# Ernst Abbe

Ernst Karl Abbe
Born January 23, 1840
Eisenach, Saxe-Weimar-Eisenach
Died January 14, 1905 (aged 64)
Jena, German Empire
Residence Germany
Nationality German
Fields Physicist
Institutions University of Jena
Alma mater University of Göttingen
University of Jena
Karl Snell
Doctoral students Heinrich Friedrich Weber
Other notable students Gottlob Frege
Known for Abbe refractometer
Abbe number

Ernst Karl Abbe (January 23, 1840 – January 14, 1905) was a German physicist, optical scientist, entrepreneur, and social reformer. Together with Otto Schott and Carl Zeiss, he laid the foundation of modern optics. Abbe developed numerous optical instruments. He was a co-owner of Carl Zeiss AG, a German manufacturer of research microscopes, astronomical telescopes, planetariums and other optical systems.

## Personal life

Else Snell

Abbe was born January 23, 1840 in Eisenach, Saxe-Weimar-Eisenach.[1] He came from a humble home — his father was a foreman in a spinnery. Supported by his father's employer, Abbe was able to attend secondary school and to obtain the general qualification for university entrance with fairly good grades. By the time he left school, his scientific talent and his strong will had already become obvious. Thus, in spite of the family's strained financial situation, his father decided to support Abbe's studies at the Universities of Jena (1857–1859) and Göttingen (1859–1861).[1] During his time as a student, Abbe gave private lessons to improve his income. His father's employer continued to fund him. Abbe was awarded his PhD in Göttingen on March 23, 1861. This was followed by two short assignments at the Göttingen observatory and at Physikalischer Verein in Frankfurt (an association of citizens interested in physics and chemistry that was founded by Johann Wolfgang von Goethe in 1824 and still exists today). On August 8, 1863 he qualified as a university lecturer at the University of Jena. In 1870, he accepted a contract as an extraordinary professor of physics and mathematics in Jena.[1][2] In 1871, he married Else Snell, daughter of the mathematician and physicist Karl Snell, one of Abbe's teachers. He became director of the Jena astronomical and meteorological observatories in 1878.[2] In 1889, he became a member of the Bavarian Academy of Sciences and Humanities. He also was a member of the Saxon Academy of Sciences. He was relieved of his teaching duties at the University of Jena in 1891. Abbe died January 14, 1905 in Jena.[1]

## Life work

Microscope by Carl Zeiss (1879) with optics by Abbe
German stamp of 1968
Ernst Abbe, relief at his grave

In 1866, he became a research director at the Zeiss Optical Works, and in 1868 he invented the apochromatic lens, a microscope lens which eliminates both the primary and secondary color distortion.[2] He designed the first refractometer, which he described in a booklet published in 1874.[3] He created the Abbe number, a measure of any transparent material's variation of refractive index with wavelength and Abbe's criterion, which tests the hypothesis, that a systematic trend exists in a set of observations (in terms of resolving power this criterion stipulates that an angular separation cannot be less than the ratio of the wavelength to the aperture diameter, see angular resolution).[4] Already a professor in Jena, he was hired by Carl Zeiss to improve the manufacturing process of optical instruments, which back then was largely based on trial and error.

Abbe was the first to define the term numerical aperture,[5] as the sine of the half angle multiplied by the refractive index of the medium filling the space between the cover glass and front lens.

Abbe is credited by many for discovering the resolution limit of the microscope, and the formula (published in 1873)

$d = \frac{\lambda}{2 NA}$

(Eq. 1)

although in another early appearance of this formula in a publication in 1874 by Helmholtz,[6] Helmholtz states this formula was first derived by Joseph Louis Lagrange, who had died 61 years prior. Abbe was in the camp of the wide aperturists, arguing that microscopic resolution is ultimately limited by the aperture of the optics, but also argued that depending on application there are other parameters that should be weighted over the aperture in the design of objectives. In Abbe's 1874 paper, titled "A Contribution to the Theory of the Microscope and the nature of Microscopic Vision",[7] Abbe states that the resolution of a microscope is inversely dependent on its aperture, but without proposing a formula for the resolution limit of a microscope.

