Journal of Optics

, Volume 46, Issue 2, pp 100–107 | Cite as

Aspheric coefficients of deformation for a Cartesian oval surface

  • Juan Camilo Valencia-Estrada
  • Marcelo Vaca Pereira-GhirghiEmail author
  • Zacarias Malacara-Hernández
  • Héctor Alejandro Chaparro-Romo
Research Article


In this paper we propose a mathematical model as a theoretical and practical contribution to the theory of aspheric surfaces, that allows the geometrical calculation of an aspherical refractive surface in cylindrical coordinates \((r,z)\), that correspond to a non-degenerated Cartesian oval of revolution, according to standard formulae [ISO-10110-12 (2007)], including: vertex curvature C, conical constant K and aspheric deformation coefficients \(A_4,\,A_6,\,A_8,\,A_{10}\) and \(A_{14}\). The results are shown for an object and its respective image located at finite distances from the vertex (origin of coordinates) on the optical axis.


Aspheric lenses Cartesian ovals No-image optics Spherical aberration free Aspheric coefficients 



To the Centro de Investigaciones en Optica A.C. CIO, León, Guanajuato, México, and the Consejo Nacional de Ciencia y Tecnología de México, CONACyT, for its economic support.

Authors contribution

JCVE developed most of the physical-mathematical model and programming. MVPG developed all simulations using OSLO®. ZMH developed the remained portion of the model and reviewed and verifed all results. ACR reviewed all equations and LaTeX  edition. All authors gave final approval for publication.


We currently have no funding or grants from anyone.

Compliance with ethical standards

Conflict of interest

We have no competing interests.

Ethics statement

This work did not involve any activity collection of human data, neither computer simulation of human behavior.

Data accessibility statement

This work does not have any experimental data.


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Copyright information

© The Optical Society of India 2016

Authors and Affiliations

  1. 1.Oledcomm SASUniversité de Versailles Saint-Quentin-en-YvelinesVélizy-VillacoublayFrance
  2. 2.OpticaCentro de Investigaciones en Óptica A.CLeón, GuanajuatoMexico

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