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

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

http://dx.doi.org/10.1364/AO.38.000011

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### Abstract

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

**Citation**

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)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-38-1-11

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### References

- S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, pp. 671–680 (1983).
- D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine learning (Addison-Wesley, Reading, Mass., 1989).
- 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).
- 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).
- T. H. Han and W. W. Chang, “Estimation of the Gilbert model parameters using the simulated annealing method,” Electron. Lett. 32, 1256–1258 (1996).
- 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).
- 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).
- 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).
- M. W. Gutowski, “Smooth genetic algorithm,” J. Phys. A Math. Gen. 27, 7893–7905 (1994).
- H. Műhlenbein and D. Schlierkamp-Voosen, “Predictive models for the breeder genetic algorithm I. Continuous parameter optimization,” Evol. Comput. 1, 25–41 (1993).
- 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.
- 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).
- 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).
- A. Chipperfield and R. Fleming, “Genetic algorithms in control system engineering,” Control Comput. 23, 88–94 (1995).
- R. Vemuri and R. Vemuri, “Genetic algorithm for MCM partitioning,” Electron. Lett. 30, 1270–1272 (1994).
- S. H. Clearwater and T. Hogg, “Problem structure heuristics and scaling behavior for genetic algorithm,” Artif. Intell. 81, 327–347 (1996).
- 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).
- F. Curatelli, “Implementation and evaluation of genetic algorithms for system partitioning,” Int. J. Electron. 78, 435–437 (1995).
- 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.
- D. Raynolds and J. Gonatann, “Stochastic modelling of genetic algorithms,” Artif. Intell. 82, 303–330 (1996).
- F. Aluffi-Pentini, V. Parisi, and F. Zirilli, “Global optimization and stochastic differential equations,” J. Optim. Theory Appl. 47, 1–16 (1985).
- A. Dekkers and E. Aarts, “Global optimization and simulated annealing,” Math. Programming, 50, 367–393 (1991).
- “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.
- P. D. T. Huibers, “Models for the wavelength dependence of the index of refraction of water,” Appl. Opt. 36, 3785–3787 (1997).
- G. T. McNeil, “Metrical fundamentals of underwater lens system,” Opt. Eng. 16, 128–139 (1977).
- W. Matthaus, “Empirische Gleichungen fúr den Brechungsindex des Meerwassers,” Beitr. Meereskd. 33, 73–78 (1974).
- X. Quan and E. S. Fry, “Empirical equation for the index of refraction of seawater,” Appl. Opt. 34, 3477–3480 (1995).
- 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).

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