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Aplanatic Lens
An aplanatic lens is a lens that is free of both spherical and coma aberrations. Aplanatic lenses can be made by combining two or three lens elements. A single-element aplanatic lens is an aspheric lens whose surfaces are surfaces of revolution of a cartesian oval In geometry, a Cartesian oval is a plane curve consisting of points that have the same linear combination of distances from two fixed points (foci). These curves are named after French mathematician René Descartes, who used them in optics. Def ..... References Lenses {{optics-stub ...
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Lens
A lens is a transmissive optical device which focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements''), usually arranged along a common axis. Lenses are made from materials such as glass or plastic, and are ground and polished or molded to a desired shape. A lens can focus light to form an image, unlike a prism, which refracts light without focusing. Devices that similarly focus or disperse waves and radiation other than visible light are also called lenses, such as microwave lenses, electron lenses, acoustic lenses, or explosive lenses. Lenses are used in various imaging devices like telescopes, binoculars and cameras. They are also used as visual aids in glasses to correct defects of vision such as myopia and hypermetropia. History The word ''lens'' comes from '' lēns'', the Latin name of the lentil (a seed of a lentil plant), b ...
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Spherical Aberration
In optics, spherical aberration (SA) is a type of optical aberration, aberration found in optical systems that have elements with spherical surfaces. Lens (optics), Lenses and curved mirrors are prime examples, because this shape is easier to manufacture. Light rays that strike a spherical surface off-centre are refraction, refracted or reflection (physics), reflected more or less than those that strike close to the centre. This deviation reduces the quality of images produced by optical systems. Overview A spherical lens has an Optical aberration#Aberration of elements, i.e. smallest objects at right angles to the axis, aplanatic point (i.e., no spherical aberration) only at a radius that equals the radius of the sphere divided by the index of refraction of the lens material. A typical value of refractive index for crown glass is 1.5 (see List of refractive indices, list), which indicates that only about 43% of the area (67% of diameter) of a spherical lens is useful. It is o ...
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Coma Aberration
In optics (especially telescopes), the coma (), or comatic aberration, in an optical system refers to aberration inherent to certain optical designs or due to imperfection in the lens or other components that results in off-axis point sources such as stars appearing distorted, appearing to have a tail ( coma) like a comet. Specifically, coma is defined as a variation in magnification over the entrance pupil. In refractive or diffractive optical systems, especially those imaging a wide spectral range, coma can be a function of wavelength, in which case it is a form of chromatic aberration. Overview Coma is an inherent property of telescopes using parabolic mirrors. Unlike a spherical mirror, a bundle of parallel rays parallel to the optical axis will be perfectly focused to a point (the mirror is free of spherical aberration), no matter where they strike the mirror. However, this is only true if the rays are parallel to the axis of the parabola. When the incoming rays strike ...
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Aspheric Lens
An aspheric lens or asphere (often labeled ''ASPH'' on eye pieces) is a lens whose surface profiles are not portions of a sphere or cylinder. In photography, a lens assembly that includes an aspheric element is often called an aspherical lens. The asphere's more complex surface profile can reduce or eliminate spherical aberration and also reduce other optical aberrations such as astigmatism, compared to a simple lens. A single aspheric lens can often replace a much more complex multi-lens system. The resulting device is smaller and lighter, and sometimes cheaper than the multi-lens design. Aspheric elements are used in the design of multi-element wide-angle and fast normal lenses to reduce aberrations. They are also used in combination with reflective elements (catadioptric systems) such as the aspherical Schmidt corrector plate used in the Schmidt cameras and the Schmidt–Cassegrain telescopes. Small molded aspheres are often used for collimating diode lasers. Aspheric lenses ...
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Surfaces Of Revolution
A surface of revolution is a surface in Euclidean space created by rotating a curve (the generatrix) around an axis of rotation. Examples of surfaces of revolution generated by a straight line are cylindrical and conical surfaces depending on whether or not the line is parallel to the axis. A circle that is rotated around any diameter generates a sphere of which it is then a great circle, and if the circle is rotated around an axis that does not intersect the interior of a circle, then it generates a torus which does not intersect itself (a ring torus). Properties The sections of the surface of revolution made by planes through the axis are called ''meridional sections''. Any meridional section can be considered to be the generatrix in the plane determined by it and the axis. The sections of the surface of revolution made by planes that are perpendicular to the axis are circles. Some special cases of hyperboloids (of either one or two sheets) and elliptic paraboloids are surf ...
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Cartesian Oval
In geometry, a Cartesian oval is a plane curve consisting of points that have the same linear combination of distances from two fixed points (foci). These curves are named after French mathematician René Descartes, who used them in optics. Definition Let and be fixed points in the plane, and let and denote the Euclidean distances from these points to a third variable point . Let and be arbitrary real numbers. Then the Cartesian oval is the locus of points ''S'' satisfying . The two ovals formed by the four equations and are closely related; together they form a quartic plane curve called the ovals of Descartes. Special cases In the equation , when and the resulting shape is an ellipse. In the limiting case in which ''P'' and ''Q'' coincide, the ellipse becomes a circle. When m = a/\!\operatorname(P, Q) it is a limaçon of Pascal. If m = -1 and 0 < a < \operatorname(P, Q) the equation gives a branch of a