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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. It is named after Ernst Abbe (1840
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 Abbe's formula for the diffraction limit, set in stone at a monument in Jena. Jablonski diagram showing the redshift of the stimulated photon. This redshift allows the stimulated photon to be ignored. Diagram of the design of a STED device. The double laser design allows for excitation and stimulated emission to be used together for STED.
where V 1 and V 2 are the Abbe numbers of the materials of the first and second lenses, respectively. Since Abbe numbers are positive, one of the focal lengths must be negative, i.e., a diverging lens, for the condition to be met. The overall focal length of the doublet f is given by the standard formula for thin lenses in contact:
Abbe condensers are difficult to use for magnifications of above 400X, as the aplanatic cone is only representative of a numerical aperture (NA) of 0.6. This condenser is composed of two lenses, a plano-convex lens somewhat larger than a hemisphere and a large bi-convex lens serving as a collecting lens to the first.
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.
By observing and recording the beam pattern, for example, one can infer the spatial mode properties of the beam and whether or not the beam is being clipped by an obstruction; By focusing the laser beam with a lens and measuring the minimum spot size, the number of times diffraction limit or focusing quality can be computed.
Crown glass is a type of optical glass used in lenses and other optical components. It has relatively low refractive index (≈1.52) and low dispersion (with Abbe numbers between 50 and 85). Crown glass is produced from alkali-lime silicates containing approximately 10% potassium oxide and is one of the earliest low dispersion glasses.