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Sine Condition
The Abbe sine condition is a condition that must be fulfilled by a lens or other optical system in order for it to produce sharp images of off-axis as well as on-axis objects. It was formulated by Ernst Abbe in the context of microscopes. The Abbe sine condition says that the sine of the object-space angle \alpha_o should be proportional to the sine of the image space angle \alpha_i Furthermore, the ratio equals the magnification of the system. In mathematical terms this is: :\frac = \frac = , M, where the variables (\alpha_o, \beta_o) are the angles (relative to the optic axis) of any two rays as they leave the object, and (\alpha_i, \beta_i) are the angles of the same rays where they reach the image plane (say, the film plane of a camera). For example, (\alpha_o, \alpha_i) might represent a paraxial ray (i.e., a ray nearly parallel with the optic axis), and (\beta_o, \beta_i) might represent a marginal ray (i.e., a ray with the largest angle admitted by the system aper ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sine Condition
The Abbe sine condition is a condition that must be fulfilled by a lens or other optical system in order for it to produce sharp images of off-axis as well as on-axis objects. It was formulated by Ernst Abbe in the context of microscopes. The Abbe sine condition says that the sine of the object-space angle \alpha_o should be proportional to the sine of the image space angle \alpha_i Furthermore, the ratio equals the magnification of the system. In mathematical terms this is: :\frac = \frac = , M, where the variables (\alpha_o, \beta_o) are the angles (relative to the optic axis) of any two rays as they leave the object, and (\alpha_i, \beta_i) are the angles of the same rays where they reach the image plane (say, the film plane of a camera). For example, (\alpha_o, \alpha_i) might represent a paraxial ray (i.e., a ray nearly parallel with the optic axis), and (\beta_o, \beta_i) might represent a marginal ray (i.e., a ray with the largest angle admitted by the system aper ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Image Distortion
In geometric optics, distortion is a deviation from rectilinear projection; a projection in which straight lines in a scene remain straight in an image. It is a form of optical aberration. Radial distortion Although distortion can be irregular or follow many patterns, the most commonly encountered distortions are radially symmetric, or approximately so, arising from the symmetry of a photographic lens. These ''radial distortions'' can usually be classified as either ''barrel'' distortions or ''pincushion'' distortions. Mathematically, barrel and pincushion distortion are quadratic, meaning they increase as the ''square'' of distance from the center. In mustache distortion the quartic (degree 4) term is significant: in the center, the degree 2 barrel distortion is dominant, while at the edge the degree 4 distortion in the pincushion direction dominates. Other distortions are in principle possible – pincushion in center and barrel at the edge, or higher order ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Microscopes
A microscope () is a laboratory instrument used to examine objects that are too small to be seen by the naked eye. Microscopy is the science of investigating small objects and structures using a microscope. Microscopic means being invisible to the eye unless aided by a microscope. There are many types of microscopes, and they may be grouped in different ways. One way is to describe the method an instrument uses to interact with a sample and produce images, either by sending a beam of light or electrons through a sample in its optical path, by detecting photon emissions from a sample, or by scanning across and a short distance from the surface of a sample using a probe. The most common microscope (and the first to be invented) is the optical microscope, which uses lenses to refract visible light that passed through a thinly sectioned sample to produce an observable image. Other major types of microscopes are the fluorescence microscope, electron microscope (both the tr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometrical Optics
Geometrical optics, or ray optics, is a model of optics that describes light propagation in terms of '' rays''. The ray in geometrical optics is an abstraction useful for approximating the paths along which light propagates under certain circumstances. The simplifying assumptions of geometrical optics include that light rays: * propagate in straight-line paths as they travel in a homogeneous medium * bend, and in particular circumstances may split in two, at the interface between two dissimilar media * follow curved paths in a medium in which the refractive index changes * may be absorbed or reflected. Geometrical optics does not account for certain optical effects such as diffraction and interference. This simplification is useful in practice; it is an excellent approximation when the wavelength is small compared to the size of structures with which the light interacts. The techniques are particularly useful in describing geometrical aspects of imaging, including optical aberra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lagrange Invariant
In optics the Lagrange invariant is a measure of the light propagating through an optical system. It is defined by :H = n\overliney - nu\overline, where and are the marginal ray height and angle respectively, and and are the chief ray height and angle. is the ambient refractive index. In order to reduce confusion with other quantities, the symbol may be used in place of . is proportional to the throughput of the optical system (related to étendue). For a given optical system, the Lagrange invariant is a constant throughout all space, that is, it is invariant upon refraction and transfer. The optical invariant is a generalization of the Lagrange invariant which is formed using the ray heights and angles of any two rays. For these rays, the optical invariant is a constant throughout all space. Newp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spherical Coordinate System
In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the ''radial distance'' of that point from a fixed origin, its ''polar angle'' measured from a fixed zenith direction, and the ''azimuthal angle'' of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the zenith, measured from a fixed reference direction on that plane. It can be seen as the three-dimensional version of the polar coordinate system. The radial distance is also called the ''radius'' or ''radial coordinate''. The polar angle may be called ''colatitude'', '' zenith angle'', '' normal angle'', or ''inclination angle''. When radius is fixed, the two angular coordinates make a coordinate system on the sphere sometimes called spherical polar coordinates. The use of symbols and the order of the coordinates differs among sources and disciplines. This article will ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wavenumber
In the physical sciences, the wavenumber (also wave number or repetency) is the '' spatial frequency'' of a wave, measured in cycles per unit distance (ordinary wavenumber) or radians per unit distance (angular wavenumber). It is analogous to temporal frequency, which is defined as the number of wave cycles per unit time (''ordinary frequency'') or radians per unit time (''angular frequency''). In multidimensional systems, the wavenumber is the magnitude of the '' wave vector''. The space of wave vectors is called '' reciprocal space''. Wave numbers and wave vectors play an essential role in optics and the physics of wave scattering, such as X-ray diffraction, neutron diffraction, electron diffraction, and elementary particle physics. For quantum mechanical waves, the wavenumber multiplied by the reduced Planck's constant is the '' canonical momentum''. Wavenumber can be used to specify quantities other than spatial frequency. For example, in optical spectroscopy, it is of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnification
Magnification is the process of enlarging the apparent size, not physical size, of something. This enlargement is quantified by a calculated number also called "magnification". When this number is less than one, it refers to a reduction in size, sometimes called ''minification'' or ''de-magnification''. Typically, magnification is related to scaling up visuals or images to be able to see more detail, increasing resolution, using microscope, printing techniques, or digital processing. In all cases, the magnification of the image does not change the perspective of the image. Examples of magnification Some optical instruments provide visual aid by magnifying small or distant subjects. * A magnifying glass, which uses a positive (convex) lens to make things look bigger by allowing the user to hold them closer to their eye. * A telescope, which uses its large objective lens or primary mirror to create an image of a distant object and then allows the user to examine the imag ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Transform
A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, which will output a function depending on temporal frequency or spatial frequency respectively. That process is also called ''analysis''. An example application would be decomposing the waveform of a musical chord into terms of the intensity of its constituent pitches. The term ''Fourier transform'' refers to both the frequency domain representation and the mathematical operation that associates the frequency domain representation to a function of space or time. The Fourier transform of a function is a complex-valued function representing the complex sinusoids that comprise the original function. For each frequency, the magnitude ( absolute value) of the complex value represents the amplitude of a constituent complex sinusoid ... [...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 lent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