Although the first theoretical derivations of Eq. 1 were published by others, it is fair to say that Abbe was the first to reach this conclusion experimentally. The objectives that the Abbe Zeiss collaboration were producing were of ideal ray geometry, allowing Abbe to find that the aperture sets the upper limit of microscopic resolution, not the curvature and placement of the lenses. Abbe's first publication of Eq. 1 occurred in 1882.[8] In this publication Abbe states, that both his theoretical and experimental investigations confirmed Eq. 1. Abbe's contemporary H. E. Fripp, English translator of Abbe's and Helmholtz's papers, puts their contributions on equal footing.

In order to produce high quality objectives, Abbe made significant contributions to the diagnosis and correction of optical aberrations, which is required for an objective to reach the resolution limit of Eq. 1. In addition to spherical aberration, Abbe discovered that the rays in optical systems must have constant angular magnification over their angular distribution to produce a diffraction limited spot, a principle known as the Abbe sine condition.[5]

Abbe invented the Abbe condenser, used for microscope illumination.[9] During his association with Carl Zeiss' microscope works, he also introduced the eight-hour workday, in remembrance of the 14-hour workday of his own father. In 1891, Ernst set up and endowed the Carl Zeiss Foundation for research in science.[2] In 1896, he reorganized the Zeiss optical works into a cooperative with profit-sharing.

The crater Abbe on the Moon was named in his honour.

## Bibliography

Abbe was a pioneer in optics, lens design, and microscopy, and an authority of his time. He left us with numerous publications of his findings, inventions, and discoveries. Below is a list of publications he authored including many links to the scanned Google Books pages.

Abbe, Ernst (1873). "Über einen neuen Beleuchtungsapparat am Mikroskop". Archiv für mikroskopische Anatomie 9: 469–480. doi:10.1007/bf02956177.

Abbe, Ernst (1873). "Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung". Archiv für Mikroskopische Anatomie 9 (1): 413–468. doi:10.1007/BF02956173. ISSN 0176-7364. Retrieved 2010-08-27.

Abbe, Ernst (1874). "A Contribution to the Theory of the Microscope and the Nature of Microscopic Vision". Proceedings of the Bristol Naturalists' Society 1: 200–261.

Abbe, Ernst (1874). "Neue Apparate zur Bestimmung des Brechungs und Zerstreuungsvermögens fester und flüssiger Körper". Jenaische Zeitschrift für Naturwissenschaft 8: 96–174.

Abbe, Ernst (1875). "A New Illuminating Apparatus for the Microscope". The Monthly Microscopical Journal 13: 77–82. doi:10.1111/j.1365-2818.1875.tb00845.x.

Abbe, Ernst (1875). "Extracts from Mr. H. E. Fripp's Translation of Professor Abbe's Paper on the Microscope". The Monthly Microscopical Journal 14: 191–201.

Abbe, Ernst (1875). "Extracts from Mr. H. E. Fripp's Translation of Professor Abbe's Paper on the Microscope (Cont.)". The Monthly Microscopical Journal 14: 245–254.

Abbe, Ernst (1878). "Über mikrometrische Messung mittelst optischer Bilder". Jenaische Zeitschrift für Naturwissenschaft: 11–17.

Abbe, Ernst (1878). "Über Blutkorper-Zahlung". Jenaische Zeitschrift für Naturwissenschaft: 98–105.

Abbe, Ernst (1878). "Über die Bedingungen des Aplanatismus der Linsensysteme". Jenaische Zeitschrift für Naturwissenschaft: 129–142.

Abbe, Ernst (1878). "Über die Grenzen der geometrischen Optik". Jenaische Zeitschrift für Naturwissenschaft: 71–109.

