## Convergence of the discrete dipole approximation. II. An extrapolation technique to increase the accuracy

JOSA A, Vol. 23, Issue 10, pp. 2592-2601 (2006)

http://dx.doi.org/10.1364/JOSAA.23.002592

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### Abstract

We propose an extrapolation technique that allows accuracy improvement of discrete dipole approximation computations. The performance of this technique was studied empirically on the basis of extensive simulations for five test cases using many different discretizations. The quality of the extrapolation improves with refining discretization, reaching extraordinary performance especially for cubically shaped particles. A 2-order-of-magnitude decrease of error is demonstrated. We also propose estimates of the extrapolation error, which are proven to be reliable. Finally, we propose a simple method to directly separate shape and discretization errors and illustrate this for one test case.

© 2006 Optical Society of America

**OCIS Codes**

(000.4430) General : Numerical approximation and analysis

(260.2110) Physical optics : Electromagnetic optics

(290.5850) Scattering : Scattering, particles

**ToC Category:**

Scattering

**History**

Original Manuscript: January 23, 2006

Manuscript Accepted: April 18, 2006

**Citation**

Maxim A. Yurkin, Valeri P. Maltsev, and Alfons G. Hoekstra, "Convergence of the discrete dipole approximation. II. An extrapolation technique to increase the accuracy," J. Opt. Soc. Am. A **23**, 2592-2601 (2006)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-23-10-2592

