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ISSN: 1023-5086


ISSN: 1023-5086

Scientific and technical

Opticheskii Zhurnal

A full-text English translation of the journal is published by Optica Publishing Group under the title “Journal of Optical Technology”

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DOI: 10.17586/1023-5086-2024-91-04-60-72

УДК: 520.2.01/.07; 535.313.1; 535.313.2

Optical system of aplanatic telescope with spherical primary mirror

For Russian citation (Opticheskii Zhurnal):

Дружин В.В., Пуряев Д.Т. Оптическая система апланатического телескопа с главным сферическим зеркалом // Оптический журнал. 2024. Т. 91. № 4. С. 60–72.


Druzhin V.V., Puryaev D.T. Optical system of aplanatic telescope with spherical primary mirror [in Russian] // Opticheskii Zhurnal. 2024. V. 91. № 4. P. 60–72.

For citation (Journal of Optical Technology):

The subject of study is the optical system of the telescope with a main spherical mirror and a mirror corrector of field aberrations. The aim of study is the description of the method of analytical calculation of the telescope system with main spherical mirror and two-mirror aplanatic corrector of spherical mirror aberrations. The method of carrying out the work is based on the analysis of realization of Fermat principle and the Abbe sine condition in the system consisting of a combination of a spherical surface and nonspherical surface of second order. The main results are the proposed mathematical equations for the mirror surface of the aplanatic system with the spherical primary mirror and two element corrector of field aberrations. The corrector contains two concave hyperbolic mirrors placed near the paraxial focus of the spherical mirror. The focal length of the telescope is equal to the paraxial focal length of the primary mirror. The results of the calculation of two variants of optical schemes of the telescope with the following values of the diameter of the entrance pupil, aperture f-number and angular field: 1) D = 6000 mm, F-no = 4, 2w = 0,12°; 2) D = 500 мм, F-no = 2 and 2w = 0,57° are demonstrated. Practical significance. Application of the spherical mirror in telescopes makes it possible to increase the accuracy of control of the shape of the surface of telescope segments during the manufacture and operation. The compact all-mirror corrector provides the operation in a wide spectral range and corrects the spherical aberration and coma, and thus allows to increase the relative aperture of the system, angular field and image quality.


ground-based telescopes, space telescopes, mirror system design, large observatories, aspherics, mirrors

OCIS codes: 110.6770, 080.4035, 220.1000, 220.2740

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