Acuña-Romo equation

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Acuña-Romo lens

In geometrical optics and optical engineering, the Acuña-Romo equation describes the solution to the problem of designing a lens without spherical aberration .

principle

The equation specifies how the second surface of a lens should be designed so that the spherical aberration generated by the first refractive surface of the lens is completely corrected for a point object on the optical axis.

Origin of the spherical aberration-free lens design

Some of the most important events for the design of the lens without spherical aberration are:

  • Diocles, in his book "Mirrors ustorios", having found that the parabolic mirror could focus the rays moving in the direction of an axis in a single point, it is possible to mention a lens with the same property.
  • Ibn Sahl deals with the optical properties of mirrors and curved lenses. He has been described as the discoverer of the law of refraction (Snell's law).
  • Rene Descartes examines Cartesian ovals and their applications in optics.
  • Christiaan Huygens suggests eliminating the spherical aberration with a set of spherical lenses. In the foreword of the work, "Traité de la lumière" also mentions that Isaac Newton and Gottfried Wilhelm Leibniz addressed the problem.
  • Levi-Civita outlines the numerical solution for the design of corrective refractive surfaces.
  • GD Wasserman and E. Wolf propose an aplanatic lens based on an integral that they solve using numerical methods.
  • Daniel Malacara Hernández presents an approximate design of a lens without spherical aberration with two aspherical surfaces.
  • Psang Dain Lin and Chung-Yu Tsai obtain the lens design without spherical aberration from the numerical solution of a system of nonlinear equations.
  • Juan Camilo Valencia Estrada shows an analytical solution to the problem for specific individual cases.
  • Rafael G. González-Acuña and Héctor A. Chaparro-Romo present the general closed shape equation for designing a lens without spherical aberration.

See also

credentials

  1. ↑ Applied Optics Volume 57, Issue 31 . In: www.osapublishing.org . OSA Publishing. November 2018. Retrieved April 29, 2019.
  2. ^ Toomer GJ: Diocles On Burning Mirrors, Sources in the History of Mathematics and the Physical Sciences 1 . Springer, New York 1976.
  3. ^ R. Rashed: Géométrie et dioptrique au Xe siècle: Ibn Sahl, al-Quhi et Ibn al-Haytham. . Les Belles Lettres, Paris 1993.
  4. ↑ Christiaan Huygens: Traité de la lumière 1690.
  5. ↑ Fokko Jan Dijksterhuis: Lenses and waves: Christiaan Huygens and the mathematical science of optics in the seventeenth century . Springer, Enschede 2004, ISBN 978-1-4020-2697-3 .
  6. ^ T. Levi-Civita: Complementi al teorema di Malus-Dupin. Nota I . In: Atti Accad. Sci. Torino . 9, No. 5, September, pp. 185-189.
  7. ^ GD Wasserman, E. Wolf: On the Theory of Aplanatic Aspheric Systems . In: Proceedings of the Physical Society . 62, No. 1, September.
  8. ↑ Daniel Malacara: Two Lenses to Colli Mate Red Laser Light . In: Applied Optics . 4, No. 12, September, pp. 1652-1654. doi : 10.1364 / AO.4.001652 .
  9. ↑ Psang Dain Lin, Chung-Yu Tsai: Determination of unit normal vectors of aspherical surfaces given unit directional vectors of incoming and outgoing rays . In: Applied Optics . 29, No. 2, September, pp. 174-178. doi : 10.1364 / JOSAA.29.000174 .
  10. ^ Juan Camilo Valencia-Estrada, Ricardo Benjamin. Flores-Hernández: Singlet lenses free of all orders of spherical aberration . In: Royal Society A proceedings . 471, September. doi : 10.1098 / rspa.2014.0608 .
  11. ↑ Rafael G. González-Acuña, Héctor A. Chaparro-Romo: General formula for bi-aspheric singlet lens design free of spherical aberration . In: Applied Optics . 57, No. 31, September, pp. 9341-9345. doi : 10.1364 / AO.57.009341 .
  12. ↑ Rafael G. González-Acuña, Gutiérrez-Vega Julio C .: Generalization of the axicon shape: the gaxicon . In: Journal of the Optical Society of America A . 35, No. 11, September, pp. 1915-1918. doi : 10.1364 / JOSAA.35.001915 .
  13. ↑ Danilo Moreno: Nuevos lentes se diseñan en laboratorios de Yachay Tech . Diario El Norte. 1st January 2019.
  14. ↑ Julio Chacón, docente YACHAY TECH, Proyecto de Investigación de Lentes libres de aberraciones esféricas. . Diario El Norte. December 6, 2018.
  15. ↑ YACHAY TECH CONTRIBUYE AL DISEÑO DE NUEVOS LENTES . YachayTech. 3rd December 2018.
  16. ↑ ¡Eureka! Encuentran la formula para resolver un antiguo problema óptico . Revista Transferencia Tec. February 21, 2019.
  17. ^ Rafael G. González-Acuña, Maximino Avendaño-Alejo, Gutiérrez-Vega Julio C .: Singlet lens for generating aberration-free patterns on deformed surfaces . In: Journal of the Optical Society of America A . 36, No. 5, September, pp. 925-929. doi : 10.1364 / JOSAA.36.000925 .