Ernst Karl Abbe (23 January 1840 – 14 January 1905) was a German businessman, optical engineer, physicist, and social reformer. He worked with Otto Schott and Carl Zeiss to create many optical tools. Abbe was also a co-owner of Carl Zeiss AG, a German company that makes scientific microscopes, astronomical telescopes, planetariums, and other optical equipment.

Personal life

Abbe was born on January 23, 1840, in Eisenach, Saxe-Weimar-Eisenach, to Georg Adam Abbe and Elisabeth Christina Barchfeldt. He came from a simple family. His father worked as a supervisor in a textile factory. With the help of his father's employer, Abbe attended secondary school and earned the qualification needed to enter university. He graduated from the Eisenach Gymnasium in 1857 with good grades. By the time he left school, his interest in science and determination were already clear. Despite the family's financial difficulties, his father supported Abbe's studies at the Universities of Jena (1857–1859) and Göttingen (1859–1861). While studying, Abbe gave private lessons to earn money. His father's employer continued to support him financially. Abbe was awarded his PhD in Göttingen on March 23, 1861. During his studies, he was influenced by Bernhard Riemann and Wilhelm Eduard Weber, who were part of the Göttingen Seven. After earning his doctorate, Abbe worked briefly at the Göttingen observatory and at the Physikalischer Verein in Frankfurt. The Physikalischer Verein was founded in 1824 by Johann Wolfgang von Goethe and still exists today. On August 8, 1863, he qualified as a university lecturer at the University of Jena. In 1870, he became an associate professor of experimental physics, mechanics, and mathematics at the University of Jena. In 1871, he married Else Snell, the daughter of Karl Snell, a mathematician and physicist who had taught Abbe. They had two daughters. He attained full professor status by 1879. In 1878, he became the director of the Jena observatory for studying the sky and weather. In 1

Life work

In 1866, he became a research director at the Zeiss Optical Works. In 1868, he invented the apochromatic lens, a microscope lens that reduces color distortion from two main sources. By 1870, he created the Abbe condenser, a tool used to illuminate microscopes. In 1871, he designed the first refractometer, which he explained in a booklet published in 1874. By 1872, he developed the laws of image formation for non-luminous objects. Zeiss Optical Works began selling his improved microscopes in 1872. By 1877, they offered models with homogenous immersion objectives, and by 1886, they sold microscopes with apochromatic objectives. He created the Abbe number, a measure of how refractive index changes with wavelength in transparent materials. He also developed Abbe's criterion, a method to test if a pattern exists in a set of observations. At the time, he was already a professor in Jena and was hired by Carl Zeiss to improve the manufacturing process of optical instruments, which previously relied heavily on trial and error.

Abbe was the first to define the term numerical aperture, which is calculated as the sine of the half angle multiplied by the refractive index of the medium between the cover glass and the front lens.

Many credit Abbe with discovering the resolution limit of the microscope, and he published a formula in 1873. However, a 1874 publication by Helmholtz noted that this formula was first derived by Joseph Louis Lagrange, who had died 61 years earlier. Helmholtz was so impressed by Abbe’s work that he offered him a professorship at the University of Berlin, which Abbe declined due to his connection with Zeiss. Abbe supported the idea that microscopic resolution is limited by the aperture of the optics but also believed other factors could be more important in some applications. In his 1874 paper titled "A Contribution to the Theory of the Microscope and the Nature of Microscopic Vision," Abbe stated that microscope resolution depends inversely on its aperture but did not propose a formula for the resolution limit.

In 1876, Abbe was offered a partnership by Zeiss and began sharing in the company’s profits. Although others had previously published theoretical derivations of a key equation, Abbe was the first to confirm it experimentally. In 1878, he built the first homogenous immersion system for microscopes. The objectives produced by Abbe and Zeiss had ideal light paths, allowing Abbe to determine that the aperture, not lens shape or placement, sets the upper limit of microscopic resolution. Abbe first published the equation in 1882, stating that both his theory and experiments supported it. His contemporary, Henry Edward Fripp, an English translator of Abbe’s and Helmholtz’s works, viewed their contributions as equally important. Abbe also improved the interference method developed by Fizeau in 1884. In 1884, Abbe, Zeiss, Zeiss’s son, Roderich Zeiss, and Otto Schott formed the Jenaer Glaswerk Schott & Genossen. This company later merged with Zeiss Optical Works and produced 44 types of optical glass. In 1895, he built an image reversal system for telescopes.

To create high-quality microscope objectives, Abbe contributed to diagnosing and correcting optical errors, such as spherical aberration and coma aberration, which are necessary to reach the resolution limit defined by the equation. He also discovered that light rays in optical systems must maintain constant angular magnification across their distribution to form a diffraction-limited spot, a principle known as the Abbe sine condition. His work was so influential that Frits Zernike used it as a basis for his phase contrast technique, which earned him a Nobel Prize in 1953. Hans Busch also used Abbe’s findings in developing the electron microscope.

During his time with Carl Zeiss’s microscope company, Abbe was a leader in optics and also promoted labor reforms. In 1890, he founded the social democratic newspaper Jenaische Zeitung. In 1900, he introduced the eight-hour workday, inspired by his father’s 14-hour workday. He also created a pension fund and a compensation fund for employees. In 1889, he established the Carl Zeiss Foundation to support scientific research and improve employee job security. He emphasized that success should depend only on ability and performance, not on origin, religion, or political views. In 1896, he reorganized Zeiss Optical Works into a cooperative with profit-sharing. His social ideas were so respected that the Prussian government used them as a model, and Alfred Weber later praised them in a 1947 book.

A crater on the Moon, named Abbe, honors his legacy.