Ernst Karl Abbe
Born	(1840-01-23)January 23, 1840 Eisenach, Saxe-Weimar-Eisenach
Died	January 14, 1905(1905-01-14) (aged 64) Jena, German Empire
Residence	Germany
Nationality	German
Fields	Physicist
Institutions	University of Jena
Alma mater	University of Göttingen University of Jena
Doctoral advisor	Wilhelm Eduard Weber Karl Snell
Doctoral students	Heinrich Friedrich Weber
Known for	Abbe refractometer Abbe number

Ernst Karl Abbe (January 23, 1840 – January 14, 1905) was a German physicist, optometrist, 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[link]

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 in Jena.^[1] 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 observatory in 1878. 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[link]

Microscope by Carl Zeiss (1879) with optics by Abbe

German stamp of 1968

Ernst Abbe, relief at his grave

He designed the first refractometer, which he described in a booklet published in 1874.^[2] 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).^[3] 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,^[4] 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

Failed to parse (Missing texvc executable; please see math/README to configure.): d = \frac{\lambda}{2 NA}

(Eq. 1)

although the first known appearance of this formula was in a 1874 publication by Helmholtz,^[5] in which 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 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".,^[6] 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.^[7] 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 into 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.^[4]

Abbe invented the Abbe condenser, used for microscope illumination.^[8] 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.

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

Bibliography[link]

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. http://books.google.com/books?id=LMkVAAAAYAAJ&dq=Abbe%20Archiv%20f%C3%BCr%20Mikroskopische%20Anatomie%201873&pg=PA469#v=onepage&q=abbe&f=false. 

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. http://books.google.com/books?id=LMkVAAAAYAAJ&dq=Abbe%20Archiv%20f%C3%BCr%20Mikroskopische%20Anatomie%201873&pg=PA413#v=onepage&q&f=false. 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. http://books.google.com/books?id=TC8UAAAAYAAJ&dq=Bristol%20Naturalists%20Society%201875&pg=PA200#v=onepage&q&f=false. 

Abbe, Ernst (1874). "Neue Apparate zur Bestimmung des Brechungs und Zerstreuungsvermögens fester und flüssiger Körper". Jenaische Zeitschrift für Naturwissenschaft 8: 96–174. http://books.google.com/books?id=87UUAAAAYAAJ&dq=Jenaische%20Zeitschrift%20f%C3%BCr%20Naturwissenschaft%20Volume%208&pg=PA96#v=onepage&q&f=false. 

Abbe, Ernst (1875). "A New Illuminating Apparatus for the Microscope". The Monthly Microscopical Journal 13: 77–82. http://books.google.com/books?id=sOEUAAAAYAAJ&dq=A%20new%20illuminating%20apparatus%20for%20the%20microscope%201875%20abbe&pg=PA77#v=onepage&q&f=false. 

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. http://books.google.com/books?id=UTA4AAAAMAAJ&dq=On%20the%20microscope%20abbe%201875%20monthly&pg=PA191#v=onepage&q&f=false. 

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. http://books.google.com/books?id=UTA4AAAAMAAJ&dq=On%20the%20microscope%20abbe%201875%20monthly&pg=PA245#v=onepage&q&f=false. 

Abbe, Ernst (1878). "Über mikrometrische Messung mittelst optischer Bilder". Jenaische Zeitschrift für Naturwissenschaft: 11–17. http://books.google.com/books?id=nbcUAAAAYAAJ&dq=ueber%20mikrometrische%20messung%20mittelst%20optischer%20bilder&pg=PR11#v=onepage&q&f=false. 

Abbe, Ernst (1878). "Über Blutkorper-Zahlung". Jenaische Zeitschrift für Naturwissenschaft: 98–105. http://books.google.com/books?id=nbcUAAAAYAAJ&dq=Uber%20Blutkoerper%20Zahlung&pg=PR98#v=onepage&q&f=false. 

Abbe, Ernst (1878). "Über die Bedingungen des Aplanatismus der Linsensysteme". Jenaische Zeitschrift für Naturwissenschaft: 129–142. http://books.google.com/books?id=nbcUAAAAYAAJ&dq=Ueber%20die%20Bedingungen%20des%20Aplanatis&pg=PA129#v=onepage&q&f=false. 

