Abstract

Local wavefront curvature transformations at an arbitrarily shaped optical surface are commonly determined by generalized Coddington equations that are developed here via a local thin optical element approximation. Eikonal distributions of the incident and refracted beams are calculated and related by an eikonal transfer function of a local thin optical element located in close proximity to a given point at a tangent plane of an optical surface. Main coefficients and terms involved in the generalized Coddington equations are derived and explained as a local nonparaxial generalization for the customary paraxial wavefront transformations.

© 2009 Optical Society of America

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  1. R. Kingslake, “Who discovered Coddington's equations?” Opt. Photonics News, May 1994, pp. 20-23.
  2. W. J. Smith, Modern Optical Engineering (McGraw-Hill Professional Publishing, 2000),Section 10.6.
  3. O. N. Stavroudis, The Optics of Rays, Wavefronts, and Caustics (Academic, 1972), pp. 136-179.
  4. S. A. Comastri and J. M. Simon, “Wavefront aberration function: its first and second field derivatives,” Optik 111, 249-260 (2000).
  5. A. E. Murray, “Skew astigmatism at toric surfaces, with special reference to spectacle lenses,” J. Opt. Soc. Am. 47, 599-601 (1957).
    [CrossRef]
  6. J. E. A. Landgrave and J. R. Moya-Cessa, “Generalized Coddington equations in ophthalmic lens design,” J. Opt. Soc. Am. A 13, 1637-1644 (1996).
    [CrossRef]
  7. D. G. Burkhard and D. L. Shealy, “Simplified formula for the illuminance of an optical system,” Appl. Opt. 20, 897-909 (1981).
    [CrossRef]
  8. J. Turunen, “Astigmatism in laser beam optical systems,” Appl. Opt. 25, 2908-2911 (1986).
    [CrossRef]
  9. D. DeJager and M. Noethen, “Gaussian beam parameters that use Coddington-based Y-NU paraprincipal ray tracing,” Appl. Opt. 31, 2199-2205 (1992).
    [CrossRef]
  10. V. Greco and G. Giusfredi, “Reflection and refraction of narrow Gaussian beams with general astigmatism at tilted optical surfaces: a derivation oriented toward lens design,” Appl. Opt. 46, 513-521 (2007).
    [CrossRef]
  11. W. Zou, K. P. Thompson, and J. P. Rolland, “Differential Shack-Hartmann curvature sensor: local principal curvature measurements,” J. Opt. Soc. Am. A 25, 2331-2337 (2008).
    [CrossRef]
  12. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge U. Press, 1999), Sec. 4.6.
  13. J. A. Kneisly II, “Local curvature of wavefronts in an optical system,” J. Opt. Soc. Am. 54, 229-235 (1964).
    [CrossRef]
  14. O. N. Stavroudis, “Simpler derivation of the formulas for generalized ray tracing,” J. Opt. Soc. Am. 66, 1330-1333 (1976).
    [CrossRef]
  15. N. Lindlein and J. Schwider, “Local wave fronts at diffractive elements,” J. Opt. Soc. Am. A 10, 2563-2572 (1993).
    [CrossRef]
  16. C. E. Campbell, “Generalized Coddington equations found via an operator method,” J. Opt. Soc. Am. A 23, 1691-1698 (2006).
    [CrossRef]
  17. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts, 2005), Sec. 5.1.
  18. M. A. Golub, “Generalized conversion from the phase function to the blazed surface-relief profile of diffractive optical elements,” J. Opt. Soc. Am. A 16, 1194-1201 (1999).
    [CrossRef]
  19. M. Testorf, “On the zero-thickness model of diffractive optical elements,” J. Opt. Soc. Am. A 17, 1132-1133 (2000).
    [CrossRef]
  20. L. D. Landau and E. M. Lifschitz, The Classical Theory of Fields, Course of Theoretical Physics, 4th ed. (Butterworth-Heinemann, 2003), Vol. 2, p. 159.

2008 (1)

2007 (1)

2006 (1)

2000 (2)

M. Testorf, “On the zero-thickness model of diffractive optical elements,” J. Opt. Soc. Am. A 17, 1132-1133 (2000).
[CrossRef]

S. A. Comastri and J. M. Simon, “Wavefront aberration function: its first and second field derivatives,” Optik 111, 249-260 (2000).

1999 (1)

1996 (1)

1993 (1)

1992 (1)

1986 (1)

1981 (1)

1976 (1)

1964 (1)

1957 (1)

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge U. Press, 1999), Sec. 4.6.

Burkhard, D. G.

Campbell, C. E.

Comastri, S. A.

S. A. Comastri and J. M. Simon, “Wavefront aberration function: its first and second field derivatives,” Optik 111, 249-260 (2000).

DeJager, D.

Giusfredi, G.

Golub, M. A.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts, 2005), Sec. 5.1.

Greco, V.

Kingslake, R.

R. Kingslake, “Who discovered Coddington's equations?” Opt. Photonics News, May 1994, pp. 20-23.

Kneisly II, J. A.

Landau, L. D.

L. D. Landau and E. M. Lifschitz, The Classical Theory of Fields, Course of Theoretical Physics, 4th ed. (Butterworth-Heinemann, 2003), Vol. 2, p. 159.

Landgrave, J. E. A.

Lifschitz, E. M.

L. D. Landau and E. M. Lifschitz, The Classical Theory of Fields, Course of Theoretical Physics, 4th ed. (Butterworth-Heinemann, 2003), Vol. 2, p. 159.

Lindlein, N.

Moya-Cessa, J. R.

Murray, A. E.

Noethen, M.

Rolland, J. P.

Schwider, J.

Shealy, D. L.

Simon, J. M.

S. A. Comastri and J. M. Simon, “Wavefront aberration function: its first and second field derivatives,” Optik 111, 249-260 (2000).

Smith, W. J.

W. J. Smith, Modern Optical Engineering (McGraw-Hill Professional Publishing, 2000),Section 10.6.

Stavroudis, O. N.

O. N. Stavroudis, “Simpler derivation of the formulas for generalized ray tracing,” J. Opt. Soc. Am. 66, 1330-1333 (1976).
[CrossRef]

O. N. Stavroudis, The Optics of Rays, Wavefronts, and Caustics (Academic, 1972), pp. 136-179.

Testorf, M.

Thompson, K. P.

Turunen, J.

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge U. Press, 1999), Sec. 4.6.

Zou, W.

Appl. Opt. (4)

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (6)

Optik (1)

S. A. Comastri and J. M. Simon, “Wavefront aberration function: its first and second field derivatives,” Optik 111, 249-260 (2000).

Other (6)

L. D. Landau and E. M. Lifschitz, The Classical Theory of Fields, Course of Theoretical Physics, 4th ed. (Butterworth-Heinemann, 2003), Vol. 2, p. 159.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts, 2005), Sec. 5.1.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge U. Press, 1999), Sec. 4.6.

R. Kingslake, “Who discovered Coddington's equations?” Opt. Photonics News, May 1994, pp. 20-23.

W. J. Smith, Modern Optical Engineering (McGraw-Hill Professional Publishing, 2000),Section 10.6.

O. N. Stavroudis, The Optics of Rays, Wavefronts, and Caustics (Academic, 1972), pp. 136-179.

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