DOI: 10.17586/2226-1494-2016-16-2-224-236


K. V. Ezhova, V. A. Zverev, T. V. Tochilina

Read the full article 
Article in Russian

For citation: Ezhova K.V., Zverev V.A., Tochilina T.V. Concentric lens systems. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2016, vol. 16, no. 2, pp. 224–236. doi:10.17586/2226-1494-2016-16-2-224-236


Subject of Research. The paper discusses theoretical foundations of synthesis of concentric lens systems for various applications based on the 3rd order aberration theory. The main difference of concentric lens systems, in addition to the special geometry of the system, is an image spherical surface shape with the radius equal to the focal length of the entire system. For such optical systems compensation is required not only of corner spherical aberration, but also of chromaticity position. Method. The paper presented mathematical apparatus that allows determining the design parameters of the concentric lens systems. The coefficients were introduced determining interrelationship of the radii of curvature for the surfaces of concentric optical systems that gave the possibility to transform the obtained analytical relations in the system of two equations with two unknowns. It is shown that the existence of solutions of the system is determined by the optical constants of the selected lens material. Main Results. The results of correction conditions analysis of the chromatic aberration of position and the sequence of the resulting system of equations have provided theoretical basis for the engineering method of a parametric synthesis of concentric lens systems and developed a mathematical model for the calculation of such systems. Practical Relevance. The undoubted practical significance of the work lies in the examples of specific systems calculation with different possible designs of construction and defining the angular spherical aberration and chromatic aberration of position calculated for each system.

Keywords: system of concentric surfaces, spherical aberration, chromatic aberration of position, primary aberrations


1. Zverev V.A., Kovaleva A.S., Timoshchuk I.N. Analysis and parametric synthesis of the optical systems of a mirror–lens concentric objective. Journal of Optical Technology, 2012, vol. 79, no. 1, pp. 1–5. doi: 10.1364/JOT.79.000001
2. Popov G.M. Kontsentricheskie Opticheskie Sistemy i ikh Primenenie v Opticheskom Priborostroenii [Concentric Optical Systems and their Application in an Optical Instrument Making]. Moscow, Nauka Publ., 1969, 135 p.
3. Mahajan V.N. Aberration Theory Made Simple. 2nd ed. SPIE Press, 2011, 208 p.
4. Ezhova K.V., Zverev V.A., Van Luen N. Aberrational properties of a thin component as the basic element in a variable magnification optical system. Journal of Optical Technology, 2013, vol. 80, no. 12, pp. 738–740. doi: 10.1364/JOT.80.000738
5. Kovaleva A.S. Calculating method for design of concentric mirror, mirror-lens, and lens systems. Journal of Instrument Engineering, 2013, vol. 56, no. 11, pp. 55–61.
6. Rusinov M. Tekhnicheskaya Optika [Technical Optics]. 2nd ed. St. Petersburg, Librokom Pibl., 2011, 487 p.
7. Grammatin A.P., Romanova G.E., Balatsenko O.N. Raschet i Avtomatizatsiya Proektirovaniya Opticheskikh Sistem [Calculation and Automation of the Design of Optical Systems]. St. Petersburg, NRU ITMO, 2013, 128 p.
8. Zverev V.A., Timoshchuk I.N. Aberrational properties of a thin mirror–lens component in a convergent pencil of rays. Journal of Optical Technology, 2015, vol. 82, no. 4, pp. 227–230. doi: 10.1364/JOT.82.000227

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
Copyright 2001-2018 ©
Scientific and Technical Journal
of Information Technologies, Mechanics and Optics.
All rights reserved.