Appendix A Annotated Biography of Key Publications Relevant to Abbe’s Beiträge 1873 A.1 Introduction This appendix supplements the material contained in Chapter 6. It contains further explanations and insights into Abbe’s seminal theory with contributions from his coworkers, colleagues, and people who attended his university lectures in Jena. In Chapter 7 I discussed the independent theoretical and experimental investi- gations of Helmholtz, Rayleigh, and Porter. Each investigator published detailed theoretical analyses of image formation in the light microscope and independently derived an equation for the limiting resolution of a light microscope due to diffraction. They independently confirmed Abbe’s seminal paper of 1873 titled “Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung.” Abbe’s paper was long, difficult to understand, and completely devoid of figures and mathematical equations. Abbe promised a second paper, complete with mathematical derivations; however, he died before completing this task. This appendix reviews the published works that followed Abbe’s seminal publication of 1873. Many of these articles were written by Abbe’s colleagues at Zeiss Werke, some were based on Abbe’s notes from his mathematical lectures at Jena University. Other contributions appeared in handbooks and textbooks of optics and microscopy. Some of these were very popular and were published in several editions. My selection includes contributions that were published after 1873 and continues with others published after Abbe’s death in 1905. This selection includes eight publications in German and one in English. George Biddell Airy was Astronomer Royal and Professor of Astronomy and Experimental Philosophy at the University of Cambridge. Abbe held a deep interest in astronomy and from 1877 to 1900 was Director of the Jena Observatory. Furthermore, Abbe was also fluent in English. Thus, it is likely that Abbe was familiar with Airy’s publications. © Springer Nature Switzerland AG 2020 379 B. R. Masters, Superresolution Optical Microscopy, Springer Series in Optical Sciences 227, https://doi.org/10.1007/978-3-030-21691-7 380 Appendix A: Annotated Biography of Key … I summarize two of these publications here; one a paper on diffraction and the other a textbook (Airy, 1835, 1866). In 1835 Airy developed his formula for the diffraction pattern, called the Airy disk, which is the image of a point source of light in an aberration-free optical system (Airy, 1835). What did Airy achieve in his publication? Airy derived the mathematical equation for the diffraction pattern from a distant star, or another point source of light that is imaged by a circular lens. The result of his analysis showed that the point source of light was not imaged as a point but as a bright disk with a series of bright rings around it. The special case of the Fraunhofer diffraction of a circular aperture is given an eponymous name: the Airy pattern (Airy, 1835). Perusal of his publication demonstrates his lucid writing style. What conclusions did Airy draw from his analysis? Beside the seminal fact that a point source of light is imaged as a bright disk with surrounding bright rings Airy calculated the positions of the rings. Furthermore, Airy noted that his calculations were in good agreement with observations (Airy, 1835). How is Airy’s seminal work related to image formation in the light microscope? In the light microscope the aperture of the microscope’s objective is what causes the diffraction effects. A point source of light in the microscope results in a diffraction pattern in the diffraction plane of the microscope’s objective. Next, I discuss Airy’s book titled “Treatise on Undulatory Optics, Designed for Students in the University.” The first edition was published in 1831 and the second edition in 1866. Airy presents his ideas as a series of propositions together with their mathematical formulation, derivations, and proofs. Then he presents specific cases that can be tested against experiments. The results of such experiments can then be compared with theory. A.2 Contribution of Nägeli and Schwendener, Das Mikroskop, Theorie und Anwendung desselben (The Microscope, Theory and Applications) (1867, 1877) Carl Nägeli and Simon Schwendener published the first edition of their classic book in 1867, publishing a second edition in 1877 (Nägeli and Schwendener, 1867, 1877). Carl Nägeli was a student of the botanist Matthias Schleiden. Schleiden motivated Carl Zeiss to start production of optical microscopes in his Jena shop. Simon Schwendener was a student of Nägeli. Working together in Jena they wrote a book titled Das Mikroskop, Theorie und Anwendung desselben. The complete book was published in 1867 and was a milestone as it contained a unique and very