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Optical Lens 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. Design requirements Performance requirements can include: #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. #Physical requirements such as weight, static volume, dynamic volume, center of gravity and overall configuration requirement ...
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Engineering Design Process
The engineering design process is a common series of steps that engineers use in creating functional products and processes. The process is highly iterative - parts of the process often need to be repeated many times before another can be entered - though the part(s) that get iterated and the number of such cycles in any given project may vary. It is a decision making process (often iterative) in which the basic sciences, mathematics, and engineering sciences are applied to convert resources optimally to meet a stated objective. Among the fundamental elements of the design process are the establishment of objectives and criteria, synthesis, analysis, construction, testing and evaluation. Common stages of the engineering design process It's important to understand that there are various framings/articulations of the engineering design process. Different terminology employed may have varying degrees of overlap, which affects what steps get stated explicitly or deemed "high leve ...
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Oscillation
Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum and alternating current. Oscillations can be used in physics to approximate complex interactions, such as those between atoms. Oscillations occur not only in mechanical systems but also in dynamic systems in virtually every area of science: for example the beating of the human heart (for circulation), business cycles in economics, predator–prey population cycles in ecology, geothermal geysers in geology, vibration of strings in guitar and other string instruments, periodic firing of nerve cells in the brain, and the periodic swelling of Cepheid variable stars in astronomy. The term '' vibration'' is precisely used to describe a mechanical oscillation. Oscillation, especially rapid oscillation, may be an undesirable phenomenon in p ...
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Prism (optics)
An optical prism is a transparent optical element with flat, polished surfaces that are designed to refract light. At least one surface must be angled — elements with two parallel surfaces are ''not'' prisms. The most familiar type of optical prism is the triangular prism, which has a triangular base and rectangular sides. Not all optical prisms are geometric prisms, and not all geometric prisms would count as an optical prism. Prisms can be made from any material that is transparent to the wavelengths for which they are designed. Typical materials include glass, acrylic and fluorite. A dispersive prism can be used to break white light up into its constituent spectral colors (the colors of the rainbow) as described in the following section. Other types of prisms noted below can be used to reflect light, or to split light into components with different polarizations. Types Dispersive ''Dispersive prisms'' are used to break up light into its constituent spectral ...
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Glass Batch
Glass batch calculation or glass batching is used to determine the correct mix of raw materials (batch) for a glass melt. Principle The raw materials mixture for glass melting is termed "batch". The batch must be measured properly to achieve a given, desired glass formulation. This batch calculation is based on the common linear regression equation: N_B = (B^T\cdot B)^\cdot B^T \cdot N_G with NB and NG being the molarities 1-column matrices of the batch and glass components respectively, and B being the batching matrix. The symbol "T" stands for the matrix transpose operation, "−1" indicates matrix inversion, and the sign "·" means the scalar product. From the molarities matrices N, percentages by weight (wt%) can easily be derived using the appropriate molar masses. Example calculation An example batch calculation may be demonstrated here. The desired glass composition in wt% is: 67 SiO2, 12 Na2O, 10 CaO, 5 Al2O3, 1 K2O, 2 MgO, 3 B2O3, and as raw materials are used san ...
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Glass Model
The calculation of glass properties (glass modeling) is used to predict glass properties of interest or glass behavior under certain conditions (e.g., during production) without experimental investigation, based on past data and experience, with the intention to save time, material, financial, and environmental resources, or to gain scientific insight. It was first practised at the end of the 19th century by A. Winkelmann and Otto Schott, O. Schott. The combination of several glass models together with other relevant functions can be used for Optimization (mathematics), optimization and six sigma procedures. In the form of statistical analysis glass modeling can aid with accreditation of new data, experimental procedures, and measurement institutions (glass laboratories). History Historically, the calculation of glass properties is directly related to the founding of glass science. At the end of the 19th century the physicist Ernst Abbe developed equations that allow calculating th ...
