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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 27, Iss. 10 — Oct. 1, 2010
  • pp: 2252–2260

Properties of caustics produced by a positive lens: meridional rays

Maximino Avendaño-Alejo, Luis Castañeda, and Ivan Moreno  »View Author Affiliations


JOSA A, Vol. 27, Issue 10, pp. 2252-2260 (2010)
http://dx.doi.org/10.1364/JOSAA.27.002252


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Abstract

We study the formation of the caustic surfaces formed in both convex-plane and plano-convex spherical lenses by considering a plane wave incident on the lens along the optical axis. Using the caustic formulas and a paraxial approximation we derive analytical expressions to evaluate the spherical aberration to third order. Furthermore, we apply the formulas to evaluate the circle of least confusion for a positive lens.

© 2010 Optical Society of America

OCIS Codes
(080.2710) Geometric optics : Inhomogeneous optical media
(260.1180) Physical optics : Crystal optics
(260.1440) Physical optics : Birefringence

History
Original Manuscript: March 12, 2010
Revised Manuscript: August 3, 2010
Manuscript Accepted: August 8, 2010
Published: September 27, 2010

Citation
Maximino Avendaño-Alejo, Luis Castañeda, and Ivan Moreno, "Properties of caustics produced by a positive lens: meridional rays," J. Opt. Soc. Am. A 27, 2252-2260 (2010)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-27-10-2252


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References

  1. 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]
  2. 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]
  3. 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]
  4. 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]
  5. P. S. Theocaris, “Properties of caustics from conic reflectors 1: Meridional rays,” Appl. Opt. 16, 1705–1716 (1977). [CrossRef] [PubMed]
  6. 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]
  7. O. Stavroudis, The Optics of Rays, Wavefronts, and Caustics (Academic, 1972), Chap. 10, pp. 161–179.
  8. 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]
  9. O. N. Stavroudis, R. C. Fronczek, and R.-S. Chang, “Geometry of the half-symmetric image,” J. Opt. Soc. Am. 68, 739–742 (1978). [CrossRef]
  10. 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]
  11. 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]
  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. G. Silva-Ortigoza, M. Marciano-Melchor, O. Carvente-Muñoz, and R. Silva-Ortigoza, “Exact computation of the caustic associated with the evolution of an aberrated wavefront,” J. Opt. A, Pure Appl. Opt. 4, 358–365 (2002). [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).
  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. M. González-Utrera, V. I. Moreno-Oliva, and R. Díaz-Uribe, “Null Hartmann screen for measuring the spherical aberration in a plane-convex lens,” in Proceedings of the 18th IMEKO TC 2 (2008), pp. 1–6.
  19. J. J. Stoker, Differential Geometry (Wiley-Interscience, 1969), Chap. 2, pp. 12–52.
  20. A. E. Conrady, Applied Optics & Optical Design Part 1 (Dover, 1957), Chap. II, pp. 72–125.
  21. H. A. Buchdahl, An Introduction to Hamiltonian Optics (Cambridge University Press, 1970), Chap. 4, pp. 35–82.
  22. W. T. Welford, Aberrations of the Symmetrical Optical System (Academic, 1974), Chap. 6, pp. 73–110.
  23. D. Malacara and Z. Malacara, Handbook of Lens Design (Marcel Dekker, 1994), Chap. 5, pp. 149–153.
  24. R. C. Spencer, “Focal region of a spherical reflector circle of least confusion,” Appl. Opt. 7, 1644–1645 (1968). [CrossRef] [PubMed]
  25. R. C. Spencer and G. Hyde, “Studies of the focal region of a spherical reflector: geometric optics,” IEEE Trans. Antennas Propag. 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. O. Stravroudis, Handbook of Optical Engineering (Marcel Dekker, 2001), Chap. 1, pp. 1–38.
  28. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University Press, 1999), Chap. V, pp. 229–260.

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