Abstract

The PyTMatrix package was designed with the objective of providing a simple, extensible interface to T-Matrix electromagnetic scattering calculations performed using an extensively validated numerical core. The interface, implemented in the Python programming language, facilitates automation of the calculations and further analysis of the results through direct integration of both the inputs and the outputs of the calculations to numerical analysis software. This article describes the architecture and design of the package, illustrating how the concepts in the physics of electromagnetic scattering are mapped into data and code models in the computer software. The resulting capabilities and their consequences for the usability and performance of the package are explored.

© 2014 Optical Society of America

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References

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  1. P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53, 805–812 (1965).
    [CrossRef]
  2. M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: A review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
    [CrossRef]
  3. M. I. Mishchenko, L. D. Travis, A. Macke, “T-matrix method and its applications,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, 2000), chap. 6.
    [CrossRef]
  4. A. Gogoi, P. Rajkhowa, A. Choudhury, G. A. Ahmed, “Development of TUSCAT: A software for light scattering studies on spherical, spheroidal and cylindrical particles,” J. Quant. Spectrosc. Radiat. Transfer 112, 2713–2721 (2011).
    [CrossRef]
  5. J. Hellmers, K. Heiken, E. Foken, J. Thomaschewski, T. Wriedt, “Customizable web service interface for light scattering simulation programs,” J. Quant. Spectrosc. Radiat. Transfer 113, 2243–2250 (2012).
    [CrossRef]
  6. J. Fung, R. W. Perry, T. G. Dimiduk, V. N. Manoharan, “Imaging multiple colloidal particles by fitting electromagnetic scattering solutions to digital holograms,” J. Quant. Spectrosc. Radiat. Transfer 113, 2482–2489 (2012).
    [CrossRef]
  7. J. Leinonen, “Python code for T-matrix scattering calculations,” https://github.com/jleinonen/pytmatrix .
  8. E. Jones, T. Oliphant, P. Peterson, and others, “SciPy: Open source scientific tools for Python,” http://www.scipy.org/ (2001–).
  9. T. E. Oliphant, “Python for scientific computing,” Comput. Sci. Eng. 9, 10–20 (2007).
    [CrossRef]
  10. M. I. Mishchenko, L. D. Travis, “Capabilities and limitations of a current FORTRAN implementation of the T-matrix method for randomly oriented, rotationally symmetric scatterers,” J. Quant. Spectrosc. Radiat. Transfer 60, 309–324 (1998).
    [CrossRef]
  11. K. Aydin, “Centimeter and millimeter wave scattering from hydrometeors,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, 2000), chap. 16.
    [CrossRef]
  12. W. Gautschi, “Algorithm 726: ORTHPOL–a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules,” ACM Trans. Math. Software 20, 21–62 (1994).
    [CrossRef]
  13. A. D. Fernandes, W. R. Atchley, “Gaussian quadrature formulae for arbitrary positive measures,” Evol. Bioinform. Online 2, 251–259 (2006).
    [PubMed]
  14. J. Testud, S. Oury, R. A. Black, P. Amayenc, X. Dou, “The concept of “normalized” distribution to describe raindrop spectra: A tool for cloud physics and cloud remote sensing,” J. Appl. Meteorol. 40, 1118–1140 (2001).
    [CrossRef]
  15. J. Leinonen, D. Moisseev, M. Leskinen, W. Petersen, “A climatology of disdrometer measurements of rainfall in Finland over five years with implications for global radar observations,” J. Appl. Meteorol. Climatol. 51, 392–404 (2012).
    [CrossRef]
  16. H. C. van de Hulst, Light Scattering by Small Particles (John Wiley, 1957).
  17. V. N. Bringi, V. Chandrasekar, Polarimetric Doppler weather radar: principles and applications (Cambridge University, 2001).
    [CrossRef]
  18. J. Leinonen, “PyTMatrix Kdp example,” https://github.com/jleinonen/pytmatrix/wiki/PyTMatrix-Kdp-example .

