Abstract

The Gaussian-random-sphere model is employed for morphological characterization of nonspherical, irregular particles using an inverse light scattering technique. The synthetic measurement data consist of reduced scattering spectra caused by an aggregate of irregular particles randomly oriented in turbid media and are generated using the discrete dipole approximation. The proposed method simultaneously retrieves the concentration and shape parameters of particles using the data collected at multiple wavelengths. The performance of the inverse algorithm is tested using noise-corrupted data, in which up to 50% noise may be added to the observed scattering spectra.

© 2012 Optical Society of America

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References

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  1. R. Xu, Particle Characterization: Light Scattering Methods (Springer, 2000).
  2. C. Tropea, “Optical particle characterization in flows,” Annu. Rev. Fluid Mech. 43, 399–426 (2011).
    [CrossRef]
  3. B. J. Berne and R. Pecora, Dynamic Light Scattering: With Applications to Chemistry, Biology, and Physics (Dover, 2000).
  4. R. Pearson, R. M. Fitzgerald, and J. Polanco, “An inverse reconstruction model to retrieve aerosol size distribution from optical depth data,” J. Opt. A 9, 56–59 (2007).
    [CrossRef]
  5. T. Gutzler, T. R. Hillman, S. A. Alexandrov, and D. D. Sampson, “Three-dimensional depth-resolved and extended-resolution micro-particle characterization by holographic light scattering spectroscopy,” Opt. Express 18, 25116–25126 (2010).
    [CrossRef]
  6. M. R. Hajihashemi and H. Jiang, “Morphologic tomography of non-spherical particles using multispectral diffusing light measurements,” J. Biomed. Opt. 16, 116014 (2011).
    [CrossRef]
  7. Xinjun Zhu, Jin Shen, Wei Liu, Xianming Sun, and Yajing Wang, “Nonnegative least-squares truncated singular value decomposition to particle size distribution inversion from dynamic light scattering data,” Appl. Opt. 49, 6591–6596 (2010).
    [CrossRef]
  8. C. Li, S. Grobmyer, N. Massol, X. Liang, Q. Zhang, L. Chen, L. Fajardo, and H. Jiang, “Noninvasive in vivo tomographic optical imaging of cellular morphology in the breast: possible convergence of microscopic pathology and macroscopic radiology,” Med. Phys. 35, 2493–2501 (2008).
    [CrossRef]
  9. K. Muinonen, E. Zubko, J. Tyynelä, Y. G. Shkuratov, and Gorden Videen, “Light scattering by Gaussian random particles with discrete-dipole approximation,” J. Quant. Spectrosc. Radiat. Transfer 106, 360–377 (2007).
    [CrossRef]
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    [CrossRef]
  11. K. Muinonen and T. Pieniluoma, “Light scattering by Gaussian random ellipsoid particles: first results with discrete-dipole approximation,” J. Quant. Spectrosc. Radiat. Transfer 112, 1747–1752 (2011).
    [CrossRef]
  12. B. T. Draine, and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994).
    [CrossRef]
  13. M. A. Yurkin and A. G. Hoekstra, “The discrete dipole approximation: an overview and recent developments,” J. Quant. Spectrosc. Radiat. Transfer 106, 558–589 (2007).
    [CrossRef]
  14. B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
    [CrossRef]
  15. B. T Draine and P. J Flatau, “User guide to the discrete dipole approximation code DDSCAT 7.1,” http://arXiv.org/abs/1002.1505v1 (2010).
  16. A. Wax and V. Backman, Biomedical Applications of Light Scattering (McGraw-Hill, 2009).
  17. H. Jiang, Diffuse Optical Tomography: Principles and Applications (CRC Press, 2010).
  18. J. Nocedal and S. J. Wright, Numerical Optimization (Springer, 2006).

