OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 28, Iss. 12 — Dec. 1, 2011
  • pp: 2619–2628

Caustics in a meridional plane produced by plano-convex conic lenses

Maximino Avendaño-Alejo, Dulce González-Utrera, and Luis Castañeda  »View Author Affiliations

JOSA A, Vol. 28, Issue 12, pp. 2619-2628 (2011)

View Full Text Article

Enhanced HTML    Acrobat PDF (723 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We study the formation of caustic surfaces formed in both convex-plano and plano-convex conic lenses by considering a plane wave incident on the lens along the optical axis. By using the caustic formulas and a paraxial approximation, we derive analytic expressions to evaluate the spherical aberration to the third order, and a formula to reduce this aberration is provided. Furthermore, we apply the formulas to evaluate the circle of least confusion for a positive lens as a function of all parameters involved in the process of refraction through the conic lenses.

© 2011 Optical Society of America

OCIS Codes
(080.2710) Geometric optics : Inhomogeneous optical media
(080.3630) Geometric optics : Lenses
(260.6970) Physical optics : Total internal reflection

Original Manuscript: June 28, 2011
Manuscript Accepted: August 1, 2011
Published: November 21, 2011

Maximino Avendaño-Alejo, Dulce González-Utrera, and Luis Castañeda, "Caustics in a meridional plane produced by plano-convex conic lenses," J. Opt. Soc. Am. A 28, 2619-2628 (2011)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. M. Avendaño-Alejo, L. Castañeda, and I. Moreno, “Properties of caustics produced by a positive lens: meridional rays,” J. Opt. Soc. Am. A 27, 2252–2260 (2010). [CrossRef]
  2. M. Avendaño-Alejo, R. Díaz-Uribe, and I. Moreno, “Caustics caused by refraction in the interface between an isotropic medium and a uniaxial crystal,” J. Opt. Soc. Am. A 25, 1586–1593(2008). [CrossRef]
  3. J. A. Lock, C. L. Adler, and E. A. Hovenac, “Exterior caustics produced in scattering of a diagonally incident plane wave by a circular cylinder: semiclassical scattering theory analysis,” J. Opt. Soc. Am. A 17, 1846–1856 (2000). [CrossRef]
  4. M. Avendaño-Alejo, I. Moreno, and L. Castañeda, “Caustics caused by multiple reflections on a circular surface,” Am. J. Phys. 78, 1195–1198 (2010). [CrossRef]
  5. A. Cordero-Dávila and J. Castro-Ramos, “Exact calculation of the circle of least confusion of a rotationally symmetric mirror,” Appl. Opt. 37, 6774–6778 (1998). [CrossRef]
  6. D. G. Burkhard and D. L. Shealy, “Formula for the density of tangent rays over a caustic surface,” Appl. Opt. 21, 3299–3306(1982). [CrossRef] [PubMed]
  7. P. S. Theocaris, “Properties of caustics from conic reflectors. 1: Meridional rays,” Appl. Opt. 16, 1705–1716 (1977). [CrossRef] [PubMed]
  8. O. N. Stavroudis, The Mathematics of Geometrical and Physical Optics, The K-function and Its Ramifications (Wiley-VCH, 2006), Chap. 12, pp. 179–186. [CrossRef]
  9. O. Stavroudis, The Optics of Rays, Wavefronts, and Caustics (Academic, 1972), Chap. 10, pp. 161–179.
  10. O. N. Stavroudis and R. C. Fronczek, “Caustic surfaces and the structure of the geometrical image,” J. Opt. Soc. Am. 66, 795–800 (1976). [CrossRef]
  11. O. N. Stavroudis, “The k function in geometrical optics and its relationship to the archetypal wave front and the caustic surface,” J. Opt. Soc. Am. A 12, 1010–1016 (1995). [CrossRef]
  12. D. L. Shealy and J. A. Hoffnagle, “Wavefront and caustics of a plane wave refracted by an arbitrary surface,” J. Opt. Soc. Am. A 25, 2370–2382 (2008). [CrossRef]
  13. G. Silva-Ortigoza, J. Castro-Ramos, and A. Cordero-Dávila, “Exact calculation of the circle of least confusion of a rotationally symmetric mirror. II,” Appl. Opt. 40, 1021–1028 (2001). [CrossRef]
  14. J. Castro-Ramos, O. de Ita Prieto, and G. Silva-Ortigoza, “Computation of the disk of least confusion for conic mirrors,” Appl. Opt. 43, 6080–6089 (2004). [CrossRef] [PubMed]
  15. D. G. Burkhard and D. L. Shealy, “Simplified formula for the illuminance in an optical system,” Appl. Opt. 20, 897–909(1981). [CrossRef] [PubMed]
  16. A. V. Gitin, “Legendre transformation: connection between transverse aberration of an optical system and its caustic,” Opt. Commun. 281, 3062–3066 (2008). [CrossRef]
  17. R. W. Hosken, “Circle of least confusion of a spherical reflector,” Appl. Opt. 46, 3107–3117 (2007). [CrossRef] [PubMed]
  18. M. Avendaño-Alejo, D. González-Utrera, N. Qureshi, L. Castañeda, and C. L. Ordóñez-Romero, “Null Ronchi-Hartmann test for a lens,” Opt. Express 18, 21131–21137 (2010). [CrossRef] [PubMed]
  19. F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw-Hill, 1976), Chap. 3, pp. 44–57.
  20. J. J. Stoker, Differential Geometry (Wiley-Interscience, 1969), Chap. 2, pp. 12–52.
  21. A. E. Conrady, Applied Optics & Optical Design (Dover, 1957), Part One, Chap. II, pp. 72–125.
  22. H. A. Buchdahl, An Introduction to Hamiltonian Optics(Cambridge University, 1970), Chap. 4, pp. 35–82.
  23. W. T. Welford, Aberrations of the Symmetrical Optical System (Academic, 1974), Chap. 6, pp. 73–110.
  24. D. Malacara and Z. Malacara, Handbook of Lens Design (Marcel Dekker, 1994), Chap. 5, pp. 149–153.
  25. R. C. Spencer and G. Hyde, “Studies of the focal region of a spherical reflector: geometric optics,” IEEE Trans. Antennas Propag. AP-16, 317–324 (1968). [CrossRef]
  26. C. Y. Tsai, “A general calculation of the 3-D disk of least confusion using skew ray tracing,” Appl. Phys. B 96, 517–525(2009). [CrossRef]
  27. Orestes Stavroudis, Handbook of Optical Engineering (Marcel Dekker, 2001), Chap. 1, pp. 1–38.
  28. M. Born and E. Wolf, “Electromagnetic theory of propagation, interference and diffraction light,” in Principles of Optics, 7th ed. (Cambridge University, 1999), Chap. V, pp. 229–260.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited