Advertisement

The Wavefront Shape, Irradiance, and Caustic Surface in an Optical System

  • Psang Dain LinEmail author
Chapter
  • 1.8k Downloads
Part of the Springer Series in Optical Sciences book series (SSOS, volume 178)

Abstract

The wavefront shape, illuminance, and caustic surface at any point along the ray path can be computed either by k-function method [1, 2] or by the differential geometry-based method [3]. The former approach was further extended by Shealy and his colleagues [4–8] for systems with multiple optical elements illuminated by a plane wavefront propagating parallel to the optical axis. However, how to generate the k-function for non-axially symmetrical systems with reflecting surfaces for a skew source ray is still highly challenging. This chapter will show that the differential geometry-based approach based on the first and second fundamental forms of the wavefront is a more general approach for discussing the shape of wavefront.

Keywords

Fundamental Form Hessian Matrix Principal Curvature Wavefront Aberration Hessian Matrice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    O.N. Stavroudis, The Optics of Rays, Wavefronts, and Caustics. (Academic press, Cambridge, 1972)Google Scholar
  2. 2.
    O.N. Stavroudis, The mathematics of geometricl and physical optics. (Wiley, 2006)Google Scholar
  3. 3.
    A Pressley, Elementary Differential Geometry, The Springer Undergraduate Mathematics Series, (2001) p. 123Google Scholar
  4. 4.
    J.A. Hoffnagle, D.L. Shealy, Refracting the k-function: Stavroudis’s solution to the eikonal equation for multielement optical systems. J. Opt. Soc. Am. A 28, 1312–1321 (2011)ADSCrossRefGoogle Scholar
  5. 5.
    D.L. Shealy, D.G. Burkhard, Caustic surfaces and irradiance for reflection and refraction from an ellipsoid, elliptic parabolid and elliptic cone. Appl. Opt. 12, 2955–2959 (1973)ADSCrossRefGoogle Scholar
  6. 6.
    D.L. Shealy, D.G. Burkhard, Caustic surface merit functions in optical design. J. Opt. Soc. Am. 66, 1122 (1976)Google Scholar
  7. 7.
    D.L. Shealy, Analytical illuminance and caustic surface calculations in geometrical optics. Appl. Opt. 15, 2588–2596 (1976)ADSCrossRefGoogle Scholar
  8. 8.
    D.L. Shealy, J.A. Hoffnagle, Wavefront and caustics of a plane wave refracted by an arbitrary surace. J. Opt. Soc. Am. A 25, 2370–2382 (2008)MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    J.A. Kneisly II, Local curvature of wavefronts in an optical system. J. Opt. Soc. of Am. 54, 229–235 (1964)Google Scholar
  10. 10.
    D.P. Mitchell, P. Hanrahan, Illumination from curved reflectors. in Proceedings of SIGGRAPH, computer graphics, vol 26, no. 2. , pp. 283–291 (1992)Google Scholar
  11. 11.
    W.J. Smith, Modern Optical Engineering, 3rd edn. (Edmund Industrial Optics, Barrington, 2001)Google Scholar
  12. 12.
    D.G. Burkhard, D.L. Shealy, Simplified formula for the illuminance in an optical system. Appl. Opt. 20, 897–909 (1981)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Singapore 2014

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringNational Cheng Kung UniversityTainanTaiwan R.O.C

Personalised recommendations