2011 (3)

M. R. Hajihashemi and H. Jiang, “Morphologic tomography of non-spherical particles using multispectral diffusing light measurements,” J. Biomed. Opt. 16, 116014 (2011).
[CrossRef]

C. Tropea, “Optical particle characterization in flows,” Annu. Rev. Fluid Mech. 43, 399–426 (2011).
[CrossRef]

K. Muinonen and T. Pieniluoma, “Light scattering by Gaussian random ellipsoid particles: first results with discrete-dipole approximation,” J. Quant. Spectrosc. Radiat. Transfer 112, 1747–1752 (2011).
[CrossRef]

2010 (2)

2008 (1)

C. Li, S. Grobmyer, N. Massol, X. Liang, Q. Zhang, L. Chen, L. Fajardo, and H. Jiang, “Noninvasive in vivo tomographic optical imaging of cellular morphology in the breast: possible convergence of microscopic pathology and macroscopic radiology,” Med. Phys. 35, 2493–2501 (2008).
[CrossRef]

2007 (3)

K. Muinonen, E. Zubko, J. Tyynelä, Y. G. Shkuratov, and Gorden Videen, “Light scattering by Gaussian random particles with discrete-dipole approximation,” J. Quant. Spectrosc. Radiat. Transfer 106, 360–377 (2007).
[CrossRef]

R. Pearson, R. M. Fitzgerald, and J. Polanco, “An inverse reconstruction model to retrieve aerosol size distribution from optical depth data,” J. Opt. A 9, 56–59 (2007).
[CrossRef]

M. A. Yurkin and A. G. Hoekstra, “The discrete dipole approximation: an overview and recent developments,” J. Quant. Spectrosc. Radiat. Transfer 106, 558–589 (2007).
[CrossRef]

2005 (1)

L. Xu, A. Taflove, and V. Backman, “Recent progress in exact and reduced-order modeling of light-scattering properties of complex structures,” IEEE J. Sel. Top. Quantum Electron. 11, 759–765 (2005).
[CrossRef]

1994 (1)

1988 (1)

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[CrossRef]

Alexandrov, S. A.

Backman, V.

L. Xu, A. Taflove, and V. Backman, “Recent progress in exact and reduced-order modeling of light-scattering properties of complex structures,” IEEE J. Sel. Top. Quantum Electron. 11, 759–765 (2005).
[CrossRef]

A. Wax and V. Backman, Biomedical Applications of Light Scattering (McGraw-Hill, 2009).

Berne, B. J.

B. J. Berne and R. Pecora, Dynamic Light Scattering: With Applications to Chemistry, Biology, and Physics (Dover, 2000).

Chen, L.

C. Li, S. Grobmyer, N. Massol, X. Liang, Q. Zhang, L. Chen, L. Fajardo, and H. Jiang, “Noninvasive in vivo tomographic optical imaging of cellular morphology in the breast: possible convergence of microscopic pathology and macroscopic radiology,” Med. Phys. 35, 2493–2501 (2008).
[CrossRef]

Draine, B. T.

B. T. Draine, and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994).
[CrossRef]

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[CrossRef]

Fajardo, L.

C. Li, S. Grobmyer, N. Massol, X. Liang, Q. Zhang, L. Chen, L. Fajardo, and H. Jiang, “Noninvasive in vivo tomographic optical imaging of cellular morphology in the breast: possible convergence of microscopic pathology and macroscopic radiology,” Med. Phys. 35, 2493–2501 (2008).
[CrossRef]

Fitzgerald, R. M.

R. Pearson, R. M. Fitzgerald, and J. Polanco, “An inverse reconstruction model to retrieve aerosol size distribution from optical depth data,” J. Opt. A 9, 56–59 (2007).
[CrossRef]

Flatau, P. J.

Grobmyer, S.

C. Li, S. Grobmyer, N. Massol, X. Liang, Q. Zhang, L. Chen, L. Fajardo, and H. Jiang, “Noninvasive in vivo tomographic optical imaging of cellular morphology in the breast: possible convergence of microscopic pathology and macroscopic radiology,” Med. Phys. 35, 2493–2501 (2008).
[CrossRef]

Gutzler, T.

Hajihashemi, M. R.

M. R. Hajihashemi and H. Jiang, “Morphologic tomography of non-spherical particles using multispectral diffusing light measurements,” J. Biomed. Opt. 16, 116014 (2011).
[CrossRef]

Hillman, T. R.

Hoekstra, A. G.

M. A. Yurkin and A. G. Hoekstra, “The discrete dipole approximation: an overview and recent developments,” J. Quant. Spectrosc. Radiat. Transfer 106, 558–589 (2007).
[CrossRef]

Jiang, H.