2012 (3)

J. Hellmers, K. Heiken, E. Foken, J. Thomaschewski, T. Wriedt, “Customizable web service interface for light scattering simulation programs,” J. Quant. Spectrosc. Radiat. Transfer 113, 2243–2250 (2012).
[CrossRef]

J. Fung, R. W. Perry, T. G. Dimiduk, V. N. Manoharan, “Imaging multiple colloidal particles by fitting electromagnetic scattering solutions to digital holograms,” J. Quant. Spectrosc. Radiat. Transfer 113, 2482–2489 (2012).
[CrossRef]

J. Leinonen, D. Moisseev, M. Leskinen, W. Petersen, “A climatology of disdrometer measurements of rainfall in Finland over five years with implications for global radar observations,” J. Appl. Meteorol. Climatol. 51, 392–404 (2012).
[CrossRef]

2011 (1)

A. Gogoi, P. Rajkhowa, A. Choudhury, G. A. Ahmed, “Development of TUSCAT: A software for light scattering studies on spherical, spheroidal and cylindrical particles,” J. Quant. Spectrosc. Radiat. Transfer 112, 2713–2721 (2011).
[CrossRef]

2007 (1)

T. E. Oliphant, “Python for scientific computing,” Comput. Sci. Eng. 9, 10–20 (2007).
[CrossRef]

2006 (1)

A. D. Fernandes, W. R. Atchley, “Gaussian quadrature formulae for arbitrary positive measures,” Evol. Bioinform. Online 2, 251–259 (2006).
[PubMed]

2001 (1)

J. Testud, S. Oury, R. A. Black, P. Amayenc, X. Dou, “The concept of “normalized” distribution to describe raindrop spectra: A tool for cloud physics and cloud remote sensing,” J. Appl. Meteorol. 40, 1118–1140 (2001).
[CrossRef]

1998 (1)

M. I. Mishchenko, L. D. Travis, “Capabilities and limitations of a current FORTRAN implementation of the T-matrix method for randomly oriented, rotationally symmetric scatterers,” J. Quant. Spectrosc. Radiat. Transfer 60, 309–324 (1998).
[CrossRef]

1996 (1)

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: A review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

1994 (1)

W. Gautschi, “Algorithm 726: ORTHPOL–a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules,” ACM Trans. Math. Software 20, 21–62 (1994).
[CrossRef]

1965 (1)

P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53, 805–812 (1965).
[CrossRef]

Ahmed, G. A.

A. Gogoi, P. Rajkhowa, A. Choudhury, G. A. Ahmed, “Development of TUSCAT: A software for light scattering studies on spherical, spheroidal and cylindrical particles,” J. Quant. Spectrosc. Radiat. Transfer 112, 2713–2721 (2011).
[CrossRef]

Amayenc, P.

J. Testud, S. Oury, R. A. Black, P. Amayenc, X. Dou, “The concept of “normalized” distribution to describe raindrop spectra: A tool for cloud physics and cloud remote sensing,” J. Appl. Meteorol. 40, 1118–1140 (2001).
[CrossRef]

Atchley, W. R.

A. D. Fernandes, W. R. Atchley, “Gaussian quadrature formulae for arbitrary positive measures,” Evol. Bioinform. Online 2, 251–259 (2006).
[PubMed]

Aydin, K.

K. Aydin, “Centimeter and millimeter wave scattering from hydrometeors,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, 2000), chap. 16.
[CrossRef]

Black, R. A.

J. Testud, S. Oury, R. A. Black, P. Amayenc, X. Dou, “The concept of “normalized” distribution to describe raindrop spectra: A tool for cloud physics and cloud remote sensing,” J. Appl. Meteorol. 40, 1118–1140 (2001).
[CrossRef]

Bringi, V. N.

V. N. Bringi, V. Chandrasekar, Polarimetric Doppler weather radar: principles and applications (Cambridge University, 2001).
[CrossRef]

Chandrasekar, V.