comprehensive discussion of microscope optics. In support of this claim I list some of the topics from the first edition’s table of contents: Theory of Microscopes; The Cardinal Points of Microscopes; Chromatic and Spherical Aberrations; Illumination with Transmitted (durchfallendem Licht) and Reflected Light (auffallendem Licht); Oblique Illumination; Testing of Microscopes for Appendix A: Annotated Biography of Key … 381 Aberrations, Angular Aperture, Magnification, and Focal Length; Performance of Microscopes; The Relation between Focal Length and Aperture Angle; Interference in the Microscope; and Definition of “Defining Power” and “Penetrating Power” (Nägeli and Schwendener, 1867). Many of these terms are discussed in Abbe’s seminal publication (Abbe, 1873). I found it very instructive to read the first edition of Das Mikroskop (1867), then Abbe’s seminal paper (1873), and finally the second edition of Das Mikroskop (1877). The first edition gives the reader a comprehensive overview of state-of-the-art light microscopes up to 1867; the second edition augments the comprehensive content with a section (without any mathematical proofs or derivations) on Abbe’s theory of image formation in the light microscope based on diffraction. Nägeli and Schwendener’s second edition of Das Mikroskop contained a 10-page section that discussed Abbe’s 1873 paper on the theory of image for- mation in the optical microscope (Nägeli and Schwendener, 1877). In great contrast to Abbe’s 1873 publication the second edition of their book had both figures and mathematical equations, making Abbe’s theory of image formation in the micro- scope comprehensible to a wide audience. Unfortunately, the authors did not dis- cuss the important experiments that Abbe carefully described in his 1873 publication. A.3 Contribution of Leopold Dippel, Das Mikroskop und Seine Anwendung, Second Edition (The Microscope and Its Applications) (1882) The next book that I discuss is Dippel’s Das Mikroskop und seine Anwendung, which was part of the Handbuch der Allegemeiner Mikroskopie, Zweite Auflage and published in 1882. Leopold Dippel was a friend of Abbe. He was writing a new textbook on the theory of the microscope and contacted Abbe to determine whether Abbe could help him with his book. Subsequently, Abbe sent Dippel several chapters on geometric optics and physical optics; the text was almost completely written by Abbe (Feffer, 1994). Most of Abbe’s manuscript discussed various types of geometric and chromatic optical aberrations. In addition, Abbe wrote about his theory of what was subsequently called the Abbe Sine Condition. More importantly, Abbe included unpublished material from both theory and experiments that supported his theory of image formation in the light microscope based on light diffraction. For those who cannot read German I explain some terms here. The German words Diffraktion and Beugung both translate into the English word diffraction. The German word for refraction is Brechung. How did Abbe’s manuscript, sent to Dippel for incorporation into Dippel’s Das Mikroskop, compare with Abbe’s 1873 publication? There were significant differ- ences. Abbe’s 1873 publication was only text—there were no figures or equations in the publication. However, in his submission to Dippel Abbe included a detailed description of his experiments; he provided details of the structure of the 382 Appendix A: Annotated Biography of Key … Diffraktionsplatte (test slide) that had various ruled lines with different interline spaces, and a description of the resulting diffraction pattern that he observed in the back focal plane of the microscope’s objective. A.4 Contribution of Siegfried Czapski, Theorie der Optischen Instrumente nach Abbe (Theory of Optical Instruments after Abbe) (1893) Siegfried Czapski (1861–1907) studied physics in Berlin with Hermann von Helmholtz and Gustav Robert Kirchhoff. After completing his studies Czapski began to work in Jena at the Carl Zeiss optic works. Many years later he became the director of the Zeiss factory, a position previously held by Abbe. In 1893 Czapski published the first edition of his major work that became a classic in the field of optical design titled Theorie der Optischen Instrumente nach Abbe. Although Czapski frequently cited Abbe throughout the book there is still one outstanding omission. While Czapski offered a concise, yet qualitative description of Abbe’s theory of image formation in the light microscope based on light diffraction, there was no mathematical derivation of Abbe’s theory of microscopic image formation. In 1894 Czapski published “Die künstliche Erweiterung der Abbildungsgrenzen” (Theory of Spherical Aberration) in the Handbuch der Physik, 2, 96. This publication has historical significance because