M. R. Hajihashemi and H. Jiang, “Morphologic tomography of non-spherical particles using multispectral diffusing light measurements,” J. Biomed. Opt. 16, 116014 (2011).
[CrossRef]

C. Li, S. Grobmyer, N. Massol, X. Liang, Q. Zhang, L. Chen, L. Fajardo, and H. Jiang, “Noninvasive in vivo tomographic optical imaging of cellular morphology in the breast: possible convergence of microscopic pathology and macroscopic radiology,” Med. Phys. 35, 2493–2501 (2008).
[CrossRef]

H. Jiang, Diffuse Optical Tomography: Principles and Applications (CRC Press, 2010).

Li, C.

C. Li, S. Grobmyer, N. Massol, X. Liang, Q. Zhang, L. Chen, L. Fajardo, and H. Jiang, “Noninvasive in vivo tomographic optical imaging of cellular morphology in the breast: possible convergence of microscopic pathology and macroscopic radiology,” Med. Phys. 35, 2493–2501 (2008).
[CrossRef]

Liang, X.

C. Li, S. Grobmyer, N. Massol, X. Liang, Q. Zhang, L. Chen, L. Fajardo, and H. Jiang, “Noninvasive in vivo tomographic optical imaging of cellular morphology in the breast: possible convergence of microscopic pathology and macroscopic radiology,” Med. Phys. 35, 2493–2501 (2008).
[CrossRef]

Liu, Wei

Massol, N.

C. Li, S. Grobmyer, N. Massol, X. Liang, Q. Zhang, L. Chen, L. Fajardo, and H. Jiang, “Noninvasive in vivo tomographic optical imaging of cellular morphology in the breast: possible convergence of microscopic pathology and macroscopic radiology,” Med. Phys. 35, 2493–2501 (2008).
[CrossRef]

Muinonen, K.

K. Muinonen and T. Pieniluoma, “Light scattering by Gaussian random ellipsoid particles: first results with discrete-dipole approximation,” J. Quant. Spectrosc. Radiat. Transfer 112, 1747–1752 (2011).
[CrossRef]

K. Muinonen, E. Zubko, J. Tyynelä, Y. G. Shkuratov, and Gorden Videen, “Light scattering by Gaussian random particles with discrete-dipole approximation,” J. Quant. Spectrosc. Radiat. Transfer 106, 360–377 (2007).
[CrossRef]

Nocedal, J.

J. Nocedal and S. J. Wright, Numerical Optimization (Springer, 2006).

Pearson, R.

R. Pearson, R. M. Fitzgerald, and J. Polanco, “An inverse reconstruction model to retrieve aerosol size distribution from optical depth data,” J. Opt. A 9, 56–59 (2007).
[CrossRef]

Pecora, R.

B. J. Berne and R. Pecora, Dynamic Light Scattering: With Applications to Chemistry, Biology, and Physics (Dover, 2000).

Pieniluoma, T.

K. Muinonen and T. Pieniluoma, “Light scattering by Gaussian random ellipsoid particles: first results with discrete-dipole approximation,” J. Quant. Spectrosc. Radiat. Transfer 112, 1747–1752 (2011).
[CrossRef]

Polanco, J.

R. Pearson, R. M. Fitzgerald, and J. Polanco, “An inverse reconstruction model to retrieve aerosol size distribution from optical depth data,” J. Opt. A 9, 56–59 (2007).
[CrossRef]

Sampson, D. D.

Shen, Jin

Shkuratov, Y. G.

K. Muinonen, E. Zubko, J. Tyynelä, Y. G. Shkuratov, and Gorden Videen, “Light scattering by Gaussian random particles with discrete-dipole approximation,” J. Quant. Spectrosc. Radiat. Transfer 106, 360–377 (2007).
[CrossRef]

Sun, Xianming

Taflove, A.

L. Xu, A. Taflove, and V. Backman, “Recent progress in exact and reduced-order modeling of light-scattering properties of complex structures,” IEEE J. Sel. Top. Quantum Electron. 11, 759–765 (2005).
[CrossRef]

Tropea, C.

C. Tropea, “Optical particle characterization in flows,” Annu. Rev. Fluid Mech. 43, 399–426 (2011).
[CrossRef]

Tyynelä, J.