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### References

- E. M. Purcell and C. R. Pennypacker, "Scattering and adsorption of light by nonspherical dielectric grains," Astrophys. J. 186, 705-714 (1973). [CrossRef]
- B. T. Draine and P. J. Flatau, "Discrete-dipole approximation for scattering calculations," J. Opt. Soc. Am. A 11, 1491-1499 (1994).
- B. T. Draine, "The discrete dipole approximation for light scattering by irregular targets," in Light Scattering by Nonspherical Particles, Theory, Measurements, and Applications, M.I.Mishchenko, J.W.Hovenier, and L.D.Travis, eds. (Academic, 2000), pp. 131-145.
- B. T. Draine and P. J. Flatau, "User guide for the discrete dipole approximation code DDSCAT 6.1," http://xxx.arxiv.org/abs/astro-ph/0409262 (2004).
- J. J. Goodman, B. T. Draine, and P. J. Flatau, "Application of fast-Fourier-transform techniques to the discrete-dipole approximation," Opt. Lett. 16, 1198-1200 (1991).
- B. T. Draine, "The discrete-dipole approximation and its application to interstellar graphite grains," Astrophys. J. 333, 848-872 (1988). [CrossRef]
- J. I. Hage, J. M. Greenberg, and R. T. Wang, "Scattering from arbitrarily shaped particles—theory and experiment," Appl. Opt. 30, 1141-1152 (1991).
- F. Rouleau and P. G. Martin, "A new method to calculate the extinction properties of irregularly shaped particles," Astrophys. J. 414, 803-814 (1993). [CrossRef]
- N. B. Piller, "Influence of the edge meshes on the accuracy of the coupled-dipole approximation," Opt. Lett. 22, 1674-1676 (1997).
- N. B. Piller and O. J. F. Martin, "Increasing the performance of the coupled-dipole approximation: a spectral approach," IEEE Trans. Antennas Propag. 46, 1126-1137 (1998). [CrossRef]
- N. B. Piller, "Coupled-dipole approximation for high permittivity materials," Opt. Commun. 160, 10-14 (1999). [CrossRef]
- A. G. Hoekstra, J. Rahola, and P. M. A. Sloot, "Accuracy of internal fields in volume integral equation simulations of light scattering," Appl. Opt. 37, 8482-8497 (1998).
- S. D. Druger and B. V. Bronk, "Internal and scattered electric fields in the discrete dipole approximation," J. Opt. Soc. Am. B 16, 2239-2246 (1999).
- Y. L. Xu and B. A. S. Gustafson, "Comparison between multisphere light-scattering calculations: rigorous solution and discrete-dipole approximation," Astrophys. J. 513, 894-909 (1999). [CrossRef]
- M. J. Collinge and B. T. Draine, "Discrete-dipole approximation with polarizabilities that account for both finite wavelength and target geometry," J. Opt. Soc. Am. A 21, 2023-2028 (2004).
- K. F. Evans and G. L. Stephens, "Microwave radiative transfer through clouds composed of realistically shaped ice crystals. Part 1. Single scattering properties," J. Atmos. Sci. 52, 2041-2057 (1995).
- H. Okamoto, A. Macke, M. Quante, and E. Raschke, "Modeling of backscattering by non-spherical ice particles for the interpretation of cloud radar signals at 94GHz. An error analysis," Contrib. Atmos. Phys. 68, 319-334 (1995).
- C. L. Liu and A. J. Illingworth, "Error analysis of backscatter from discrete dipole approximation for different ice particle shapes," Atmos. Res. 44, 231-241 (1997).
- H. Lemke, H. Okamoto, and M. Quante, "Comment on error analysis of backscatter from discrete dipole approximation for different ice particle shapes [Liu, C.-L., Illingworth, A. J., 1997, Atmos. Res. 44, 231-241]," Atmos. Res. 49, 189-197 (1998).
- C. L. Liu and A. J. Illingworth, "Reply to comment by Lemke, Okamoto and Quante on 'Error analysis of backscatter from discrete dipole approximation for different ice particle shapes'," Atmos. Res. 50, 1-2 (1999).
- M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, "Convergence of the discrete dipole approximation. I. Theoretical analysis," J. Opt. Soc. Am. A 23, 2578-2591 (2006).
- W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, 1990).
- B. T. Draine and J. J. Goodman, "Beyond Clausius-Mossotti—wave propagation on a polarizable point lattice and the discrete dipole approximation," Astrophys. J. 405, 685-697 (1993). [CrossRef]
- "Amsterdam DDA," http://www.science.uva.nl/research/scs/software/adda.
- A. G. Hoekstra, M. D. Grimminck, and P. M. A. Sloot, "Large scale simulations of elastic light scattering by a fast discrete dipole approximation," Int. J. Mod. Phys. C 9, 87-102 (1998). [CrossRef]
- M. A. Yurkin, K. A. Semyanov, P. A. Tarasov, A. V. Chernyshev, A. G. Hoekstra, and V. P. Maltsev, "Experimental and theoretical study of light scattering by individual mature red blood cells by use of scanning flow cytometry and discrete dipole approximation," Appl. Opt. 44, 5249-5256 (2005). [CrossRef]
- "Description of the national computer cluster Lisa," http://www.sara.nl/userinfo/lisa/description/index.html (2005).
- J. Rahola, "On the eigenvalues of the volume integral operator of electromagnetic scattering," SIAM (Soc. Ind. Appl. Math.) J. Sci. Comput. (USA) 21, 1740-1754 (2000). [CrossRef]
- M. Frigo and S. G. Johnson, "The design and implementation of FFTW3," Proc. IEEE 93, 216-231 (2005).
- P. J. Flatau, "Improvements in the discrete-dipole approximation method of computing scattering and absorption," Opt. Lett. 22, 1205-1207 (1997).
- J. Rahola, "Solution of dense systems of linear equations in the discrete-dipole approximation," SIAM (Soc. Ind. Appl. Math.) J. Sci. Comput. (USA) 17, 78-89 (1996). [CrossRef]
- C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
- M. Min, J. W. Hovenier, A. Dominik, A. de Koter, and M. A. Yurkin, "Absorption and scattering properties of arbitrary shaped particles in the Rayleigh domain: a rapid computational method and a theoretical foundation for the statistical approach," J. Quant. Spectrosc. Radiat. Transf. 97, 161-180 (2006).
- P. C. Chaumet, A. Sentenac, and A. Rahmani, "Coupled dipole method for scatterers with large permittivity," Phys. Rev. E 70, 036606 (2004). [CrossRef]

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