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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 30, Iss. 3 — Mar. 1, 2013
  • pp: 501–508

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

Maximino Avendaño-Alejo  »View Author Affiliations

JOSA A, Vol. 30, Issue 3, pp. 501-508 (2013)

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We study the formation of caustic surfaces formed in both convex-plano and plano-convex aspheric lenses by considering a plane wave incident on the lens along the optical axis. Using the caustic formulas and a paraxial approximation we derive expressions to evaluate the spherical aberration at third-order and also provide a formula to reduce it, where the first-order aspheric term is given in a simply analytic equation. Furthermore, we redefine the method 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 aspheric lenses.

© 2013 Optical Society of America

OCIS Codes
(260.6970) Physical optics : Total internal reflection
(080.1005) Geometric optics : Aberration expansions
(080.2468) Geometric optics : First-order optics

Original Manuscript: December 13, 2012
Revised Manuscript: January 30, 2013
Manuscript Accepted: February 1, 2013
Published: February 22, 2013

Maximino Avendaño-Alejo, "Caustics in a meridional plane produced by plano-convex aspheric lenses," J. Opt. Soc. Am. A 30, 501-508 (2013)

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  1. A. Epple and H. Wang, “Design to manufacture from the perspective of optical design and fabrication,” in Optical Fabrication and Testing, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OFB1.
  2. 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]
  3. M. Avendaño-Alejo, D. González-Utrera, and L. Castañeda, “Caustics in a meridional plane produced by plano-convex conic lenses,” J. Opt. Soc. Am. A 28, 2619–2628 (2011). [CrossRef]
  4. 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]
  5. M. Avendaño-Alejo, R. Daz-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]
  6. 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]
  7. D. G. Burkhard and D. L. Shealy, “Simplified formula for the illuminance in an optical system,” Appl. Opt. 20, 897–909 (1981). [CrossRef]
  8. S. Maca-García, M. Avendaño-Alejo, and L. Castañeda, “Caustics in a meridional plane produced by concave conic mirrors,” J. Opt. Soc. Am. A 29, 1977–1985 (2012). [CrossRef]
  9. 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]
  10. R. W. Hosken, “Circle of least confusion of a spherical reflector,” Appl. Opt. 46, 3107–3117 (2007). [CrossRef]
  11. 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]
  12. 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]
  13. 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]
  14. 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]
  15. P. S. Theocaris, “Properties of caustics from conic reflectors. 1: meridional rays,” Appl. Opt. 16, 1705–1716 (1977). [CrossRef]
  16. O. N. Stavroudis, The Mathematics of Geometrical and Physical Optics, the K-function and Its Ramifications (Wiley-VCH, 2006), Chap. 12, pp. 179–186.
  17. 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]
  18. A. V. Gitin, “Legendre transformation: Connection between transverse aberration of an optical system and its caustic,” Opt. Commun. 281, 3062–3066 (2008). [CrossRef]
  19. A. E. Conrady, Applied Optics and Optical Design: Part one (Dover, 1957), Chap. II, pp. 72–125.
  20. H. A. Buchdahl, An Introduction to Hamiltonian Optics(Cambdridge University, 1970), Chap. 4, pp. 35–82.
  21. W. T. Welford, Aberrations of the Symmetrical Optical System (Academic, 1974), Chap. 6, pp. 73–110.
  22. 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]
  23. D. Malacara and Z. Malacara, Handbook of Lens Design(Dekker, 1994), Chap. 2, pp. 45–82.
  24. G. W. Forbes, “Robust, efficient computational methods for axially symmetric optical aspheres,” Opt. Express 18, 19700–19712 (2010). [CrossRef]
  25. G. W. Forbes, “Shape specification for axially symmetric optical surfaces,” Opt. Express 15, 5218–5226 (2007). [CrossRef]
  26. F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw-Hill, 1976), Chap. 3, pp. 44–57.
  27. J. Stoker, Differential Geometry (Wiley-Interscience, 1969), Chap. 2, pp. 12–52.
  28. 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]
  29. 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]

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