# Ernst Abbe

Ernst Karl Abbe HonFRMS (23 January 1840 – 14 January 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.

Ernst Karl Abbe
Born23 January 1840
Died14 January 1905 (aged 64)
ResidenceGermany
NationalityGerman
Alma materUniversity of Göttingen
University of Jena
Known forAbbe refractometer
Abbe number
Scientific career
FieldsPhysicist
InstitutionsUniversity of Jena
Karl Snell
Doctoral studentsHeinrich Friedrich Weber
Other notable studentsGottlob Frege

## Personal life

Else Snell

Abbe was born 23 January 1840 in Eisenach, Saxe-Weimar-Eisenach,[1] to Georg Adam Abbe and Elisabeth Christina Barchfeldt.[2] 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, at the Eisenach Gymnasium, which he graduated from in 1857.[3] 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 23 March 1861.[3] While at school, he was influenced by Bernhard Riemann and Wilhelm Eduard Weber, who also happened to be one of the Göttingen Seven.[4] 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).[4] On 8 August 1863 he qualified as a university lecturer at the University of Jena. In 1870, he accepted a contract as an associate professor of experimental physics, mechanics and mathematics in Jena.[1][5] In 1871, he married Else Snell, daughter of the mathematician and physicist Karl Snell, one of Abbe's teachers,[nb 1] with whom he had two daughters.[2] He attained full professor status by 1879.[2] He became director of the Jena astronomical and meteorological observatory in 1878.[5][nb 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 14 January 1905 in Jena.[1] He was an atheist.[6]

## Life work

Microscope by Carl Zeiss (1879) with optics by Abbe

The resolution limit formula engraved in an Ernst Abbe memorial in Jena

German stamp of 1968

Ernst Abbe, relief at his grave

In 1866, he became a research director at the Zeiss Optical Works, and in 1886 he invented the apochromatic lens, a microscope lens which eliminates both the primary and secondary color distortion.[5] By 1870, Abbe invented the Abbe condenser, used for microscope illumination.[5] In 1871, he designed the first refractometer, which he described in a booklet published in 1874.[2][7] He developed the laws of image of non-luminous objects by 1872.[2] Zeiss Optical Works began selling his improved microscopes in 1872, by 1877 they were selling microscopes with homogenous immersion objective, and in 1886 his apochromatic objective microscopes were being sold.[8] 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).[9] 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,[10] 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)

${\displaystyle d={\frac {\lambda }{2nA}}}$

(Eq. 1)

although in a publication in 1874 by Helmholtz[11] (another early appearance of this formula), Helmholtz states this formula was first derived by Joseph Louis Lagrange, who had died 61 years prior. Helmholtz was so impressed as to offer a professorship at the University of Berlin, which he refused due to his ties to Zeiss.[4] 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",[12] 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.

In 1876, Abbe was offered a partnership by Zeiss and began to share in the considerable profits.[4] 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. In 1878, he built the first homogenous immersion system for the microscope.[2] 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.[13] In this publication, Abbe states that both his theoretical and experimental investigations confirmed Eq. 1. Abbe's contemporary Henry Edward Fripp, English translator of Abbe's and Helmholtz's papers, puts their contributions on equal footing. He also perfected the interference method by Fizeau, in 1884.[2] Abbe, Zeiss, Zeiss' son, Roderich Zeiss, and Otto Schott formed, in 1884, Jenaer Glaswerk Schott & Genossen. This company, which in time would in essence merge with Zeiss Optical Works, was responsible for research and production of 44 initial types of optical glass.[8] Working with telescopes, he built image reversal system in 1895.[2]

In order to produce high quality objectives, Abbe made significant contributions to the diagnosis and correction of optical aberrations, both spherical aberration and coma aberration, 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.[10] So monumental and advanced were Abbe's calculations and achievements that Frits Zernike based his phase contrast work on them, for which he was awarded the Nobel Prize in 1953, and Hans Busch used them to work on the development of the electron microscope.[4]

