Journal of Optics

, Volume 46, Issue 2, pp 100–107

# Aspheric coefficients of deformation for a Cartesian oval surface

• Marcelo Vaca Pereira-Ghirghi
• Zacarias Malacara-Hernández
• Héctor Alejandro Chaparro-Romo
Research Article

## Abstract

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.

## Keywords

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

## Notes

### Acknowledgements

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.

### Funding

We currently have no funding or grants from anyone.

### 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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