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Hidden visions

Updated Thursday, 3rd August 2006

Abbe's mathematical research revolutionised photography and his philanthropy opened up opportunities for people who, like him, had humble beginnings.

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Scientists using a microscope Copyrighted  image Icon Copyright: BBC

Ernst Abbe was the son of a spinner who found it hard to provide for his family. He showed early promise and was educated by support from his father's employer and scholarships. He earned degrees from the University of Jena and the University of Goettingen. His doctorate was on thermodynamics and was received in 1861.

In 1863 he joined the teaching staff at the University. In 1866 he had been approached by Carl Zeiss, a German lens manufacturer, and asked to investigate various optical problems. In 1870 he was appointed Professor of physics and mathematics at the University of Jena and made a partner in the Zeiss Company in 1876.

This association led him to an investigation of the physical factors that limit the resolution of microscopes and the manufacturing processes needed to approach these limits in practice.
It turns out that the limit of resolution of an optical system depends on the wavelength of the light used. Hence Abbe was able to ascertain that optical microscopes had very precise limits. It also follows that if you want to see smaller things, you need to use electromagnetic waves with a shorter wavelength.

He developed methods for the in-process measurement of refractive index (a measure of the speed at which light waves travel through a medium) and a device to measure the focal length of lenses. His studies led to the diffraction theory of image formation from which many modern methods used in image enhancement and processing have developed.

His compound microscope was the first in which an optical design resulted from the theoretical understanding and minimisation of the effects of aberrations (imperfections in a transmitted image), diffraction (interference caused by the obstruction of a wavefront) and coma (an off-axis lens aberration that gives a variation of magnification).

He also came up with a way of measuring the amount of dispersion (the spreading out of visible light into its constituent colours) in a medium. The higher the Abbe number, then the less the light spreads and the closer their index of refraction. It is from Abbe's work that we get the idea of a numerical aperture, related to the f-number where:

f-stop equals one over two times NA

- where NA is the numerical aperture or the amount of light and is given by

NA equals n zero times sine theta max

where n zero is the refractive index, and theta max is the half angle of the cone of light that falls on the lens.

Abbe became the owner of the company with the death of Carl Zeiss in 1888. He was a socialist and saw this as his chance to influence the world of science while helping those who were, as he had been himself, socially disadvantaged. During this period he founded the Carl Zeiss Foundation for research in science and social improvement and introduced socially advanced ideas into management, including the eight hour workday, holiday pay, sick pay and pensions.





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