OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 38, Iss. 1 — Jan. 1, 1999
  • pp: 11–17

Modeling the Temperature Dependence of the Index of Refraction of Liquid Water in the Visible and the Near-Ultraviolet Ranges by a Genetic Algorithm

Aleksandra B. Djurišić and Božidar V. Stanić  »View Author Affiliations

Applied Optics, Vol. 38, Issue 1, pp. 11-17 (1999)

View Full Text Article

Acrobat PDF (205 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A simple formula describing the dependence of the index of refraction of water on wavelength in the visible and the near-UV ranges and at temperature from 0 °C to 100 °C is given. Parameters of the formula were determined by minimization of discrepancies between calculated and experimental data by use of an elite genetic algorithm with adaptive mutations. This algorithm was devised with a particular application in mind, the determination of model parameters. Its superiority over the simple genetic algorithm in locating the global minimum was demonstrated on a family of multiminima test functions for as many as 100 variables.

© 1999 Optical Society of America

OCIS Codes
(010.0010) Atmospheric and oceanic optics : Atmospheric and oceanic optics
(010.7340) Atmospheric and oceanic optics : Water
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(120.4530) Instrumentation, measurement, and metrology : Optical constants
(160.0160) Materials : Materials
(160.4760) Materials : Optical properties

Aleksandra B. Djurišić and Božidar V. Stanić, "Modeling the Temperature Dependence of the Index of Refraction of Liquid Water in the Visible and the Near-Ultraviolet Ranges by a Genetic Algorithm," Appl. Opt. 38, 11-17 (1999)

Sort:  Author  |  Year  |  Journal  |  Reset


  1. S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, pp. 671–680 (1983).
  2. D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine learning (Addison-Wesley, Reading, Mass., 1989).
  3. A. B. Djurišić, A. D. Rakić, and J. M. Elazar, “Modeling the optical constants of solids using acceptance-probability-controlled simulated annealing with adaptive move generation procedure,” Phys. Rev. E 55, 4797–4803 (1997).
  4. A. D. Rakić, J. M. Elazar, and A. B. Djurišić, “Acceptance-probability-controlled simulated annealing: a method for modeling the optical constants of solids,” Phys. Rev. E 52, 6862–6867 (1995).
  5. T. H. Han and W. W. Chang, “Estimation of the Gilbert model parameters using the simulated annealing method,” Electron. Lett. 32, 1256–1258 (1996).
  6. A. Franke, A. Stendal, O. Stenzel, and C. von Borczyskowski, “Gaussian quadrature approach to the calculation of the optical constants in the vicinity of inhomogeneously broadened absorption lines,” Pure Appl. Opt. 5, 845–853 (1996).
  7. A. D. Rakić and M. L. Majewski, “Modeling the optical dielectric function of GaAs and AlAs: Extension of Adachi’s model,” J. Appl. Phys. 80, 5909–5914 (1996).
  8. M. K. Vai, S. Prasad, N. C. Li, and F. Kai, “Modeling the microwave devices using simulated annealing optimization,” IEEE Trans. Electron. Devices 36, 761–762 (1989).
  9. M. W. Gutowski, “Smooth genetic algorithm,” J. Phys. A Math. Gen. 27, 7893–7905 (1994).
  10. H. Műhlenbein and D. Schlierkamp-Voosen, “Predictive models for the breeder genetic algorithm I. Continuous parameter optimization,” Evol. Comput. 1, 25–41 (1993).
  11. K. P. Wong and Y. W. Wong, “Floating-point number coding method for genetic algorithms,” in Proceedings of IEEE Australian and New Zealand Conference on Intelligent Information Systems 93 (University of Perth, Western Australia, 1993), pp. 512–516.
  12. K. P. Wong and Y. W. Wong, “Genetic and genetic/simulated annealing approaches to economic dispatch,” IEE Proc. Gen. Transm. Distrib. 141, 507–513 (1994).
  13. A. B. Djurišić, J. M. Elazar, and A. D. Rakić, “Modeling the optical constants of solids using genetic algorithms with parameter space size adjustment,” Opt. Commun. 134, 407–414 (1997).
  14. A. Chipperfield and R. Fleming, “Genetic algorithms in control system engineering,” Control Comput. 23, 88–94 (1995).
  15. R. Vemuri and R. Vemuri, “Genetic algorithm for MCM partitioning,” Electron. Lett. 30, 1270–1272 (1994).
  16. S. H. Clearwater and T. Hogg, “Problem structure heuristics and scaling behavior for genetic algorithm,” Artif. Intell. 81, 327–347 (1996).
  17. R. R. Brooks, S. S. Iyengar, and J. Chen, “Automatic correlation and calibration of noisy sensor readingsusing elite genetic algorithms,” Artif. Intell. 81, 329–354 (1996).
  18. F. Curatelli, “Implementation and evaluation of genetic algorithms for system partitioning,” Int. J. Electron. 78, 435–437 (1995).
  19. T. Bäck and H.-P. Schwefel, “Evolution strategies I: variants and their computational application,” in Genetic Algorithms in Engineering and Computer Science, G. Winter, J. Periaux, M. Galan, and P. Cuesta, eds. (Wiley, New York, 1995), pp. 111–126.
  20. D. Raynolds and J. Gonatann, “Stochastic modelling of genetic algorithms,” Artif. Intell. 82, 303–330 (1996).
  21. F. Aluffi-Pentini, V. Parisi, and F. Zirilli, “Global optimization and stochastic differential equations,” J. Optim. Theory Appl. 47, 1–16 (1985).
  22. A. Dekkers and E. Aarts, “Global optimization and simulated annealing,” Math. Programming, 50, 367–393 (1991).
  23. “Optical Constants,” in Group III: Condensed Matter, Vol. 38A of Landolt-Börnstein Numerical Data and Functional Relationships in Science and Technology, New Series, K.-H. Hellwege and O. Madelung, eds. (Springer-Verlag Berlin, 1996), pp. 17–22.
  24. P. D. T. Huibers, “Models for the wavelength dependence of the index of refraction of water,” Appl. Opt. 36, 3785–3787 (1997).
  25. G. T. McNeil, “Metrical fundamentals of underwater lens system,” Opt. Eng. 16, 128–139 (1977).
  26. W. Matthaus, “Empirische Gleichungen fúr den Brechungsindex des Meerwassers,” Beitr. Meereskd. 33, 73–78 (1974).
  27. X. Quan and E. S. Fry, “Empirical equation for the index of refraction of seawater,” Appl. Opt. 34, 3477–3480 (1995).
  28. P. Schiebener, J. Straub, J. M. H. Levelt, S. Engers, and J. S. Gallagher, “Refractive index of water and steam as a function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 19, 677–717 (1990).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited