Gullstrand, Allvar

(b. Landskrona, Sweden, 5 June 1862; d. Uppsala, Sweden, 21 July 1930)

ophthalmology, geometrical optics.

Allvar Gullstrand was the son of a prominent physician who was city physician of Landskrona. Under the influence of his father he began the study of medicine in 1880 and soon specialized in physiological optics. He studied in Uppsala, Vienna, and Stockholm. He finished his medical studies in 1884 and obtained the license to practice medicine in 1888. After receiving his doctorate in 1890, he was appointed in 1892 as lecturer at the Royal Caroline Institute. At the same time he worked as chief physician at an ophthalmological clinic and in 1892 was appointed head of the eye clinic in Stockholm.

In 1894 Gullstrand became professor of ophthalmology at the University of Uppsala, where he received an honorary degree in 1907. Six years later, the university created a special chair for him, without teaching obligations, in physiological and physical optics. Gullstrand also received an honorary degree from the University of Jena, and in 1911 from the University of Dublin. That same year, the Nobel Prize in physiology or medicine was awarded to him for his investigations of the dioptrics of the eye.

Allvar Gullstrand’s greatest achievements lie in the field of ophthalmological optics, the study of the human eye as an optical system. This study engendered his interest in geometrical optics. He then drew the attention of the optical designers to several misconceptions and so made important contributions to this field as well.

Gullstrand started his work in ophthalmology with a paper on the astigmatism of the cornea. He became interested in the accommodation mechanism of the human eye and in an exact theory discussed the influence which the layers of the crystalline lens play. This was a difficult mathematical problem which had not been attacked in detail before. It led to the conception of a new and more accurate model of the human eye, a big step beyond Helmholtz. This is described in Gullstrand’s masterly commentaries on the occasion of his reediting Helmholtz’ Handbook of Physiological Optics. These commentaries contain by far the clearest and best description of all of Gullstrand’s ideas on geometrical and physiological optics.

Gullstrand invented a slit lamp, which, in combination with a microscope, allowed him to locate exactly a foreign body in the eye with respect to all three dimensions. He designed aspheric lenses for aphakic eyes, that is, eyes from which the lens has been removed as a result of cataracts. He investigated the effect of the rotation of the eye around the fulcrum, and through his friendship with M. von Rohr many of his ideas led to the construction of optical instruments, particularly the great Gullstrand ophthalmoscope, which was manufactured by Zeiss.

In the field of geometrical optics Gullstrand wrote many extensive papers that went beyond the frontiers of optical knowledge for his time. He developed the theory of the fourth-order aberration of a general optical ray, independent of the axis of a rotational symmetry system. Especially, he made contributions to the knowledge of umbilic points, that is, points in which the two principal curvatures are the same. He then investigated how the characteristic quantities of general bundles change with refraction, thus obtaining what he called the system laws of optical systems. But Gullstrand did not restrict himself solely to the consideration of spherical surfaces; one of his longest papers deals with the construction and tracing through of aspheric surfaces.

Unacquainted with the work of H. R. Hamilton, he solved difficult mathematical problems simply by developing the necessary quantities in a series around the coordinates of the principal ray. He considered mathematical methods, such as the calculus of variation and vector methods, to be false ornaments. This prejudice makes his papers long and clumsy, but they contain a number of valuable and little-known results. H. Boegehold, C. W. Oseen, and the writer have endeavored to give simpler derivations of his beautiful results. However, there are limitations to his method. In the case of a branch point, for example, the series development does not work.

Gullstrand was a fighter, discovering several inaccuracies in the normal treatment of optical problems; he spent much of his time studying these inaccuracies, which were mostly a result of approximate pictures being applied to describe finite realities. For instance, the Sturm conoid described an astigmatic bundle as a bundle of rays going through two straight lines perpendicular to each other and to the principal ray. Gullstrand showed that such a manifold bundle of rays is not a normal system, that is, it cannot originate from an object point. Another fallacy was that the collinear image formation, which is the coordination of lines in object and image space such that the rays from any object point unite in a fixed image point, could not have been taken as an approximation to the real image formation, because the former cannot be obtained by optical means (with the trivial exception of the plane mirror). Unfortunately, books are still published disregarding these simple truths.

Gullstrand represents a scientist of very rigorous standards, and as such, he was highly respected by his peers for his intelligence and integrity. His advice was widely sought, even outside his special sphere of interest; among other honors, he was a member and late president of the Nobel Prize committee.

BIBLIOGRAPHY

I. Original Works. Gullstrand’s works include “Objektive Differential-Diagnostik und photographische Abbildung von Augenmuskellahmungen,” in Kungliga Svenska vetenskapsakademiens handllingar, 18 (1892); “Allgemeine Theorie der monochromatischen Aberrationen und ihre nächesten Ergebnisse für die Ophthalmologie,” in Nova acta Regiae Societatis scientiarum upsaliensis (1900); “Die Farbe der Macula centralis retinae,” in Archiv für Ophthalmologie, 62 (1905), 1–72, 378; “Die reelle optische Abbildung,” in Kungliga Svenska vetenskapsakademiens handlingar, 41 (1906), 1–119; “Tatsachen und Fiktionen in der Lehre von der optischen Abbildung,” in Archiv für Optik (1907), 1–41, 81–97; and “Abbildung in heterogenen Medien und die Dioptrik der Kristallinse des Menschen,” in Kungliga Svenska vetenskapskademiens handlingar, 43 (1908), 1–58.

See also Eingührung in die Methoden der Dioptrik des Auges des Menschen (Leipzig, 1911); “Die reflexlose Ophthalmoskopie,” in Archiv für Augenheikunde, 68 (1911), 101–144; “Das allgemeine optische Abbildungs sysytem,” in Kungliga Svenska vetenskapsakademiens handlingar, 55 (1915), 1–139; “Ueber aspharische Flächen in optischen Instrumenten,” ibid., 60 (1919), 1–155; “Optische Systemsgesetze zweiter und dritter Ordnung,” ibid., 63 (1924), 1–175; and “Engiges über optische Bilder,” in Naturwissenschaften, 14 (1926), 653–664.

II. Secondary Literature. For information about Gullstrand and his work see H. Boegehold, “Uber die Entwicklung der Theorie der optischen Instrumente seit Abbe,” in Ergebnisse der exakten Naturwissenschaften, 8 (1929), 1–146; M. Herzberger, “Allvar Gullstrand,” in Optica acta, 3 (1960), 237–241; J. W. Nordenson, “Allvar Gullstrand,” in Klinische Monatsblatter für Augenheilkunde, pp. 560–566; C. W. Oseen, “Allvar Gullstrand,” in Kungliga Svenska vetenskapsakademiens arsbok, (1937); “Une méthode nouvelle de l’optique géometrique,” in Kungliga Svenska vetenskapsakademiens handlingar, 3 (1936), 1–41; and M. von Rohr, “Allvar Gullstrand,” in Zeitschrift für ophthalmologische Optik, 18 (1930), 129–134.

Maximilian J. Herzberger