V. N. Bringi, V. Chandrasekar, Polarimetric Doppler weather radar: principles and applications (Cambridge University, 2001).
[CrossRef]

Choudhury, A.

A. Gogoi, P. Rajkhowa, A. Choudhury, G. A. Ahmed, “Development of TUSCAT: A software for light scattering studies on spherical, spheroidal and cylindrical particles,” J. Quant. Spectrosc. Radiat. Transfer 112, 2713–2721 (2011).
[CrossRef]

Dimiduk, T. G.

J. Fung, R. W. Perry, T. G. Dimiduk, V. N. Manoharan, “Imaging multiple colloidal particles by fitting electromagnetic scattering solutions to digital holograms,” J. Quant. Spectrosc. Radiat. Transfer 113, 2482–2489 (2012).
[CrossRef]

Dou, X.

J. Testud, S. Oury, R. A. Black, P. Amayenc, X. Dou, “The concept of “normalized” distribution to describe raindrop spectra: A tool for cloud physics and cloud remote sensing,” J. Appl. Meteorol. 40, 1118–1140 (2001).
[CrossRef]

Fernandes, A. D.

A. D. Fernandes, W. R. Atchley, “Gaussian quadrature formulae for arbitrary positive measures,” Evol. Bioinform. Online 2, 251–259 (2006).
[PubMed]

Foken, E.

J. Hellmers, K. Heiken, E. Foken, J. Thomaschewski, T. Wriedt, “Customizable web service interface for light scattering simulation programs,” J. Quant. Spectrosc. Radiat. Transfer 113, 2243–2250 (2012).
[CrossRef]

Fung, J.

J. Fung, R. W. Perry, T. G. Dimiduk, V. N. Manoharan, “Imaging multiple colloidal particles by fitting electromagnetic scattering solutions to digital holograms,” J. Quant. Spectrosc. Radiat. Transfer 113, 2482–2489 (2012).
[CrossRef]

Gautschi, W.

W. Gautschi, “Algorithm 726: ORTHPOL–a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules,” ACM Trans. Math. Software 20, 21–62 (1994).
[CrossRef]

Gogoi, A.

A. Gogoi, P. Rajkhowa, A. Choudhury, G. A. Ahmed, “Development of TUSCAT: A software for light scattering studies on spherical, spheroidal and cylindrical particles,” J. Quant. Spectrosc. Radiat. Transfer 112, 2713–2721 (2011).
[CrossRef]

Heiken, K.

J. Hellmers, K. Heiken, E. Foken, J. Thomaschewski, T. Wriedt, “Customizable web service interface for light scattering simulation programs,” J. Quant. Spectrosc. Radiat. Transfer 113, 2243–2250 (2012).
[CrossRef]

Hellmers, J.

J. Hellmers, K. Heiken, E. Foken, J. Thomaschewski, T. Wriedt, “Customizable web service interface for light scattering simulation programs,” J. Quant. Spectrosc. Radiat. Transfer 113, 2243–2250 (2012).
[CrossRef]

Leinonen, J.

J. Leinonen, D. Moisseev, M. Leskinen, W. Petersen, “A climatology of disdrometer measurements of rainfall in Finland over five years with implications for global radar observations,” J. Appl. Meteorol. Climatol. 51, 392–404 (2012).
[CrossRef]

Leskinen, M.

J. Leinonen, D. Moisseev, M. Leskinen, W. Petersen, “A climatology of disdrometer measurements of rainfall in Finland over five years with implications for global radar observations,” J. Appl. Meteorol. Climatol. 51, 392–404 (2012).
[CrossRef]

Macke, A.

M. I. Mishchenko, L. D. Travis, A. Macke, “T-matrix method and its applications,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, 2000), chap. 6.
[CrossRef]

Mackowski, D. W.

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: A review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

Manoharan, V. N.

