“Be good, be true, be just ... and remain true to yourself.” — Motto of Abbe’s life from the funeral speech of Siegfried Czapski 18 | OPN February 2007 www.osa-opn.org Ernst Abbe and the Foundation of Scientific Microscopes Barry R. Masters Last year marked the 100th anniversary of the death of Ernst Abbe, who passed away on January 14, 1906—just a few days short of his 65th birthday. Abbe is well known for his seminal contributions to scientific microscope construction, which include his diffraction theory for image formation, and the formulation of the sine condition and Abbe number. He was also a noted entrepreneur, astronomer and social reformer. rnst Abbe was born in Eisenach, Germany, on Abbe remained in Göttingen for his doctoral research under January 23, 1840. He spent his childhood in the supervision of two professors: Wilhelm Eduard Weber and poverty—which perhaps explains why he was com- Karl Snell. His doctoral thesis focused on experimental substan- Emitted to social welfare for the rest of his life. After graduating tiation of the theorem of the mechanical equivalence between from secondary school, he began his studies at the University of heat and mechanical energy. He received his doctoral degree in Jena. There, Abbe attended lectures in mathematics and physics. 1861. One year later, he submitted research on the laws of the Early on, his professors noted his acumen in science. Abbe distribution of errors in an observation series to the philosophy won a scientific competition in his third semester and, later, he faculty at the University of Jena for his Habilitation paper (a was awarded a scholarship by city officials at Eisenach. After German post-doctoral requirement for teaching as a professor at completing two years at Jena, Abbe took up three additional a university). years of studies at the University of Göttingen, where he at- Over the next 10 years, Abbe published several scientific tended lectures in mathematics given by Bernhard Reimann, as papers and was subsequently appointed as a lecturer of astron- well as lectures in meterology, optics and astronomy. omy in 1877 at the University of Jena. In addition, Abbe was At Göttingen, Abbe studied the theory and practice of made the director of the observatory at the University of Jena precision measurements (i.e., the assessment of extremely weak (1877-1900). electric currents and magnetic fields) as well as the design In 1866, Abbe met Carl Zeiss, who proposed that Abbe and construction of measuring instruments and the theory of establish a scientific foundation for the manufacture of optical experimental error. microscopes. Zeiss had begun his production of single-lens Historical Zeiss-Archive, Carl Zeiss Jena GmbH Historical Zeiss-Archive, OPN February 2007 | 19 1047-6938/07/02/0019/6-$15.00 ©OSA dissecting microscopes in Jena in 1847 after Mat- ously possible. Simultaneously, Abbe worked on his thias Schleiden—a German botanist and co-founder theoretical calculations. He designed and performed of the cell theory—suggested that he get into that practical demonstrations that verified as well as line of business. made his theory of microscope image formations Using lenses purchased from other manufactur- based on diffraction theory clear to a wide audience. ers, Zeiss had fabricated in 1857 the first compound The important result for microscope objec- microscope consisting of a microscope objective and tive design and production, was that—for the first an ocular. At that time, lenses were ground and com- time—the theoretical optical basis for microscope binations were tested for their optical performance; design had matched the theoretical foundations that there was no scientific basis for the design of high were used in telescope lens design. That was a major quality lenses. The historical method of lens grind- milestone because the production of microscope ing, testing and selection was about to change. objectives and other microscope optical components The 26-year-old Abbe started work for Carl had previously been a trial-and-error process. Zeiss as an independent contractor. Over the next The next step was to improve the glass that was few years, Abbe developed several precision opti- used in the manufacture of lenses—which required cal instruments to measure the shape and optical the manufacture of new types of optical glasses with constants of lenses. Abbe’s focometer measured the the correct dispersion (change of refractive index focal lengths of lens elements, lens combinations or with frequency of the light). With the acquisition a complete optical system. The Abbe refractometer of the Schott glass works, this became a reality. By measured the refractive index of glasses or liquids 1884, Abbe, Otto School and Carl and Roderich based on the angle of total reflection. The Abbe Zeiss (the son of Carl Zeiss) joined forces in Jena spectrometer measured the refractive index and and formed