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Abbe Number
In optics and lens design, the Abbe number, also known as the V-number or constringence of a transparent material, is an approximate measure of the material's dispersion (change of refractive index versus wavelength), with high values of ''V'' indicating low dispersion. It is named after Ernst Abbe (1840–1905), the German physicist who defined it. The term V-number should not be confused with the normalized frequency in fibers. The Abbe number, ''Vd'', of a material is defined as :V_D = \frac, where ''n''C, ''n''d and ''n''F are the refractive indices of the material at the wavelengths of the Fraunhofer ''C'', ''d'', and ''F'' spectral lines (656.3  nm, 587.56 nm, and 486.1 nm respectively). This formulation only applies to the visible spectrum. Outside this range requires the use of different spectral lines. For non-visible spectral lines the term V-number is more commonly used. The more general formulation defined as, :V = \frac, where ''n''short, ''n''c ...
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Entrance Pupil
In an optical system, the entrance pupil is the optical image of the physical aperture stop, as 'seen' through the front (the object side) of the lens system. The corresponding image of the aperture as seen through the back of the lens system is called the exit pupil. If there is no lens in front of the aperture (as in a pinhole camera), the entrance pupil's location and size are identical to those of the aperture. Optical elements in front of the aperture will produce a magnified or diminished image that is displaced from the location of the physical aperture. The entrance pupil is usually a virtual image: it lies behind the first optical surface of the system. The geometric location of the entrance pupil is the vertex of the camera's angle of view and consequently its center of perspective, perspective point, view point, projection centre or no-parallax point. This point is important in panoramic photography, because the camera must be rotated around it in order to avoid ...
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Image
An image is a visual representation of something. It can be two-dimensional, three-dimensional, or somehow otherwise feed into the visual system to convey information. An image can be an artifact, such as a photograph or other two-dimensional picture, that resembles a subject. In the context of signal processing, an image is a distributed amplitude of color(s). In optics, the term “image” may refer specifically to a 2D image. An image does not have to use the entire visual system to be a visual representation. A popular example of this is of a greyscale image, which uses the visual system's sensitivity to brightness across all wavelengths, without taking into account different colors. A black and white visual representation of something is still an image, even though it does not make full use of the visual system's capabilities. Images are typically still, but in some cases can be moving or animated. Characteristics Images may be two or three-dimensional, such as a ...
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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 : \ ...
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Birefringence
Birefringence is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light. These optically anisotropic materials are said to be birefringent (or birefractive). The birefringence is often quantified as the maximum difference between refractive indices exhibited by the material. Crystals with non-cubic crystal structures are often birefringent, as are plastics under mechanical stress. Birefringence is responsible for the phenomenon of double refraction whereby a ray of light, when incident upon a birefringent material, is split by polarization into two rays taking slightly different paths. This effect was first described by Danish scientist Rasmus Bartholin in 1669, who observed it in calcite, a crystal having one of the strongest birefringences. In the 19th century Augustin-Jean Fresnel described the phenomenon in terms of polarization, understanding light as a wave with field components in transverse po ...
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Annealing (glass)
Annealing is a process of slowly cooling hot glass objects after they have been formed, to relieve residual internal stresses introduced during manufacture. Especially for smaller, simpler objects, annealing may be incidental to the process of manufacture, but in larger or more complex products it commonly demands a special process of annealing in a temperature-controlled kiln known as a lehr.E. F. Collins (1921) Electrically heated glass annealing lehr. Journal of the American Ceramic Society 4 (5), pp. 335–349 Annealing of glass is critical to its durability. Glass that has not been properly annealed retains thermal stresses caused by quenching, which will indefinitely decrease the strength and reliability of the product. Inadequately annealed glass is likely to crack or shatter when subjected to relatively small temperature changes or to mechanical shock or stress. It even may fail spontaneously. To anneal glass, it is necessary to heat it to its annealing temperature, ...
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Refractive Index
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 ''� ...
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