Kepler also made fundamental contributions to optics and mathematics. In 1604, he published the Supplement to Witelo, by which the Optical Part of Astronomy is Handed on. Witelo (13th century) had composed a text titled The Perspective which, together with The Common Perspective by John Peckham (c. 1232-1292), were the most important medieval treatises on optics. Kepler's work ? much more then a "supplement' to Witelo's one ? laid the foundations of modern geometrical optics.
In a later work, the Dioptrics published in 1611, Kepler explained the optical principles of the telescope, a new instrument with which Galileo had recently accomplished his extraordinary discoveries. In the Dioptrics, Kepler introduced a new kind of eyepiece formed by a convergent (biconvex or plano-convex) lens. The "Galileian" telescope, whose eyepiece consists of a divergent (biconcave or plano-concave) lens, produces erect images, but its field of view is very limited. In contrast, the "Keplerian" (or "astronomical") telescope produces upside down images, but its field of view is much larger and brighter. Within a few decades, this new configuration completely replaced the Galileian one.