K. Muinonen, E. Zubko, J. Tyynelä, Y. G. Shkuratov, and Gorden Videen, “Light scattering by Gaussian random particles with discrete-dipole approximation,” J. Quant. Spectrosc. Radiat. Transfer 106, 360–377 (2007).
[CrossRef]

Videen, Gorden

K. Muinonen, E. Zubko, J. Tyynelä, Y. G. Shkuratov, and Gorden Videen, “Light scattering by Gaussian random particles with discrete-dipole approximation,” J. Quant. Spectrosc. Radiat. Transfer 106, 360–377 (2007).
[CrossRef]

Wang, Yajing

Wax, A.

A. Wax and V. Backman, Biomedical Applications of Light Scattering (McGraw-Hill, 2009).

Wright, S. J.

J. Nocedal and S. J. Wright, Numerical Optimization (Springer, 2006).

Xu, L.

L. Xu, A. Taflove, and V. Backman, “Recent progress in exact and reduced-order modeling of light-scattering properties of complex structures,” IEEE J. Sel. Top. Quantum Electron. 11, 759–765 (2005).
[CrossRef]

Xu, R.

R. Xu, Particle Characterization: Light Scattering Methods (Springer, 2000).

Yurkin, M. A.

M. A. Yurkin and A. G. Hoekstra, “The discrete dipole approximation: an overview and recent developments,” J. Quant. Spectrosc. Radiat. Transfer 106, 558–589 (2007).
[CrossRef]

Zhang, Q.

C. Li, S. Grobmyer, N. Massol, X. Liang, Q. Zhang, L. Chen, L. Fajardo, and H. Jiang, “Noninvasive in vivo tomographic optical imaging of cellular morphology in the breast: possible convergence of microscopic pathology and macroscopic radiology,” Med. Phys. 35, 2493–2501 (2008).
[CrossRef]

Zhu, Xinjun

Zubko, E.

K. Muinonen, E. Zubko, J. Tyynelä, Y. G. Shkuratov, and Gorden Videen, “Light scattering by Gaussian random particles with discrete-dipole approximation,” J. Quant. Spectrosc. Radiat. Transfer 106, 360–377 (2007).
[CrossRef]

Annu. Rev. Fluid Mech. (1)

C. Tropea, “Optical particle characterization in flows,” Annu. Rev. Fluid Mech. 43, 399–426 (2011).
[CrossRef]

Appl. Opt. (1)

Astrophys. J. (1)

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

L. Xu, A. Taflove, and V. Backman, “Recent progress in exact and reduced-order modeling of light-scattering properties of complex structures,” IEEE J. Sel. Top. Quantum Electron. 11, 759–765 (2005).
[CrossRef]

J. Biomed. Opt. (1)

M. R. Hajihashemi and H. Jiang, “Morphologic tomography of non-spherical particles using multispectral diffusing light measurements,” J. Biomed. Opt. 16, 116014 (2011).
[CrossRef]

J. Opt. A (1)

R. Pearson, R. M. Fitzgerald, and J. Polanco, “An inverse reconstruction model to retrieve aerosol size distribution from optical depth data,” J. Opt. A 9, 56–59 (2007).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Quant. Spectrosc. Radiat. Transfer (3)

M. A. Yurkin and A. G. Hoekstra, “The discrete dipole approximation: an overview and recent developments,” J. Quant. Spectrosc. Radiat. Transfer 106, 558–589 (2007).
[CrossRef]

K. Muinonen and T. Pieniluoma, “Light scattering by Gaussian random ellipsoid particles: first results with discrete-dipole approximation,” J. Quant. Spectrosc. Radiat. Transfer 112, 1747–1752 (2011).
[CrossRef]

K. Muinonen, E. Zubko, J. Tyynelä, Y. G. Shkuratov, and Gorden Videen, “Light scattering by Gaussian random particles with discrete-dipole approximation,” J. Quant. Spectrosc. Radiat. Transfer 106, 360–377 (2007).
[CrossRef]

Med. Phys. (1)

C. Li, S. Grobmyer, N. Massol, X. Liang, Q. Zhang, L. Chen, L. Fajardo, and H. Jiang, “Noninvasive in vivo tomographic optical imaging of cellular morphology in the breast: possible convergence of microscopic pathology and macroscopic radiology,” Med. Phys. 35, 2493–2501 (2008).
[CrossRef]

Opt. Express (1)

Other (6)

B. J. Berne and R. Pecora, Dynamic Light Scattering: With Applications to Chemistry, Biology, and Physics (Dover, 2000).

R. Xu, Particle Characterization: Light Scattering Methods (Springer, 2000).

B. T Draine and P. J Flatau, “User guide to the discrete dipole approximation code DDSCAT 7.1,” http://arXiv.org/abs/1002.1505v1 (2010).