J. Fung, R. W. Perry, T. G. Dimiduk, V. N. Manoharan, “Imaging multiple colloidal particles by fitting electromagnetic scattering solutions to digital holograms,” J. Quant. Spectrosc. Radiat. Transfer 113, 2482–2489 (2012).
[CrossRef]

Mishchenko, M. I.

M. I. Mishchenko, L. D. Travis, “Capabilities and limitations of a current FORTRAN implementation of the T-matrix method for randomly oriented, rotationally symmetric scatterers,” J. Quant. Spectrosc. Radiat. Transfer 60, 309–324 (1998).
[CrossRef]

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: A review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

M. I. Mishchenko, L. D. Travis, A. Macke, “T-matrix method and its applications,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, 2000), chap. 6.
[CrossRef]

Moisseev, D.

J. Leinonen, D. Moisseev, M. Leskinen, W. Petersen, “A climatology of disdrometer measurements of rainfall in Finland over five years with implications for global radar observations,” J. Appl. Meteorol. Climatol. 51, 392–404 (2012).
[CrossRef]

Oliphant, T. E.

T. E. Oliphant, “Python for scientific computing,” Comput. Sci. Eng. 9, 10–20 (2007).
[CrossRef]

Oury, S.

J. Testud, S. Oury, R. A. Black, P. Amayenc, X. Dou, “The concept of “normalized” distribution to describe raindrop spectra: A tool for cloud physics and cloud remote sensing,” J. Appl. Meteorol. 40, 1118–1140 (2001).
[CrossRef]

Perry, R. W.

J. Fung, R. W. Perry, T. G. Dimiduk, V. N. Manoharan, “Imaging multiple colloidal particles by fitting electromagnetic scattering solutions to digital holograms,” J. Quant. Spectrosc. Radiat. Transfer 113, 2482–2489 (2012).
[CrossRef]

Petersen, W.

J. Leinonen, D. Moisseev, M. Leskinen, W. Petersen, “A climatology of disdrometer measurements of rainfall in Finland over five years with implications for global radar observations,” J. Appl. Meteorol. Climatol. 51, 392–404 (2012).
[CrossRef]

Rajkhowa, P.

A. Gogoi, P. Rajkhowa, A. Choudhury, G. A. Ahmed, “Development of TUSCAT: A software for light scattering studies on spherical, spheroidal and cylindrical particles,” J. Quant. Spectrosc. Radiat. Transfer 112, 2713–2721 (2011).
[CrossRef]

Testud, J.

J. Testud, S. Oury, R. A. Black, P. Amayenc, X. Dou, “The concept of “normalized” distribution to describe raindrop spectra: A tool for cloud physics and cloud remote sensing,” J. Appl. Meteorol. 40, 1118–1140 (2001).
[CrossRef]

Thomaschewski, J.

J. Hellmers, K. Heiken, E. Foken, J. Thomaschewski, T. Wriedt, “Customizable web service interface for light scattering simulation programs,” J. Quant. Spectrosc. Radiat. Transfer 113, 2243–2250 (2012).
[CrossRef]

Travis, L. D.

M. I. Mishchenko, L. D. Travis, “Capabilities and limitations of a current FORTRAN implementation of the T-matrix method for randomly oriented, rotationally symmetric scatterers,” J. Quant. Spectrosc. Radiat. Transfer 60, 309–324 (1998).
[CrossRef]

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: A review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

M. I. Mishchenko, L. D. Travis, A. Macke, “T-matrix method and its applications,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, 2000), chap. 6.
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (John Wiley, 1957).

Waterman, P. C.

P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53, 805–812 (1965).
[CrossRef]

Wriedt, T.

J. Hellmers, K. Heiken, E. Foken, J. Thomaschewski, T. Wriedt, “Customizable web service interface for light scattering simulation programs,” J. Quant. Spectrosc. Radiat. Transfer 113, 2243–2250 (2012).
[CrossRef]

ACM Trans. Math. Software (1)

W. Gautschi, “Algorithm 726: ORTHPOL–a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules,” ACM Trans. Math. Software 20, 21–62 (1994).
[CrossRef]

Comput. Sci. Eng. (1)

T. E. Oliphant, “Python for scientific computing,” Comput. Sci. Eng. 9, 10–20 (2007).
[CrossRef]

Evol. Bioinform. Online (1)

A. D. Fernandes, W. R. Atchley, “Gaussian quadrature formulae for arbitrary positive measures,” Evol. Bioinform. Online 2, 251–259 (2006).
[PubMed]

J. Appl. Meteorol. (1)

J. Testud, S. Oury, R. A. Black, P. Amayenc, X. Dou, “The concept of “normalized” distribution to describe raindrop spectra: A tool for cloud physics and cloud remote sensing,” J. Appl. Meteorol. 40, 1118–1140 (2001).
[CrossRef]

J. Appl. Meteorol. Climatol. (1)

J. Leinonen, D. Moisseev, M. Leskinen, W. Petersen, “A climatology of disdrometer measurements of rainfall in Finland over five years with implications for global radar observations,” J. Appl. Meteorol. Climatol. 51, 392–404 (2012).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (5)

M. I. Mishchenko, L. D. Travis, “Capabilities and limitations of a current FORTRAN implementation of the T-matrix method for randomly oriented, rotationally symmetric scatterers,” J. Quant. Spectrosc. Radiat. Transfer 60, 309–324 (1998).
[CrossRef]

M. I. Mishchenko, L. D. Travis, D. W. Mackowski, “T-matrix computations of light scattering by nonspherical particles: A review,” J. Quant. Spectrosc. Radiat. Transfer 55, 535–575 (1996).
[CrossRef]

A. Gogoi, P. Rajkhowa, A. Choudhury, G. A. Ahmed, “Development of TUSCAT: A software for light scattering studies on spherical, spheroidal and cylindrical particles,” J. Quant. Spectrosc. Radiat. Transfer 112, 2713–2721 (2011).
[CrossRef]

J. Hellmers, K. Heiken, E. Foken, J. Thomaschewski, T. Wriedt, “Customizable web service interface for light scattering simulation programs,” J. Quant. Spectrosc. Radiat. Transfer 113, 2243–2250 (2012).
[CrossRef]

J. Fung, R. W. Perry, T. G. Dimiduk, V. N. Manoharan, “Imaging multiple colloidal particles by fitting electromagnetic scattering solutions to digital holograms,” J. Quant. Spectrosc. Radiat. Transfer 113, 2482–2489 (2012).
[CrossRef]

Proc. IEEE (1)

P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53, 805–812 (1965).
[CrossRef]

Other (7)

H. C. van de Hulst, Light Scattering by Small Particles (John Wiley, 1957).

V. N. Bringi, V. Chandrasekar, Polarimetric Doppler weather radar: principles and applications (Cambridge University, 2001).
[CrossRef]

J. Leinonen, “PyTMatrix Kdp example,” https://github.com/jleinonen/pytmatrix/wiki/PyTMatrix-Kdp-example .

J. Leinonen, “Python code for T-matrix scattering calculations,” https://github.com/jleinonen/pytmatrix .

E. Jones, T. Oliphant, P. Peterson, and others, “SciPy: Open source scientific tools for Python,” http://www.scipy.org/ (2001–).

M. I. Mishchenko, L. D. Travis, A. Macke, “T-matrix method and its applications,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, 2000), chap. 6.
[CrossRef]

K. Aydin, “Centimeter and millimeter wave scattering from hydrometeors,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, 2000), chap. 16.
[CrossRef]

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Equations (5)

Equations on this page are rendered with MathJax. Learn more.

E sca = exp ( i k R ) R SE inc
I sca = 1 R 2 ZI inc
σ vv = 2 π Z 11 + Z 12 + Z 21 + Z 22
σ ev = 4 π k Im [ S 11 ( n , n ) ] .
0 π p ( β ) Z ( α , β ) d β i = 1 N w i Z ( α , β i )

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