Abbe, Ernst (1879-06-11). "On Stephenson's System of Homogeneous Immersion for Microscope Objectives". Journal of the Royal Microscopical Society 2: 256–265. doi:10.1111/j.1365-2818.1879.tb01651.x.

Abbe, Ernst (1879). "On New Methods for Improving Spherical Correction applied to the Construction of Wide-angled Object-glasses". Journal of the Royal Microscopical Society 2: 812–824. doi:10.1111/j.1365-2818.1879.tb01548.x.

Abbe, Ernst (1879-05-02). "Über die Bestimmung von Zeit und Polhöhe aus Beobachtungen in Höhenparallen". Jenaische Zeitschrift für Naturwissenschaft: 57–66.

Abbe, Ernst (1879-02-21). "Über die Bestimmung der Brechungs-Verhältnisse fester Körper mittelst des Refractometers". Jenaische Zeitschrift für Naturwissenschaft: 35–44.

Abbe, Ernst (1880). "Conditions on Aplanatism of Systems of Lenses". Journal of the Royal Microscopical Society 3: 509–515.

Abbe, Ernst (1880). "Some Remarks on the Apertometer". Journal of the Royal Microscopical Society 3: 20–31. doi:10.1111/j.1365-2818.1880.tb05648.x.

Abbe, Ernst (1880). "The Essence of Homogeneous Immersion". Journal of the Royal Microscopical Society. 2 1: 526.

Abbe, Ernst (1880). "Illumination for Binocular Microscopes with HIgh Powers". Journal of the Royal Microscopical Society. 2 1: 690–692.

Abbe, Ernst (1880). "Penetrating Power of Objectives". Journal of the Royal Microscopical Society. 2 1: 831–832.

Abbe, Ernst (1881). "Beschreibung eines neuen stereoskopischen Oculars". Repertorium für Experimental-Physik für Physikalische Technik 17: 197–224.

Abbe, Ernst (1881). "Origin of Homogeneous Immersion". Journal of the Royal Microscopical Society. 2 1: 131–134.

Abbe, Ernst (1881). Conditions of Microstereoscopic Vision – "Penetration". 2 1. pp. 680–689.

Abbe, Ernst (1881). "On the Estimation of Aperture in the Microscope". Journal of the Royal Microscopical Society 1 (3): 388–423. doi:10.1111/j.1365-2818.1881.tb05909.x.

Abbe, Ernst (1881). "On the Conditions of Orthoscopic and Pseudoscopic Effects in the Binocular Microscope". Journal of the Royal Microscopical Society. 2 1: 203–211. doi:10.1111/j.1365-2818.1881.tb05902.x.

Abbe, Ernst (1881). "Abbe's Stereoscopic Eye-piece". Journal of the Royal Microscopical Society. 2 1: 298–299.

Abbe, Ernst (1881). "Conditions of Aplanatism for Wide-angled Pencils". Journal of the Royal Microscopical Society. 2 1: 831.

Abbe, Ernst (1882). "Miniatured Images". Journal of the Royal Microscopical Society. 2 2: 693–696.

Abbe, Ernst (1882). "The Relation of Aperture and Power in the Microscope". Journal of the Royal Microscopical Society 2 (3): 300–309. doi:10.1111/j.1365-2818.1882.tb00190.x.

Abbe, Ernst (1882). "The Relation of Aperture and Power in the Microscope (continued).". Journal of the Royal Microscopical Society. 2 2 (1): 460–473. doi:10.1111/j.1365-2818.1882.tb04805.x.

Abbe, Ernst (1883). "The Relation of Aperture and Power in the Microscope (continued)". Journal of the Royal Microscopical Society. 2 3 (1): 790–812. doi:10.1111/j.1365-2818.1883.tb05956.x.