Abbe, Ernst (1878). "Über die Grenzen der geometrischen Optik". Jenaische Zeitschrift für Naturwissenschaft: 71–109. http://books.google.com/books?id=nbcUAAAAYAAJ&dq=Ueber%20die%20Grenzen%20der%20geometrischen%20Optik&pg=RA1-PA71#v=onepage&q&f=false. 

Abbe, Ernst (1879-06-11). "On Stephenson's System of Homogeneous Immersion for Microscope Objectives". Journal of the Royal Microscopical Society 2: 256–265. http://books.google.com/books?id=d_MVAAAAYAAJ&dq=Stephenson's%20System%20abbe&pg=PA256#v=onepage&q&f=false. 

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. http://books.google.com/books?id=d_MVAAAAYAAJ&dq=Stephenson's%20System%20abbe&pg=PA812#v=onepage&q&f=false. 

Abbe, Ernst (1879-05-02). "Über die Bestimmung von Zeit und Polhöhe aus Beobachtungen in Höhenparallen". Jenaische Zeitschrift für Naturwissenschaft: 57–66. http://books.google.com/books?id=nbcUAAAAYAAJ&dq=Uber%20die%20Bestimmung%20von%20Zeit%20and%20Abbe&pg=PA57#v=onepage&q&f=false. 

Abbe, Ernst (1879-02-21). "Über die Bestimmung der Brechungs-Verhältnisse fester Körper mittelst des Refractometers". Jenaische Zeitschrift für Naturwissenschaft: 35–44. http://books.google.com/books?id=nbcUAAAAYAAJ&dq=Uber%20die%20Bestimmung%20von%20Zeit%20and%20Abbe&pg=PA35#v=onepage&q&f=false. 

Abbe, Ernst (1880). "Conditions on Aplanatism of Systems of Lenses". Journal of the Royal Microscopical Society 3: 509–515. http://books.google.com/books?id=xe4BAAAAYAAJ&dq=Conditions%20of%20microsteroscopic%20vision%201%20Abbe&pg=PA831#v=onepage&q&f=false. 

Abbe, Ernst (1880). "Some Remarks on the Apertometer". Journal of the Royal Microscopical Society 3: 20–31. http://books.google.com/books?id=YOAUAAAAYAAJ&dq=Some%20remarks%20on%20the%20apertometer%20abbe%20v%203&pg=PA20#v=onepage&q&f=false. 

Abbe, Ernst (1880). "The Essence of Homogenous Immersion". Journal of the Royal Microscopical Society. 2 1: 526. http://books.google.com/books?id=xe4BAAAAYAAJ&dq=Conditions%20of%20microsteroscopic%20vision%201%20Abbe&pg=PA526#v=onepage&q&f=false. 

Abbe, Ernst (1880). "Illumination for Binocular Microscopes with HIgh Powers". Journal of the Royal Microscopical Society. 2 1: 690–692. http://books.google.com/books?id=xe4BAAAAYAAJ&dq=Conditions%20of%20microsteroscopic%20vision%201%20Abbe&pg=PA690#v=onepage&q&f=false. 

Abbe, Ernst (1880). "Penetrating Power of Objectives". Journal of the Royal Microscopical Society. 2 1: 831–832. http://books.google.com/books?id=xe4BAAAAYAAJ&dq=Conditions%20of%20microsteroscopic%20vision%201%20Abbe&pg=PA831#v=onepage&q&f=false. 

Abbe, Ernst (1881). "Beschreibung eines neuen stereoskopischen Oculars". Repertorium für Experimental-Physik für Physikalische Technik 17: 197–224. http://books.google.com/books?id=1UzPAAAAMAAJ&dq=Beschreibung%20eines%20neuen%20stereo%20a%20197&pg=PA197#v=onepage&q&f=false. 

Abbe, Ernst (1881). "Origin of Homogeneous Immersion". Journal of the Royal Microscopical Society. 2 1: 131–134. http://books.google.com/books?id=xe4BAAAAYAAJ&dq=Journal%20of%20the%20Royal%20Microscopical%20Society%20Abbe%20On%20the%20Function%20of%20Aperture&pg=PA131#v=onepage&q&f=false. 

Abbe, Ernst (1881). Conditions of Microstereoscopic Vision – "Penetration". 2. 1. pp. 680–689. http://books.google.com/books?id=xe4BAAAAYAAJ&dq=Conditions%20of%20microsteroscopic%20vision%201%20Abbe&pg=PA680#v=onepage&q&f=false. 

