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Angular Aperture
The angular aperture of a lens is the angular size of the lens aperture as seen from the focal point: :a = 2 \arctan \left( \frac \right) = 2 \arctan \left( \frac \right) where :f is the focal length :D is the diameter of the aperture. Relation to numerical aperture In a medium with an index of refraction close to 1, such as air, the angular aperture is approximately equal to twice the numerical aperture of the lens. Formally, the numerical aperture in air is: :\mathrm = \sin a/2 = \sin \arctan \left( \frac \right) In the paraxial approximation, with a small aperture, D References {{reflistSee also * * *Accept ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angular Aperture
The angular aperture of a lens is the angular size of the lens aperture as seen from the focal point: :a = 2 \arctan \left( \frac \right) = 2 \arctan \left( \frac \right) where :f is the focal length :D is the diameter of the aperture. Relation to numerical aperture In a medium with an index of refraction close to 1, such as air, the angular aperture is approximately equal to twice the numerical aperture of the lens. Formally, the numerical aperture in air is: :\mathrm = \sin a/2 = \sin \arctan \left( \frac \right) In the paraxial approximation, with a small aperture, D References {{reflistSee also * * *Accept ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lens (optics)
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), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angular Size
The angular diameter, angular size, apparent diameter, or apparent size is an angular distance describing how large a sphere or circle appears from a given point of view. In the vision sciences, it is called the visual angle, and in optics, it is the angular aperture (of a lens). The angular diameter can alternatively be thought of as the angular displacement through which an eye or camera must rotate to look from one side of an apparent circle to the opposite side. Humans can resolve with their naked eyes diameters of up to about 1 arcminute (approximately 0.017° or 0.0003 radians). This corresponds to 0.3 m at a 1 km distance, or to perceiving Venus as a disk under optimal conditions. Formula The angular diameter of a circle whose plane is perpendicular to the displacement vector between the point of view and the center of said circle can be calculated using the formula :\delta = 2\arctan \left(\frac\right), in which \delta is the angular diameter, and d is the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aperture
In optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture and focal length of an optical system determine the cone angle of a bundle of rays that come to a focus in the image plane. An optical system typically has many openings or structures that limit the ray bundles (ray bundles are also known as ''pencils'' of light). These structures may be the edge of a lens or mirror, or a ring or other fixture that holds an optical element in place, or may be a special element such as a diaphragm placed in the optical path to limit the light admitted by the system. In general, these structures are called stops, and the aperture stop is the stop that primarily determines the ray cone angle and brightness at the image point. In some contexts, especially in photography and astronomy, ''aperture'' refers to the diameter of the aperture stop rather than the physical stop or the opening itself. For example, in a telescope, the aperture ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Focus (optics)
In geometrical optics, a focus, also called an image point, is a point where light rays originating from a point on the object converge. Although the focus is conceptually a point, physically the focus has a spatial extent, called the blur circle. This non-ideal focusing may be caused by aberrations of the imaging optics. In the absence of significant aberrations, the smallest possible blur circle is the Airy disc, which is caused by diffraction from the optical system's aperture. Aberrations tend to worsen as the aperture diameter increases, while the Airy circle is smallest for large apertures. An image, or image point or region, is in focus if light from object points is converged almost as much as possible in the image, and out of focus if light is not well converged. The border between these is sometimes defined using a "circle of confusion" criterion. A principal focus or focal point is a special focus: * For a lens, or a spherical or parabolic mirror, it is a point ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Focal Length
The focal length of an optical system is a measure of how strongly the system converges or diverges light; it is the inverse of the system's optical power. A positive focal length indicates that a system converges light, while a negative focal length indicates that the system diverges light. A system with a shorter focal length bends the rays more sharply, bringing them to a focus in a shorter distance or diverging them more quickly. For the special case of a thin lens in air, a positive focal length is the distance over which initially collimated (parallel) rays are brought to a focus, or alternatively a negative focal length indicates how far in front of the lens a point source must be located to form a collimated beam. For more general optical systems, the focal length has no intuitive meaning; it is simply the inverse of the system's optical power. In most photography and all telescopy, where the subject is essentially infinitely far away, longer focal length (lower opti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diameter
