Ernst Abbe

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Ernst Karl Abbe
Ernst Abbe (HeidICON 29803) (cropped).jpg
Born(1840-01-23)23 January 1840
Died14 January 1905(1905-01-14) (aged 64)
Residence Germany
Nationality German
Alma mater University of Göttingen
University of Jena
Known for Abbe refractometer
Abbe number
Scientific career
Fields Physicist
Institutions University of Jena
Doctoral advisor Wilhelm Eduard Weber
Karl Snell
Doctoral students Heinrich Friedrich Weber
Other notable students Gottlob Frege

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.

Germany Federal parliamentary republic in central-western Europe

Germany, officially the Federal Republic of Germany, is a country in Central and Western Europe, lying between the Baltic and North Seas to the north and the Alps, Lake Constance and the High Rhine to the south. It borders Denmark to the north, Poland and the Czech Republic to the east, Austria and Switzerland to the south, France to the southwest, and Luxembourg, Belgium and the Netherlands to the west.

Physicist scientist who does research in physics

A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate causes of phenomena, and usually frame their understanding in mathematical terms. Physicists work across a wide range of research fields, spanning all length scales: from sub-atomic and particle physics, through biological physics, to cosmological length scales encompassing the universe as a whole. The field generally includes two types of physicists: experimental physicists who specialize in the observation of physical phenomena and the analysis of experiments, and theoretical physicists who specialize in mathematical modeling of physical systems to rationalize, explain and predict natural phenomena. Physicists can apply their knowledge towards solving practical problems or to developing new technologies.

Optical engineering field centered around the applications of optics

Optical engineering is the field of study that focuses on applications of optics. Optical engineering deals with design of optical instruments such as lenses, microscopes, telescopes, and other equipment that utilizes the properties of light using physics and chemistry. Other prominent optical engineering applications include optical sensors and measurement systems, lasers, fiber optic communication systems, optical disc systems, etc.


Personal life

Else Snell Else Abbe.png
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]

Eisenach Place in Thuringia, Germany

Eisenach is a town in Thuringia, Germany with 42,000 inhabitants, located 50 kilometres west of Erfurt, 70 km southeast of Kassel and 150 km northeast of Frankfurt. It is the main urban centre of western Thuringia and bordering northeastern Hessian regions, situated near the former Inner German border. A major attraction is Wartburg castle, which has been a UNESCO world heritage site since 1999.

Saxe-Weimar-Eisenach grand duchy

Saxe-Weimar-Eisenach was created as a duchy in 1809 by the merger of the Ernestine duchies of Saxe-Weimar and Saxe-Eisenach, which had been in personal union since 1741. It was raised to a Grand duchy in 1815 by resolution of the Vienna Congress. In 1903, it officially changed its name to the Grand Duchy of Saxony, but this name was rarely used. The Grand Duchy came to an end in the German Revolution of 1918–19 with the other monarchies of the German Empire. It was succeeded by the Free State of Saxe-Weimar-Eisenach, which was merged into the new state of Thuringia two years later.

University of Jena university located in Jena, Thuringia, Germany

Friedrich Schiller University Jena is a public research university located in Jena, Thuringia, Germany.

Life work

Microscope by Carl Zeiss (1879) with optics by Abbe Microscope Zeiss 1879.jpg
Microscope by Carl Zeiss (1879) with optics by Abbe
The resolution limit formula engraved in an Ernst Abbe memorial in Jena Ernst-Abbe-Denkmal Jena Furstengraben - 20140802 125709.jpg
The resolution limit formula engraved in an Ernst Abbe memorial in Jena
German stamp of 1968 Stamps of Germany (BRD) 1968, MiNr 548.jpg
German stamp of 1968
Ernst Abbe, relief at his grave Abbe-Grab kl.jpg
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.

Carl Zeiss AG German manufacturer of optical systems

Carl Zeiss AG, branded as ZEISS, is a German manufacturer of optical systems and optoelectronics, founded in Jena, Germany in 1846 by optician Carl Zeiss. Together with Ernst Abbe and Otto Schott he layed the foundation for today's multi-national company. The current company emerged from a reunification of Carl Zeiss companies in East and West Germany with a consolidation phase in the 1990s. ZEISS is active in four business segments with approximately equal revenue, Industrial Quality and Research, Medical Technology, Consumer Markets and Semiconductor Manufacturing Technology in almost 50 countries, has 30 production sites and around 25 development sites worldwide.


An apochromat, or apochromatic lens (apo), is a photographic or other lens that has better correction of chromatic and spherical aberration than the much more common achromat lenses.

A refractometer is a laboratory or field device for the measurement of an index of refraction (refractometry). The index of refraction is calculated from Snell's law while for mixtures, the index of refraction can be calculated from the composition of the material using several mixing rules such as the Gladstone–Dale relation and Lorentz–Lorenz equation.

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.

Numerical aperture dimensionless number that characterizes the range of angles over which the system can accept or emit light

In optics, the numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light. By incorporating index of refraction in its definition, NA has the property that it is constant for a beam as it goes from one material to another, provided there is no refractive power at the interface. The exact definition of the term varies slightly between different areas of optics. Numerical aperture is commonly used in microscopy to describe the acceptance cone of an objective, and in fiber optics, in which it describes the range of angles within which light that is incident on the fiber will be transmitted along it.

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





(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]

Otto Schott German chemist, glass technologist, and inventor

Friedrich Otto Schott was a German chemist, glass technologist, and the inventor of borosilicate glass. He was the son of a window glass maker, Simon Schott. From 1870 to 1873 Schott studied chemical technology at the technical college in Aachen and at the universities of Würzburg and Leipzig. He attained a doctorate in glass chemistry at Friedrich Schiller University of Jena for his thesis “Contributions to the Theory and Practice of Glass Fabrication”.

Schott AG company

Schott AG is company specializing in the manufacture of glass and glass-ceramics. It is headquartered in Mainz, Germany.

Telescope Optical instrument that makes distant objects appear magnified

A telescope is an optical instrument that makes distant objects appear magnified by using an arrangement of lenses or curved mirrors and lenses, or various devices used to observe distant objects by their emission, absorption, or reflection of electromagnetic radiation. The first known practical telescopes were refracting telescopes invented in the Netherlands at the beginning of the 17th century, by using glass lenses. They were used for both terrestrial applications and astronomy.

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 ]


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.

See also


  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]


  1. 1 2 3 4 Blasius 1953 , pp. 2–3
  2. 1 2 3 4 5 6 7 8 9 10 11 12 Debus et al. 1968 , p. 2
  3. 1 2 Günther 1970 , p. 6
  4. 1 2 3 4 5 Günther 1970 , p. 7
  5. 1 2 3 4 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. 1 2 3 4 5 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. 1 2 Abbe 1881
  11. Helmholtz & Fripp 1876
  12. Abbe 1876
  13. Abbe 1883
  14. Günther 1970 , p. 9

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Further reading