Abbe, Ernst (1881). "On the Estimation of Aperture in the Microscope". Journal of the Royal Microscopical Society. 2 1: 388–423. http://books.google.com/books?id=xe4BAAAAYAAJ&dq=Conditions%20of%20microsteroscopic%20vision%201%20Abbe&pg=PA388#v=onepage&q&f=false. 

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. http://books.google.com/books?id=xe4BAAAAYAAJ&dq=Conditions%20of%20microsteroscopic%20vision%201%20Abbe&pg=PA203#v=onepage&q&f=false. 

Abbe, Ernst (1881). "Abbe's Stereoscopic Eye-piece". Journal of the Royal Microscopical Society. 2 1: 298–299. http://books.google.com/books?id=xe4BAAAAYAAJ&dq=Conditions%20of%20microsteroscopic%20vision%201%20Abbe&pg=PA298#v=onepage&q&f=false. 

Abbe, Ernst (1881). "Conditions of Aplanatism for Wide-angled Pencils". Journal of the Royal Microscopical Society. 2 1: 831. http://books.google.com/books?id=mXBJAAAAYAAJ&dq=Microscopy%20Society%20Journal%201880%20Abbe%20509&pg=PA509#v=onepage&q&f=false. 

Abbe, Ernst (1882). "Miniatured Images". Journal of the Royal Microscopical Society. 2 2: 693–696. http://books.google.com/books?id=Oks4AAAAMAAJ&dq=Miniature%20images%202%201882%20Journal%20Abbe&pg=PA693#v=onepage&q&f=false. 

Abbe, Ernst (1882). "The Relation of Aperture and Power in the Microscope". Journal of the Royal Microscopical Society. 2 2 (1): 300–309. http://books.google.com/books?id=KPQVAAAAYAAJ&dq=Journal%20of%20Microscopy%201881%20%22The%20Relation%20of%20Aperture%20and%20Power%20in%20the%20Microscope%22&pg=PA300#v=onepage&q&f=false. 

Abbe, Ernst (1882). "The Relation of Aperture and Power in the Microscope (continued).". Journal of the Royal Microscopical Society. 2 2 (1): 460–473. http://books.google.com/books?id=4r4EAAAAQAAJ&dq=Journal%20of%20the%20Royal%20Microscopical%20Society%20%201881&pg=PA460#v=onepage&q&f=false. 

Abbe, Ernst (1883). "The Relation of Aperture and Power in the Microscope (continued)". Journal of the Royal Microscopical Society. 2 3 (1): 790–812. http://books.google.com/books?id=aHhJAAAAYAAJ&dq=The%20Relation%20of%20Aperture%20and%20Power%20in%20the%20Microscope%20abbe&pg=PA790#v=onepage&q&f=false. 

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. http://books.google.com/books?id=th4AAAAAMAAJ&dq=Note%20on%20the%20proper%20definition%20of%20the%20amplifying%20power%20of%20a%20lens%20or%20a%20lens%20system&pg=PA348#v=onepage&q&f=false. 

Abbe, Ernst (1884). "On the Mode of vision with Objectives of Wide Aperture". Journal of the Royal Microscopical Society 4 (1): 20–27. http://books.google.com/books?id=th4AAAAAMAAJ&dq=Journal%20of%20the%20Royal%20Microscopical%20society%201884&pg=PA20#v=onepage&q&f=false. 

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, http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1&Sect2=HITOFF&d=PALL&p=1&u=%2Fnetahtml%2FPTO%2Fsrchnum.htm&r=1&f=G&l=50&s1=0584976.PN.&OS=PN/0584976&RS=PN/0584976, retrieved 2010-08-27 

Abbe, Ernst; Paul Rudoph (1890-08-26), Photographic Objective, Jena, http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1&Sect2=HITOFF&d=PALL&p=1&u=%2Fnetahtml%2FPTO%2Fsrchnum.htm&r=1&f=G&l=50&s1=0435271.PN.&OS=PN/0435271&RS=PN/0435271, 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. 

See also[link]

• Abbe prism
• Abbe refractometer
• Abbe error
• Aberration in optical systems
• Calculation of glass properties
• German inventors and discoverers

Wikimedia Commons has media related to: Ernst Abbe

References[link]

Further reading[link]

• Gunther, N. (1970). "Abbe, Ernst". Dictionary of Scientific Biography (New York, NY, USA: Charles Scribner's Sons) 1: 6–9. 

