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Ernst Karl Abbe HonFRMS (23 January 1840 – 14 January 1905) was a German businessman, ... [The Theory of Image Formation in the Microscope] (in German ...
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).
If y is the max radial size of the image then θ is the field of view of the lens. While the image created by a lens is continuous, it can be modeled as a set of discrete field points, each representing a point on the object. The quality of the image is limited by the aberrations in the lens and the diffraction created by the finite aperture stop.
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.
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.
The Arlow-Abbe condenser is a modified Abbe condenser that replaces the iris diaphragm, filter holder, lamp and lamp optics with a small OLED or LCD digital display unit. The display unit allows for digitally synthesised filters for dark-field, Rheinberg, oblique and dynamic (constantly changing) illumination under direct computer control.
An Abbe diagram, also called 'the glass veil', is produced by plotting the Abbe number of a material versus its refractive index . Glasses can then be categorised and selected according to their positions on the diagram.
The Porro–Abbe system reduces the lateral beam axis offset by 23% compared to a traditional double Porro prism system in binoculars. [2] The prism is not dispersive since light enters and exits the prism only at normal incidence. Since the light is four times reflected, an even number of times, the image's handedness is not changed.