Abbe, Ernst (1884). "Note on the Proper Definition of the Amplifying Power of a Lens or Lens-System". Journal of the Royal Microscopical Society 4 (1): 348–351. doi:10.1111/j.1365-2818.1884.tb01110.x.

Abbe, Ernst (1884). "On the Mode of vision with Objectives of Wide Aperture". Journal of the Royal Microscopical Society 4 (1): 20–27. doi:10.1111/j.1365-2818.1884.tb02005.x.

ABBE, E. (1895). DOUBLE PRISM FOR TOTALLY-REFLECTING REFRACTOMETERS. Google Patents.

Abbe, E.; O. Lummer; F. Reiche (1910). Die Lehre von der Bildentstehung im Mikroskop. Vieweg.

Abbe, E. (1886). "The new microscope". S Ber Jena Ges Med 2: 107–108.

Abbe, E.; P. Rudolph (1897). "Anamorphotisches Linsensystem". German Pat. 99722.

Abbe, E. (1895). Motive und Erläuterungen zum Entwurf eines Statuts der Carl Zeiss-Stiftung. Vopelius.

Abbe, E. (1906). Sozialpolitische Schriften. G. Fischer.

Abbe, E. (1890). "Messapparate für Physiker". Zeitschrift für Instrumentenkunde 10: 446–447.

Abbe, Ernst (1897-06-22), Telescope, Jena, retrieved 2010-08-27

Abbe, Ernst; Paul Rudoph (1890-08-26), Photographic Objective, Jena, retrieved 2010-08-27

Abbe, E. (1876). "Die optischen Hilfsmittel der Mikroskopie. Bericht über die wissenschaftlichen Apparate auf der Londoner internationalen Ausstellung (1876), Hrsg. Hoffmann, AW (1878), Braunschweig, 383". Abbe, E.(1904), Gesammelte Abhandlungen, Bd 1.

Abbe, Ernst (1886). Über Verbesserungen des Mikroscope mit Hilfe neuer Arten optischen Glases.

 Wikimedia Commons has media related to: Ernst Abbe

## References

1. ^ a b c d Ewald Blasius (1953), "Abbe, Ernst Carl", Neue Deutsche Biographie (NDB) (in German) (Berlin: Duncker & Humblo) 1: 2–3
2. ^ a b c d "Abbe, Ernst". Encyclopedia Britannica. I: A-Ak - Bayes (15th ed.). Chicago, IL: Encyclopedia Britannica, Inc. 2010. p. 11. ISBN 978-1-59339-837-8.
3. ^ Abbe, E. (1874). Neue Apparate zur Bestimmung des Brechungs – und Zerstreuungsvermögens fester und fluüssiger Körper. Jena: Mauke's Verlag.
4. ^ American Congress on Surveying and Mapping (1994). Glossary of the mapping sciences. Maryland: American Society for Photogrammetry and Remote Sensing.
5. ^ a b Abbe, Ernst (1881). "On the Estimation of Aperture in the Microscope". Journal of the Royal Microscopical Society 1 (3): 388–423. doi:10.1111/j.1365-2818.1881.tb05909.x.
6. ^ Helmholtz, Hermann (July 1876). "On the Limits of the Optical Capacity of the Microscope". The Monthly microscopical journal 16 (1): 15–39. doi:10.1111/j.1365-2818.1876.tb05606.x.
7. ^ Abbe, Ernst (1874). "A Contribution to the Theory of the Microscope and the nature of Microscopic Vision". Proceedings of the Bristol Naturalists' Society 1: 200–261.
8. ^ Abbe, Ernst (1883). "The Relation of Aperture and Power in the Microscope (continued)". Journal of the Royal Microscopical Society. 2 3 (6): 790–812. doi:10.1111/j.1365-2818.1883.tb05956.x.
9. ^ "Abbe, Ernst – Encyclopædia Britannica – Encyclopædia Britannica Premium Service". Retrieved 2008-05-11.