Huygens eyepiece

The Huygens eyepiece was developed in the 17th century by the Dutch astronomer, mathematician and physicist Christiaan Huygens and is therefore one of the oldest lens systems . Huygens' optical calculations had shown that splitting the plano-convex single ocular lens into two single lenses, the color errors ( chromatic aberration ) in the near-axis area of the lens, as well as spherical aberrations and astigmatism , could be reduced.

Historical development

Christiaan Huygens began to be interested in the theory of lenses in 1653, whereupon his close brother Constantijn Huygens joined his project and together they learned the art of lens grinding in order to be able to manufacture lenses, lens systems and telescopes . The results of the ground lenses were initially good up to an excellent grinding technique, which at that time was already supported by machines.

Huygen's theory, which derived the rules for the relationship between the shape of the lens and the amount of aberration , was more than extraordinary in its day. This was the basis for the development of his lenses, lens systems and the associated telescopes and microscopes .

In 1662 Huygens succeeded in producing an eyepiece through innumerable practical attempts, of which he initially concluded in his notes, despite errors such as color fringes on the edge, that it could not be improved any further.

"We are giving here, if not the best combination of all lenses, which would take a long time to explore and might possibly be impossible, but one that experience has shown to be suitable."

From a theoretical point of view, he also approached the development of the eyepiece. In 1666 Huygens assumed that he had calculated the optimal combination of a convex lens together with a concave eyepiece in order to cancel out spherical aberrations . Huygens commissioned his brother to put his optical calculations into practice and to send him these ground lenses. However, the productions did not correspond to Christian Huygens' ideas, since despite supposedly correct calculations, aberrations disturbed the optical image. He did not question his theory of the manufactured lenses, but looked for the reason in the incorrect execution of the grinding by his brother and concluded on the basis of the failure.

Three years later, on February 1, 1669, he finally succeeded in configuring two lenses that canceled out the disturbing colors (spherical aberrations) and the so-called Huygensche eyepiece could be used in telescopes and microscopes.

construction

Huygens eyepiece

The Huygens eyepiece was made up of two plano-convex lenses made of the same type of glass, separated from each other by a layer of air. The flat sides of the lenses are directed towards the eye. The larger of the two lenses is called the field lens (or collective lens ), the smaller one is called the eye lens , which acts like a magnifying glass.

The chromatic magnification difference can be eliminated by a certain arrangement . This placement of the two lenses implies that the focal length of the field lens must be three times that of the eye lens and that the distance is twice the focal length of the eye lens. This eyepiece construction still had color fringes, but Christiaan Huygens succeeded with his construction to reduce the spherical aberrations, the astigmatism and the distortions. The Huygensche eyepiece can be described as the most important improvement of the eyepiece in the 17th century, partly supported by its use until today.

The focal plane lies between the lenses. If the lenses are made of material with identical refractive indices and the system is used as a telescope with one eye at rest for observation of an (almost) infinitely distant object, the ideal (lowest color error) distance of the lenses can be calculated as follows:

{\ displaystyle d = {\ frac {f_ {A} + f_ {B}} {2}}}

where and are the focal lengths of the two lenses. ${\ displaystyle f_ {A}}$ ${\ displaystyle f_ {B}}$

Usage today

The optical design of the Huygens eyepiece is now considered obsolete, as the eye has to be brought very close to the eyepiece . It also only allows a small field of view , has a high image distortion (especially with telescopes with a small focal length ) and still has residual color errors. Nevertheless, the eyepieces are still used in cheap telescopes and microscopes today, as the production is comparatively cheap. In optics, too, this lens system is still used as an example of a very simple, compound lens.

The greatest advantage of the Huygens eyepiece can be seen when observing the sun using the projection method . Because the individual lenses are not glued together, which is why the system can hardly be damaged even by intense sunlight. The main risk with other systems is that the cement between the lenses ( Canada balsam ) will overheat and then dissolve, form streaks or even start to burn.

A further development of the system is the Kellner eyepiece or the Mittenzwey eyepiece , which has two meniscuses (concave-convex) instead of the plano-convex lenses and thus has a larger field of view, which amounts to up to 50 °.

literature

Dijksterhuis, Fokko Jan: Huygens and the light of the 17th century, In: Bohlmann, Fink, Weiss (Hrsg.): Lichtgefüge des 17. Jahrhundert, Munich 2008.
Franke, Georg: Christian Huygens, In: Fassmann, Kurt (Ed.): The greats of world history, Zurich 1974.
Gerlach, Ernst (Ed.): Leibniz and Huygens correspondence with Papin. In addition to Papin's biography and some associated letters and files, Berlin 1881.
Gerlach, Dieter: History of microscopy. Frankfurt am Main 2009.
Huygens, Christian: Oeuvres Completes de Christian Huygens. Publièe par la socìetè Hollandaise des Science, Vol. 13.1 en La Dioptique, La Haye 1916.
Rienk, Vermij: Newton and Huygens, In: Mandelbrote, Pulte (Ed.): The Reception of Isaac Newton in Europe, London 2019.
Yoder, Joella: Unrolling time. Christian Huygens and the mathematization of nature, New York 1988.

Individual evidence

^ Georg Franke: Christian Huygens . In: Kurt Fassmann (Ed.): The greats of world history . Zurich 1974, p. 997-1013 .
↑ Fokko Jan Dijksterhuis: Huygens and the light of the 17th century . In: Bohlmann, Fink, Weiss (ed.): Light structure of the 17th century . Munich 2008, p. 59-77 .
^ Christian Huygens: Oeuvres Completes de Christian Huygens . In: Hollandaise des Science (ed.): La Dioptique . tape 13.1 . La Haye 1916.
↑ Fokko Jan Dijksterhuis: Huygens and the light of the 17th century . In: Bohlmann, Fink, Weiss (ed.): Light structure of the 17th century . Munich 2008, p. 59-77 .
↑ Dieter Gerlach: History of microscopy . Frankfurt am Main 2009, p. 118-119 .

[1] Georg Franke: Christian Huygens . In: Kurt Fassmann (Ed.): The greats of world history . Zurich 1974, p. 997-1013 .

[2] Fokko Jan Dijksterhuis: Huygens and the light of the 17th century . In: Bohlmann, Fink, Weiss (ed.): Light structure of the 17th century . Munich 2008, p. 59-77 .

[3] Christian Huygens: Oeuvres Completes de Christian Huygens . In: Hollandaise des Science (ed.): La Dioptique . tape 13.1 . La Haye 1916.

[4] Fokko Jan Dijksterhuis: Huygens and the light of the 17th century . In: Bohlmann, Fink, Weiss (ed.): Light structure of the 17th century . Munich 2008, p. 59-77 .

[5] Dieter Gerlach: History of microscopy . Frankfurt am Main 2009, p. 118-119 .