the company that today is Schott. dispersion of various glasses. In 1870, Abbe devel- The success of the Zeiss and Schott factories In 1866, Abbe met Carl Zeiss, who proposed that Abbe establish a scientific foundation for the manufacture of optical microscopes. Zeiss had begun his production of single-lens dissecting microscopes in Jena in 1847 after Matthias Schleiden—a German botanist and co-founder of the cell theory—suggested that he get into that line of business. oped his apertometer, which measured the numerical aperture in the subsequent years was in large part based on the “Fraun- of microscope objectives. hofer method,” which includes: (1) the development and Microscope design followed in the footsteps of the Keplerian perfection of manufacturing methods; (2) the mathematical for- telescope, and multi-lens oculars were rapidly adapted from mulation of the fundamental theories; and (3) the improvement those of telescopes from Ramsden and Huygens. Another key of the raw materials (in this case glass). Fraunhofer produced a example is the problem of chromatic aberration, which was series of telescope objectives from his secret recipes for special solved by Isaac Newton in his reflecting telescopes that incorpo- glasses; however, when he attempted to construct microscope rated a concave mirror in place of a lens. Soon afterward came objectives, he failed to achieve the same achromatic qualities the development of reflecting microscopes. that characterized his telescope objectives. Abbe eventually became a co-owner of the firms Zeiss and It was Fraunhofer who worked on the problem of minimiz- Schott. He did not accept any salary for his work as the direc- ing chromatic aberrations in optical systems through the devel- tor of the observatory and as a university teacher so that less opment of new types of glasses. Fraunhofer developed a method fortunate staff members could benefit from the funds. A major to measure the refractive indices of glasses and used the dark breakthrough for Abbe as well as the Zeiss factory was the 1870 lines of the solar spectrum for calibrating the lines. Later, he formulation of the Abbe sine condition, which determines the developed a diffraction grating to directly measure the frequen- design of a spherically corrected lens that is free from coma (an cies of the spectral lines. optical aberration). Abbe is also respected for his pioneering work to improve By 1871, Abbe had completed his calculations for the design workplace conditions at the Zeiss factories. Beginning in 1887, of microscope objectives, and, in 1872, these calculations he helped to implement several innovative reforms that employ- permitted the Zeiss factory to manufacture water immersion ees today take for granted: a pension fund for staff and their microscope objectives of much higher quality than was previ- dependents, an eight-hour work day, paid vacations, a company 20 | OPN February 2007 www.osa-opn.org health insurance plan, sick pay and company Abbe addressed this issue by designing lenses regulations to prohibit discrimination due to with minimum off-axis aberrations with his ethnicity, religion or political affiliation. theoretical conception of the Abbe sine condi- In 1889, Abbe set up the Carl Zeiss tion. The light from two point stars is incoher- Foundation as the sole owner of the Zeiss ent, whereas, in a microscope, the light from the and Schott factories. The Foundation’s rules object is coherent or partially coherent and thus stipulated that the university and the city can interfere. of Jena should benefit from the profits. The At first, Abbe calculated the image of a point city responded by awarding Abbe an honor- on the optical axis in the image space from the ary doctoral degree from Jena in 1896. At corresponding point on axis in object space. Fürstengraben, the University of Jena erected Then, he realized that there must be a constant a memorial to Abbe consisting of a stone magnification for all points on the surface of an globe, on which the Abbe resolution formula object that slightly extends from the optical axis. for oblique illumination is carved. Finally, he deduced the mathematical relation- From about 1890, the Carl Zeiss Founda- ship between the bundle of rays from an object tion began to manufacture a wide range and the bundle of rays on the image side of a of optical instruments in addition to their lens. line of optical microscopes: optical measur- For conjugate points (i.e., the same points in ing instruments, camera lenses, binoculars, the object and in the image), Abbe found that astronomical instruments and photometric the ratio of the sines of the two angles of the instruments. Abbe laid the scientific founda- bundle of rays in object space and in image space tion for the design, manufacture and testing (on the two sides of a lens) must be a constant of these optical systems. over the full aperture of the optical system.