• Sella, Andrea (November 2008). "Abbé's refractometer". Chemistry World: 67. http://www.rsc.org/chemistryworld/Issues/2008/November/AbbesRefractometer.asp. 

External links[link]

• Paselk, Richard A.. "The Evolution of the Abbe Refractometer". http://www.humboldt.edu/~scimus/Essays/EvolAbbeRef/EvolAbbeRef.htm. Retrieved 2008-05-11. 
• Basic Principles of Refractometers (and Polarimeters)
• O'Connor, John J.; Robertson, Edmund F., "Ernst Abbe", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Abbe.html .
• Molecular Expressions's biography
• Works by Ernst Abbe at Project Gutenberg
• Abbe Refractometer by Carl Zeiss made in 1904

Carl Zeiss
Carl Zeiss
Born	(1816-09-11)11 September 1816 Weimar, Germany
Died	3 December 1888(1888-12-03) (aged 72) Jena, Germany
Nationality	German
Fields	Optics
Institutions	Carl Zeiss AG
Alma mater	University of Jena
Known for	Optical Lenses

Large microscope by Carl Zeiss (1879)

Carl Zeiss (11 September 1816 – 3 December 1888) was a German maker of optical instruments commonly known for the company he founded, Carl Zeiss Jena (now: Carl Zeiss AG). Zeiss made contributions to lens manufacturing that have aided the modern production of lenses. Raised in Weimar, Germany, he became a notable lens-maker in the 1840s when he created high-quality lenses that were "wide open", or in other words, had a very large aperture range that allowed for very bright images. He did this in the city of Jena at a self-opened workshop, where he started his lens-making career. At first his lenses were only used in the production of microscopes, but when cameras were invented, his company began manufacturing high-quality lenses for cameras.

Youth[link]

Zeiss began his life in pre-imperial Germany where he went to a grammar school, and undertook apprenticeship under Dr. Friedrich Körner, mechanic and supplier to the court. He later attended lectures in mathematics, experimental physics, anthropology, mineralogy and optics at the University of Jena. After seven years he opened a small workshop with hardly any tools. He made many lenses but had little recognition until 1847 when he hired his second and third apprentice.

Life[link]

In 1847 Carl Zeiss started making microscopes full-time. His first innovation was simpler single-lens microscopes intended for dissecting work. He sold 23 of them during the first year of production. Zeiss decided he needed a new challenge, so he began making compound microscopes. He created the Stand I which went to market in 1857.

In 1861 he was awarded a gold medal at the Thuringian Industrial Exhibition for his designs. They were considered to be among the best scientific instruments in Germany. By this point, he had about twenty people working for him and an expanding business. In 1866 the Zeiss workshop sold their thousandth microscope.

In 1872, he joined up with physicist Ernst Abbe. Their combined efforts lead to the discovery of the Abbe sine condition. Theoretically, the Abbe sine condition could greatly improve how well lenses could be made. However, a form of glass strong enough to fully test the theory did not exist at the time. Abbe then met Otto Schott, a thirty-year-old glass chemist who had just received his doctorate. They collaborated and in 1886, produced a new type of glass that could fully use the Abbe sine condition. This new type of glass made possible a new class of microscope objective, the apochromatic (often abbreviated 'apo'). Zeiss used water immersion to form a compensating eyepiece which produced images with little or no color distortion.

Zeiss's son had entered the business with him, but retired soon after Zeiss's death of natural causes on 3 December 1888. The business was incorporated as the Carl-Zeiss-Stiftung in 1889. It gained an international reputation for the manufacture of optical instruments of all kinds, and remains in business to this day, where the company might be most known for its broad selection of optical scopes and binoculars.

Publications[link]

• Auerbach, Das Zeisswerk und die Carl Zeiss-Stiftung in Jena (third edition, Jena, 1907)

See also[link]

• Calculation of glass properties - a significant contribution to the success of the companies Zeiss and Schott
• Optical Museum Jena

External links[link]

Wikimedia Commons has media related to: Carl Zeiss

• Carl Zeiss Biography
• Zeiss Company History Site
• Zeiss microscopes resource site
• First simple microscope made by Carl Zeiss in 1847/1848
• Early compound microscope made by Carl Zeiss