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Glasses' Abbe numbers, along with their mean refractive indices, are used in the calculation of the required refractive powers of the elements of achromatic lenses in order to cancel chromatic aberration to first order. These two parameters which enter into the equations for design of achromatic doublets are exactly what is plotted on an Abbe ...
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).
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.
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.
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 the design of optimized optical microscopes in Jena, Germany, stimulated by co-operation with the optical workshop of Carl Zeiss.
* σ PSF is the Gaussian standard deviation of the point spread function, whose FWHM following the Ernst Abbe equation d = λ/(2 N.A.). (unit m) * a is the size of each image pixel. (unit m) * N sig is the photon counts of the total PSF over all pixels of interest. (unitless)
The choice of glass gives the mean refractive index, often written as (for the refractive index at the Fraunhofer "d" spectral line wavelength), and the Abbe number (for the reciprocal of the glass dispersion). To make the linear dispersion of the system zero, the system must satisfy the equations
In laser physics, numerical aperture is defined slightly differently.Laser beams spread out as they propagate, but slowly. Far away from the narrowest part of the beam, the spread is roughly linear with distance—the laser beam forms a cone of light in the "far field".