[OPTICAL REVIEW Vol. 12, No. 3 (2005) 190-195]

© 2005 The Optical Society of Japan

## A Variation of Schwarzschild Telescope: Golden Section Solution with Two Concentric Spheres and Its Extension to Finite Distance Solutions

Kyoji NARIAI^{*} and Hiroshi IWAMOTO^{†}

Department of Science and Technology, Meisei University, Hodokubo 2-1-1, Hino, Tokyo 191-8588, Japan

(Received October 7, 2004; Accepted December 6, 2004)

Imaging by two concentric spheres is studied by geometrical method. As the system is symmetric with respect to the common center of curvature, peripheral aberrations, namely coma, astigmatism, and distortion, do not appear. The imaging surface is a sphere that shares the center of curvature with two mirrors. As we solve the zero spherical aberration condition for imaging of an object at infinite distance, the golden section number appears as the ratio of the distance between two mirrors and the radius of the primary mirror. For imaging of an object at finite distance, we have to increase the radius of the second mirror. This system also has no peripheral aberrations. Making the object surface spherical, we can obtain a flat image surface. As the spherical aberration is zero in the original system, spherical aberration, coma, and astigmatism remain zero when the object surface is curved.

Key words: schwarzschild telescope, golden section number, concentric spheres, anastigmat, finite distance imaging, flat imaging field

^{*}E-mail address: nariai.kyoji@phys.meisei-u.ac.jp

^{†}E-mail address: 01s1009@stu.meisei-u.ac.jp