Abstract

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

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2012 (1)

2011 (1)

2010 (4)

2009 (1)

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]

2008 (3)

2007 (2)

2004 (1)

2001 (1)

2000 (1)

1998 (1)

1995 (1)

1982 (1)

1981 (1)

1977 (1)

1968 (1)

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]

Adler, C. L.

Avendaño-Alejo, M.

Buchdahl, H. A.

H. A. Buchdahl, An Introduction to Hamiltonian Optics(Cambdridge University, 1970), Chap. 4, pp. 35–82.

Burkhard, D. G.

Castañeda, L.

Castro-Ramos, J.

Conrady, A. E.

A. E. Conrady, Applied Optics and Optical Design: Part one (Dover, 1957), Chap. II, pp. 72–125.

Cordero-Dávila, A.

Daz-Uribe, R.

de Ita Prieto, O.

Epple, A.

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.

Forbes, G. W.

Gitin, A. V.

A. V. Gitin, “Legendre transformation: Connection between transverse aberration of an optical system and its caustic,” Opt. Commun. 281, 3062–3066 (2008).
[CrossRef]

González-Utrera, D.

Hoffnagle, J. A.

Hosken, R. W.

Hovenac, E. A.

Hyde, G.

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]

Jenkins, F. A.

F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw-Hill, 1976), Chap. 3, pp. 44–57.

Lock, J. A.

Maca-García, S.

Malacara, D.

D. Malacara and Z. Malacara, Handbook of Lens Design(Dekker, 1994), Chap. 2, pp. 45–82.

Malacara, Z.

D. Malacara and Z. Malacara, Handbook of Lens Design(Dekker, 1994), Chap. 2, pp. 45–82.

Moreno, I.

Ordóñez-Romero, C. L.

Qureshi, N.

Shealy, D. L.

Silva-Ortigoza, G.

Spencer, R. C.

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]

Stavroudis, O. N.

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]

O. N. Stavroudis, The Mathematics of Geometrical and Physical Optics, the K-function and Its Ramifications (Wiley-VCH, 2006), Chap. 12, pp. 179–186.

Stoker, J.

J. Stoker, Differential Geometry (Wiley-Interscience, 1969), Chap. 2, pp. 12–52.

Theocaris, P. S.

Tsai, C. Y.

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]

Wang, H.

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.

Welford, W. T.

W. T. Welford, Aberrations of the Symmetrical Optical System (Academic, 1974), Chap. 6, pp. 73–110.

White, H. E.

F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw-Hill, 1976), Chap. 3, pp. 44–57.

Am. J. Phys. (1)

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]

Appl. Opt. (7)

Appl. Phys. B (1)

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]

IEEE Trans. Antennas Propag. (1)

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]

J. Opt. Soc. Am. A (7)

Opt. Commun. (1)

A. V. Gitin, “Legendre transformation: Connection between transverse aberration of an optical system and its caustic,” Opt. Commun. 281, 3062–3066 (2008).
[CrossRef]

Opt. Express (3)

Other (8)

F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw-Hill, 1976), Chap. 3, pp. 44–57.

J. Stoker, Differential Geometry (Wiley-Interscience, 1969), Chap. 2, pp. 12–52.

D. Malacara and Z. Malacara, Handbook of Lens Design(Dekker, 1994), Chap. 2, pp. 45–82.

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.

A. E. Conrady, Applied Optics and Optical Design: Part one (Dover, 1957), Chap. II, pp. 72–125.

H. A. Buchdahl, An Introduction to Hamiltonian Optics(Cambdridge University, 1970), Chap. 4, pp. 35–82.

W. T. Welford, Aberrations of the Symmetrical Optical System (Academic, 1974), Chap. 6, pp. 73–110.

O. N. Stavroudis, The Mathematics of Geometrical and Physical Optics, the K-function and Its Ramifications (Wiley-VCH, 2006), Chap. 12, pp. 179–186.

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