 Properties of a Thin Lens
Figure 4.1 is an illustration of a positive thin lens. Any lens system analysis must start with several known factors that will generally be provided by the end user, i.e., the customer. From these given starting factors it will be possible, using thin-lens theory and formulas, to generate the missing information required to completely describe the final lens system. In the case shown in Fig. 4.1, for example, it is given that the system detector (image size) will be 25 mm in diameter and that the full field of view of the lens will be 10 deg. Other system considerations dealing with detector sensitivity - thus required image brightness - dictate that a lens speed (f/#) of f/2.0 will be required. Since we know the image size and the field of view, applying the formulas shown in Fig. 4.1, we can calculate the effective focal length (EFL) of the lens. The image size dimension used for this calculation is measured from the optical axis and is designated as y1. In this case, the maximum value for y1 is 12.5 mm.
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Simple lens
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We propose a general solution for determining the cardinal points and effective focal length of a liquid-filled variable focus lens to aid in understanding the dynamic behavior of the lens when the focal length is changed. A prototype of a variable focus lens was fabricated and used to validate the solution. A simplified solution was also presented that can be used to quickly and conveniently calculate the performance of the lens. We expect that the proposed solutions will improve the design of optical systems that contain variable focus lenses, such as machine vision systems with zoom and focus functions.
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Lens design uses a calculation of the lens' surfaces that permits us to obtain an image from a given object. A set of general rules and laws permits us to calculate the essential points of the optical system, such as distances, thickness, pupils, and focal distances, among others. Now, the theory on which classical lens design is based has changed radically, as our theoretical foundations do not rely on the classical ray-tracing rules. We show that with the rules expressed in a reduced vector analytical solution set of equations, we can take into account all optical elements, i.e., refractive, reflective, and catadioptric. These foundations permit us to keep under control the system aberration budget in every surface. It reduces the computation time dramatically. The examples presented here were possible because of the versatility of this theoretical approach.
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