During his association with Carl Zeiss' microscope works, not only was he at the forefront of the field of optics but also labor reform as he also, in 1900, introduced the eight-hour workday, in remembrance of the 14-hour workday of his own father.[8] In addition, he created a pension fund and a discharge compensation fund.[2] In 1889, Ernst Abbe set up and endowed the Carl Zeiss Foundation for research in science.[2] The aim of the foundation was "to secure the economic, scientific, and technological future and in this way to improve the job security of their employees."[8] He made it a point that the success of an employee was based solely on their ability and performance, not on their origin, religion, or political views.[8] In 1896, he reorganized the Zeiss optical works into a cooperative with profit-sharing.[5] His social views were so respected as to be used by the Prussian state as a model and idealized by Alfred Weber in the 1947 book Schriften der Heidelberger Aktionsgruppe zur Demokratie und Zum Freien Sozialismus.[14]

The crater Abbe on the Moon was named in his honour.[citation needed]

## 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.

• —— (1884). —— (ed.). "On the Mode of Vision with Objectives of Wide Aperture". Journal of the Royal Microscopical Society. London, UK: Williams & Norgate. 4 (1): 20–27. doi:10.1111/j.1365-2818.1884.tb02005.x.
• —— (1886). "The new microscope". S Ber Jena Ges Med. 2: 107–108.[full citation needed]
• —— (1886). Über Verbesserungen des Mikroscope mit Hilfe neuer Arten optischen Glases [About Enhancements of the Microscope Using New Types of Optical Glass] (in German).
• —— (1890). "Messapparate für Physiker" [Measuring Equipment for Physicists]. Zeitschrift für Instrumentenkunde (in German). 10: 446–447.
• —— (1895). Double Prism for Totally-Reflecting Refractometers. Google Patents.
• —— (1895). Motive und Erläuterungen zum Entwurf eines Statuts der Carl Zeiss-Stiftung [Motives and Explanations on the Draft Statute of the Carl Zeiss Foundation] (in German). Vopelius.
• ——; Rudolph, P. (1897). "Anamorphotisches Linsensystem" [Anamorphic Lens System]. German Pat (in German). 99722.
• —— (1904). Gesammelte Abhandlungen [Collected Essay] (in German). 5 volumes, released from 1904 until 1940. New York, NY: Hildesheim. LCCN 94235187.
• ——; Lummer, Otto; Reiche, Fritz (1910). Die Lehre von der Bildentstehung im Mikroskop [The Theory of Image Formation in the Microscope] (in German). Braunschweig, Germany: F. Vieweg und Sohn. LCCN 10017693.
• —— (1921). Sozialpolitische Schriften [Socio-political Writings] (in German). Jena, Germany: Gustav Fischer. LCCN 49036118.

## Notes

1. ^ Some sources give his wife's name as Elisabeth.[2]
2. ^ The dates of his job appointments at the University of Jena, including his appointment as director of the Jena Observatory has some uncertainty, as sources give different dates, as following. 1870: assistant lecturer on mechanics and experimental physics; 1873: associate professor; 1877: director of the Jena Observatory meteorological and astronomy departments.[2]

## Citations

1. ^ a b c d Blasius 1953, pp. 2–3
2. Debus et al. 1968, p. 2
3. ^ a b Günther 1970, p. 6
4. Günther 1970, p. 7
5. Hoiberg 2010, p. 11
6. ^ Joseph McCabe (1945). A Biographical Dictionary of Ancient, Medieval, and Modern Freethinkers. Haldeman-Julius Publications. Retrieved 7 April 2013. He was not only a distinguished German physicist and one of the most famous inventors on the staff at the Zeiss optical works at Jena but a notable social reformer, By a generous scheme of profit-sharing he virtually handed over the great Zeiss enterprise to the workers. Abbe was an intimate friend of Haeckel and shared his atheism (or Monism). Leonard Abbot says in his life of Ferrer that Abbe had "just the same ideas and aims as Ferrer."
7. ^ Abbe 1874
8. Pfeiffer 1991, p. 445
9. ^ Joint Committee of Civil Engineers, American Congress on Surveying and Mapping, and American Society for Photogrammetry and Remote Sensing 1994
10. ^ a b Abbe 1881
11. ^ Helmholtz & Fripp 1876
12. ^ Abbe 1876
13. ^ Abbe 1883
14. ^ Günther 1970, p. 9