Optimal cubature on the sphere and other orientation averaging schemes

Journal of Quantitative Spectroscopy and Radiative Transfer

Volumn 112, Issue 11, 2011, Pages 1741-1746

  Penttilä, Antti ^a   Lumme, Kari ^a  

^a UNIVERSITY OF HELSINKI   (Finland)

Author keywords

Cubature; Orientation averaging; Scattering; T matrix method

Indexed keywords

CUBATURE; FAST CONVERGENCE; NUMERICAL ORIENTATION AVERAGING; SCATTERING PROBLEMS; T-MATRIX METHOD;

CONVERGENCE OF NUMERICAL METHODS; OPTIMIZATION; SCATTERING;

SPHERES;

LIGHT SCATTERING; MATRIX; NUMERICAL METHOD; OPTIMIZATION; PERFORMANCE ASSESSMENT;

EID: 79958749324     PISSN: 00224073     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jqsrt.2011.02.001     Document Type: Article

References (13)

1. Mishchenko M., Travis L. Capabilities and limitations of a current FORTRAN implementation of the T-matrix method for randomly oriented, rotationally symmetric scatterers. J Quant Spectrosc Radiat Transf 1998, 60:309-324. doi:10.1016/S0022-4073(98)00008-9.
2. Mackowski D., Mishchenko M. Calculation of the T-matrix and the scattering matrix for ensembles of spheres. J Opt Soc Am A 1996, 13:2266-2278. doi:10.1364/JOSAA.13.002266.
3. Okada Y., Mann I., Mukai T., Köhler M. Extended calculation of polarization and intensity of fractal aggregates based on rigorous method for light scattering simulations with numerical orientation averaging. J Quant Spectrosc Radiat Transf 2008, 109(15):2613-2627. doi:10.1016/j.jqsrt.2008.05.014.
4. Draine B., Flatau P. The discrete dipole approximation for scattering calculations. J Opt Soc Am A 1994, 11:1491-1499. doi:10.1364/JOSAA.11.001491.
5. Yurkin M., Maltsev V., Hoekstra A. The discrete dipole approximation for simulation of light scattering by particles much larger than the wavelength. J Quant Spectrosc Radiat Transf 2007, 106:546-557. doi:10.1016/j.jqsrt.2007.01.033.
6. Sloan I., Womersley R. Extremal systems of points and numerical integration on the sphere. Adv Comput Math 2004, 21:107-125. doi:10.1023/B:ACOM.0000016428.25905.da.
7. Womersley R., Sloan I. How good can polynomial interpolation on the sphere be?. Adv Comput Math 2001, 14(3):195-226. doi:10.1023/A:1016630227163.
8. Okada Y. Efficient numerical orientation averaging of light scattering properties with a quasi-Monte-Carlo method. J Quant Spectrosc Radiat Transf 2008, 109(9):1719-1742. doi:10.1016/j.jqsrt.2008.01.002.
9. Niederreiter H. Random number generation and quasi-Monte Carlo methods. In: CBMS-NSF regional conference series in applied mathematics, vol. 63. Soc Industr Applied Math; 1992.
10. Lebedev V., Laikov D. A quadrature formula for the sphere of the 131st algebraic order of accuracy. Doklady Math 1999, 59(3):477-481.
11. Mishchenko M., Dlugach J., Liu L., Rosenbush V., Kiselev N., Shkuratov Y. Direct solutions of the Maxwell equations explain opposition phenomena observed for high-albedo solar system objects. Astrophys J 2009, 705:L118-L122. doi:10.1088/0004-637X/705/2/L118.
12. Mishchenko M., Dlugach J., Liu L. Azimuthal asymmetry of the coherent backscattering cone: theoretical results. Phys Rev A 2009, 80(5). 053824-1-10. doi:10.1103/PhysRevA.80.053824.
13. Mackowski D. T-matrix approach to calculating circular polarization of aggregates made of optically active materials. J Quant Spectrosc Radiat Transf 2011, 112:1726-1732. 10.1016/j.jqsrt.2011.02.003.