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According to Abbe's theory of image formation, developed in 1873, the resolving capability of an optical component is ultimately limited by the spreading out of each image point due to diffraction. Unless the aperture of the optical component is large enough to collect all the diffracted light, the finer aspects of the image will not correspond ...
Memorial in Jena, Germany to Ernst Karl Abbe, who approximated the diffraction limit of a microscope as = , where d is the resolvable feature size, λ is the wavelength of light, n is the index of refraction of the medium being imaged in, and θ (depicted as α in the inscription) is the half-angle subtended by the optical objective lens (representing the numerical aperture).
Ernst Karl Abbe HonFRMS (23 January 1840 – 14 January 1905) was a German businessman, optical engineer, physicist, and social reformer. Together with Otto Schott and Carl Zeiss, he developed numerous optical instruments.
The images of the Gauss theory being of the third order, the next problem is to obtain an image of 5th order, or to make the coefficients of the powers of 3rd degree zero. This necessitates the satisfying of five equations; in other words, there are five alterations of the 3rd order, the vanishing of which produces an image of the 5th order.
When the imaging system obeys the Abbe sine condition, the ratio of the sines of these angles equal the (lateral absolute) magnification of the system. In optics , 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.
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In optics and lens design, the Abbe number, also known as the Vd-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 Vd indicating low dispersion.
The ratio of the height of the image to the height of the object is the magnification. The spatial extent of the image surface and the focal length of the lens determines the field of view of the lens. Image formation of mirror these have a center of curvature and its focal length of the mirror is half of the center of curvature.