In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle. Both definitions are also valid for the diameter of a sphere. In more modern usage, the length d of a diameter is also called the diameter. In this sense one speaks of diameter rather than diameter (which refers to the line segment itself), because all diameters of a circle or sphere have the same length, this being twice the radius r. :d = 2r \qquad\text\qquad r = \frac. For a convex shape in the plane, the diameter is defined to be the largest distance that can be formed between two opposite parallel lines tangent to its boundary, and the is often defined to be the smallest such distance. Both quantities can be calculated efficiently using rotating calipers. For a curve of constant width such as the Reuleaux triangle, the width and diameter are the same because all ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Index Of Refraction
In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or refracted, when entering a material. This is described by Snell's law of refraction, , where ''θ''1 and ''θ''2 are the angle of incidence and angle of refraction, respectively, of a ray crossing the interface between two media with refractive indices ''n''1 and ''n''2. The refractive indices also determine the amount of light that is reflected when reaching the interface, as well as the critical angle for total internal reflection, their intensity ( Fresnel's equations) and Brewster's angle. The refractive index can be seen as the factor by which the speed and the wavelength of the radiation are reduced with respect to their vacuum values: the speed of light in a medium is , and similarly the wavelength in that medium is , where ''λ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Aperture
In optics, the numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light. By incorporating index of refraction in its definition, NA has the property that it is constant for a beam as it goes from one material to another, provided there is no refractive power at the interface. The exact definition of the term varies slightly between different areas of optics. Numerical aperture is commonly used in microscopy to describe the acceptance cone of an objective (and hence its light-gathering ability and resolution), and in fiber optics, in which it describes the range of angles within which light that is incident on the fiber will be transmitted along it. General optics In most areas of optics, and especially in microscopy, the numerical aperture of an optical system such as an objective lens is defined by :\mathrm = n \sin \theta, where is the index of refraction of the medium i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paraxial Approximation
In geometric optics, the paraxial approximation is a small-angle approximation used in Gaussian optics and ray tracing of light through an optical system (such as a lens). A paraxial ray is a ray which makes a small angle (''θ'') to the optical axis of the system, and lies close to the axis throughout the system. Generally, this allows three important approximations (for ''θ'' in radians) for calculation of the ray's path, namely: : \sin \theta \approx \theta,\quad \tan \theta \approx \theta \quad \text\quad\cos \theta \approx 1. The paraxial approximation is used in Gaussian optics and ''first-order'' ray tracing. Ray transfer matrix analysis is one method that uses the approximation. In some cases, the second-order approximation is also called "paraxial". The approximations above for sine and tangent do not change for the "second-order" paraxial approximation (the second term in their Taylor series expansion is zero), while for cosine the second order approximation is : \ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
F-number
In optics, the f-number of an optical system such as a camera lens is the ratio of the system's focal length to the diameter of the entrance pupil ("clear aperture").Smith, Warren ''Modern Optical Engineering'', 4th Ed., 2007 McGraw-Hill Professional, p. 183. It is also known as the focal ratio, f-ratio, or f-stop, and is very important in photography. It is a dimensionless number that is a quantitative measure of lens speed; increasing the f-number is referred to as ''stopping down''. The f-number is commonly indicated using a lower-case hooked f with the format ''N'', where ''N'' is the f-number. The f-number is the reciprocal of the relative aperture (the aperture diameter divided by focal length). Notation The f-number is given by: N = \frac \ where f is the focal length, and D is the diameter of the entrance pupil (''effective aperture''). It is customary to write f-numbers preceded by "", which forms a mathematical expression of the entrance pupil diameter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Aperture
In optics, the numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light. By incorporating index of refraction in its definition, NA has the property that it is constant for a beam as it goes from one material to another, provided there is no refractive power at the interface. The exact definition of the term varies slightly between different areas of optics. Numerical aperture is commonly used in microscopy to describe the acceptance cone of an objective (and hence its light-gathering ability and resolution), and in fiber optics, in which it describes the range of angles within which light that is incident on the fiber will be transmitted along it. General optics In most areas of optics, and especially in microscopy, the numerical aperture of an optical system such as an objective lens is defined by :\mathrm = n \sin \theta, where is the index of refraction of the medium i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
