Asian Journal of Physics Vol 32, Nos 3 & 4 (2023) 207-210

The eikonal equation via adaptive control theory

Vasudevan Lakshminarayanan
School of Optometry and Vision Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada
Dedicated to Prof Jay M Enoch


The eikonal equation can be considered as the fundamental equation in geometric optics. It is demonstrated here that the equation can be derived as a control theoretic problem using the method of dynamic programming. © Anita Publications. All rights reserved.
Keywords: Geometric optics, Eikonal equation, Adaptive Control, Dynamic programming, Fermat’s principle.


Peer Review Information
Method: Single- anonymous; Screened for Plagiarism? Yes
Buy this Article in Print © Anita Publications. All rights reserve

References

  1. Lakshminarayanan V, Ghatak A K, Thyagarajan K, Lagrangian Optics, (Kluwer, Boston, MA), 2002.
  2. Goldstein H, Classical Mechanics, (Addison Wesley, Cambridge, MA), 1956.
  3. Bertsekas D, Dynamic Programming and Optimal Control, Vol I, 4th Edn, (Athena Scientific, Nashua, NH), 2017.
  4. Denardo E V, Dynamic programming: models and applications, (Dover, NY), 2012.
  5. Bellman R, Dynamic Programming, (Princeton University Press, Princeton, NJ), 2010.
  6. Kalaba R, Dynamic programming, Fermat’s principle and the eikonal equation, J Opt Soc Am, 51(1961)1150–1151.
  7. Lakshminarayanan V, Varadharajan L S, Dynamic programming, Fermat’s principle and the eikonal equation – revisited, J Optim Theory Appl, 95(1997)713–716.
  8. Calvo M L, Lakshminarayanan V, Light propagation in optical waveguides, a dynamic programming approach, J Opt Soc Am A, 14(1997)872–880.
  9. Calvo M L, Lakshminarayanan V, Spatial pulse characterization in periodically segmented waveguides using the dynamic programming approach, Opt Commun, 169(1999)223–231.
  10. Brandstatter J J, Dynamic programming, Fermat’s principle and the eikonal equation for anisotropic media, J Opt Soc Am, 64(1974)317–318.
  11. Calvo M L, Perez-Rios J, Lakshminarayanan V, dynamic programming applications in optics, Chapter 3, pp 53–94, in Lakshminarayanan V, Calvo M L, Aleiva T, Mathematical Optics, Classical, Quantum and Computational Methods, (CRC Press, Boca Raton, FL), 2013.