The Jacobian Matrix of a Ray with Respect to System Variable Vector

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


The automation in optical design work has made variational raytracing to estimate the Jacobian matrix with respect to system variables by using finite difference method [1–14].


Optical System Jacobian Matrix Finite Difference Method Boundary Surface Variable Vector 
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.


  1. 1.
    C.G. Wynne, P. Wormell, Lens design by computer. Appl. Opt. 2, 1223–1238 (1963)ADSCrossRefGoogle Scholar
  2. 2.
    D.P. Fede, Automatic optical design, Appl. Opt. 2, 1209–1226 (1963)Google Scholar
  3. 3.
    M. Rimmer, Analysis of perturbed lens systems. Appl. Opt. 9, 533–537 (1970)ADSCrossRefGoogle Scholar
  4. 4.
    H.H. Hopkins, H.J. Tiziani, A theoretical and experimental study of lens centering errors and their influence on optical image quality. Brit. J. Appl. Phys. 17, 33–54 (1966)ADSCrossRefGoogle Scholar
  5. 5.
    T.B. Andersen, Optical aberration functions: chromatic aberrations and derivatives with respect to refractive indices for symmetrical systems. Appl. Opt. 21, 4040–4044 (1982)ADSCrossRefGoogle Scholar
  6. 6.
    S.K. Gupta, R. Hradaynath, Angular tolerance on Dove prisms. Appl. Opt. 22, 3146–3147 (1983)ADSCrossRefGoogle Scholar
  7. 7.
    J.F. Lee, C.Y. Leung, Method of calculating the alignment tolerance of a Porro prism resonator. Appl. Opt. 28, 3691–3697 (1989)ADSCrossRefGoogle Scholar
  8. 8.
    B.D. Stone, Perturbations of optical systems. J. Opt. Soc. Am. A 14, 2837–2849 (1997)ADSCrossRefGoogle Scholar
  9. 9.
    D.S. Grey, The inclusion of tolerance sensitivities in the merit function for lens optimization. SPIE 147, 63–65 (1978)ADSCrossRefGoogle Scholar
  10. 10.
    E.G. Herrera, M. Strojnik, Interferometric tolerance determination for a Dove prism using exact ray trace. Opt. Commun. 281, 897–905 (2008)ADSCrossRefGoogle Scholar
  11. 11.
    W. Mao, Adjustment of reflecting prisms. Opt. Eng. 34, 79–82 (1995)ADSCrossRefGoogle Scholar
  12. 12.
    K.N. Chandler, On the effect of small errors in angles of corner-cube reflectors. J. Opt. Soc. Am. 50, 203–206 (1960)ADSCrossRefGoogle Scholar
  13. 13.
    N. Lin, Orientation conjugation of reflecting prism rotation and second-order approximation of image rotation. Opt. Eng. 33, 2400–2407 (1994)ADSCrossRefGoogle Scholar
  14. 14.
    E. Gutierrez, M. Strojnik, G. Paez, Tolerance determination for a Dove prism using exact ray trace. Proc. SPIE 6307, 63070K (2006)ADSCrossRefGoogle Scholar
  15. 15.
    B.D. Stone, Determination of initial ray configurations for asymmetric systems. J. Opt. Soc. Am. A 14, 3415–3429 (1997)ADSCrossRefGoogle Scholar
  16. 16.
    T. B. Andersen, Optical aberration functions: derivatives with respect to axial distances for symmetrical systems. Appl. Opt. 21, 1817–1823 (1982)Google Scholar
  17. 17.
    T.B. Andersen, Optical aberration functions: derivatives with respect to surface parameters for symmetrical systems. Appl. Opt. 24, 1122–1129 (1985)ADSCrossRefGoogle Scholar
  18. 18.
    D.P. Feder, Calculation of an optical merit function and its derivatives with respect to the system parameters. J. Opt. Soc. Am. 47, 913–925 (1957)MathSciNetADSCrossRefGoogle Scholar
  19. 19.
    D.P. Feder, Differentiation of ray-tracing equations with respect to constructional parameters of rotationally symmetric systems. J. Opt. Soc. Am. 58, 1494–1505 (1968)ADSCrossRefGoogle Scholar
  20. 20.
    O. Stavroudis, A simpler derivation of the formulas for generalized ray tracing. J. Opt. Soc. Am. 66, 1330–1333 (1976)Google Scholar
  21. 21.
    J. Kross, Differential ray tracing formulae for optical calculations: principles and applications. SPIE Opt. Des. Method Large Opt. 1013, 10–18 (1988)Google Scholar
  22. 22.
    W. Oertmann, Differential ray tracing formulae; applications especially to aspheric optical systems, SPIE Opt. Des. Method Large Opt., 1013, 20–26 (1988)Google Scholar
  23. 23.
    P.D. Lin, C.Y. Tsai, Determination of first-order derivatives of skew-ray at aspherical surface. J. Opt. Soc. Am. A 29, 1141–1153 (2012)ADSCrossRefGoogle Scholar
  24. 24.
    C. Olson, R.N. Youngworth, Alignment analysis of optical systems using derivative information. Proc of SPIE 7068, 1–10 (2008)ADSGoogle 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