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Displacement (vector)
In geometry and mechanics, a displacement is a vector whose length is the shortest distance from the initial to the final position of a point P undergoing motion.[1] It quantifies both the distance and direction of the net or total motion along a straight line from the initial position to the final position of the point trajectory. A displacement may be identified with the translation that maps the initial position to the final position. A displacement may be also described as a relative position (resulting from the motion), that is, as the final position xf of a point relatively to its initial position xi
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Radius
In classical geometry, a radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the Latin radius, meaning ray but also the spoke of a chariot wheel.[1] The plural of radius can be either radii (from the Latin plural) or the conventional English plural radiuses.[2] The typical abbreviation and mathematical variable name for radius is r. By extension, the diameter d is defined as twice the radius:[3] If an object does not have a center, the term may refer to its circumradius, the radius of its circumscribed circle or circumscribed sphere. In either case, the radius may be more than half the diameter, which is usually defined as the maximum distance between any two points of the figure. The inradius of a geometric figure is usually the radius of the largest circle or sphere contained in it
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Center Of Curvature
In geometry, the center of curvature of a curve is found at a point that is at a distance from the curve equal to the radius of curvature lying on the normal vector. It is the point at infinity if the curvature is zero. The osculating circle to the curve is centered at the centre of curvature. Cauchy defined the center of curvature C as the intersection point of two infinitely close normal lines to the curve.[1] The locus of centers of curvature for each point on the curve comprise the evolute of the curve
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Quadric Surface
In mathematics, a quadric or quadric surface (quadric hypersurface in higher dimensions), is a generalization of conic sections (ellipses, parabolas, and hyperbolas). It is a hypersurface (of dimension D) in a (D + 1)-dimensional space, and it is defined as the zero set of an irreducible polynomial of degree two in D + 1 variables (D = 1 in the case of conic sections)
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Optical Design
Optical lens design is the process of designing a lens to meet a set of performance requirements and constraints, including cost and manufacturing limitations. Parameters include surface profile types (spherical, aspheric, holographic, diffractive, etc.), as well as radius of curvature, distance to the next surface, material type and optionally tilt and decenter. The process is computationally intensive, using ray tracing or other techniques to model how the lens affects light that passes through it. Performance requirements can include:
  1. Optical performance (image quality): This is quantified by various metrics, including encircled energy, modulation transfer function, Strehl ratio, ghost reflection control, and pupil performance (size, location and aberration control); the choice of the image quality metric is application specific.[1][2][
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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.[1] 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
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Cardinal Point (optics)

In Gaussian optics, the cardinal points consist of three pairs of points located on the optical axis of a rotationally symmetric, focal, optical system. These are the focal points, the principal points, and the nodal points.[1] For ideal systems, the basic imaging properties such as image size, location, and orientation are completely determined by the locations of the cardinal points; in fact only four points are necessary: the focal points and either the principal or nodal points. The only ideal system that has been achieved in practice is the plane mirror,[2] however the cardinal points are widely used to approximate the behavior of real optical systems
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