"JOURNAL OF RADIO ELECTRONICS" (Zhurnal Radioelektroniki ISSN 1684-1719, N 3, 2018

contents of issue       DOI  10.30898/1684-1719.2018.3.10      full text in Russian (pdf)    



A. S. Venetskiy

Kotelnikov Institute of Radioengineering and Electronics of Russian Academy of Sciences, Mokhovaya str. 11-7, Moscow 125009, Russia


The paper is received on March 20, 2018


Abstract. Two-mirror aplanatic systems are used in optical telescopes. These systems have no aberrations proportional to the first degree of displacement of the source from the focus. The two-mirror aplanatic systems have two free parameters that is not enough to minimize aberrations proportional to the second etc. powers of displacement of the source.  When using a three-mirror aplanatic system we have an additional degree of freedom due to the choice of the form of the third mirror. Therefore, it is interesting to construct the theory of aberrations for the case of three-mirror systems. For this purpose the new formula for the eikonal distribution on the output surface of the three-mirror system is derived in this paper.   The error of the formula is proportional to the fourth degree of displacement from the focus. The condition of absence of astigmatism on the axis of the system and at an arbitrary radius in the aperture is derived. The approximate equation of the focal curve is obtained. The accuracy of obtained formula for eikonal and its aberration in three-mirror system was verified.

Key words: three-mirror systems, aplanatic systems, aberrations, astigmatism.


1.     Mikhelson N.N. Optika astronomicheskih teleskopov i metody ee rascheta [Optics of radio-astronomical telescope and methods of its calculation]. Moscow, Fizmatlit Publ. 1995. 384p. (In Russian).

2.     Korsch D. Closed Form Solution for Three-Mirror Telescopes, Corrected for Spherical Aberration, Coma, Astigmatism and Field Curvature. Applied Optics, Vol.11, No.12, 1972.

3.     Venetskiy A.S., Kaloshin V.A. On Eikonal Distribution in the Aperture of a Two-Mirror Telescopic System, Journal of Communications Technology and Electronics, 2012, Vol.57, No.9, pp.1016-1023, DOI: 10.1134/S1064226912090124

4.     Venetskiy A.S., Kaloshin V.A.  Eikonal Aberration  in Planar Two-Reflector Antennas, Journal of Communications Technology and Electronics, 2014, Vol.59, No.11, pp.1102-1110. DOI: 10.1134/S106426914100088.

5.     Venetskiy A.S., Kaloshin V.A.  On Eikonal Aberrations  in Axisymmetric Double-Reflector Telescopic Systems, Journal of Communications Technology and Electronics, 2016, Vol.61, No.4, pp.385-394. DOI: 10.1134/S106426916040136.

6.     A. S. Venetskiy, V. A. Kaloshin, K. T. Nguyen, E. V. Frolova. Synthesis and study of ultra-wideband planar three-mirror system. Zhurnal Radioelektroniki - Journal of Radio Electronics. 2018. No. 1. Available at: http://jre.cplire.ru/jre/jan18/4/text.pdf.

7.     Head A.K. A Class of Aplanatic Optical Systems. Proc. Phys. Soc. LXXI, 4. pp.546-551.


For citation:

A. S. Venetskiy. Aberrations in three-mirror axisymmetrical aplanatic systems. Zhurnal Radioelektroniki - Journal of Radio Electronics. 2018. No. 3. Available at http://jre.cplire.ru/jre/mar18/13/text.pdf

DOI  10.30898/1684-1719.2018.3.10