A. Wax and V. Backman, Biomedical Applications of Light Scattering (McGraw-Hill, 2009).

H. Jiang, Diffuse Optical Tomography: Principles and Applications (CRC Press, 2010).

J. Nocedal and S. J. Wright, Numerical Optimization (Springer, 2006).

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Figures (9)

Fig. 1.
Fig. 1.

Gaussian random spheres with different shape deviations. (a) Gaussian sphere with σ=0.05. (b) Top view of the Gaussian sphere with σ=0.05 represented by 27 216 dipoles. (c) Gaussian sphere with σ=0.3 (d) Top view of the Gaussian sphere with σ=0.3 represented by 30 433 dipoles.

Fig. 2.
Fig. 2.

(a) Simulation setup, (b) the exact images of reduced scattering coefficient at the shortest wavelength (638 nm), (c) the exact images of reduced scattering coefficient at the longest wavelength (775 nm).

Fig. 3.
Fig. 3.

The percentages of reconstruction error versus iteration number with different levels of noise in input data. (a) 10%-noise corrupted data, (b) 20%-noise corrupted data, (c) 50%-noise corrupted data.

Fig. 4.
Fig. 4.

Reconstructed parameters images using 10%-noise corrupted data. (a) mean particle size, (b) volume fraction, (c) shape deviation.

Fig. 5.
Fig. 5.

Reconstructed parameters with different levels of noise in input data. (a) particle size, 10% noise; (b) particle size, 20% noise; (c) particle size, 50% noise; (d) volume fraction, 10% noise; (e) volume fraction, 20% noise; (f) volume fraction, 50% noise; (g) shape deviation, 10% noise; (h) shape deviation, 20% noise; (i) shape deviation, 50% noise.

Fig. 6.
Fig. 6.

The exact images of reduced scattering coefficient at the first and fifth wavelengths; (a) 638 nm, (b) 775 nm.

Fig. 7.
Fig. 7.

The percentages of reconstruction errors versus iteration number with different levels of noise in input data. (a) 10%-noise corrupted data, (b) 20%-noise corrupted data, (c) 50%-noise corrupted data.

Fig. 8.
Fig. 8.

Reconstructed parameters images using 10%-noise added data. (a) mean particle size, (b) volume fraction, (c) shape deviation.

Fig. 9.
Fig. 9.

Reconstructed parameters with different levels of noise in input data. (a) particle size, 10% noise; (b) particle size, 20% noise; (c) particle size, 50% noise; (d) volume fraction, 10% noise; (e) volume fraction, 20% noise; (f) volume fraction, 50% noise; (g) shape deviation, 10% noise; (h) shape deviation, 20% noise; (i) shape deviation, 50% noise.

Tables (2)

Tables Icon

Table 1. The Parameters Used to Generate Synthetic Data at the Target Inclusion and Background Medium

Tables Icon

Table 2. The Parameters to Generate the Synthetic Data Using Eq. (7) in the Two Target Inclusion and Background Medium

Equations (13)

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

r(θ,ϕ)=aexp(s(θ,ϕ))1+σ2,
s(θ,ϕ)=l=0m=llslmYlm(θ,ϕ).
j=1NAij·P¯j=E¯inc,ii=1,2,,N.
Csca=k4|E0|2dΩ|j=1N[Pjn^·(n^·Pj)]exp(ikn^·r¯j)|2,
g=cosθ=k3Csca|E0|2dΩn^·k¯|j=1N[Pjn^·(n^·Pj)]exp(ikn^·r¯j)|2,
Qsca=Cscaπre2.
μs(λ)=ϕre,minre,maxσminσmax12πsrsσexp(12((rerem)2sr2+(σσm)2sσ2))(πre2Qsca(σ,re,m,λ)(1g(σ,re,m,λ))dredσ.
χ2=λj(μs(λj)oμs(λj)c)2.
Δχ=[μs(λ1)oμs(λ1)c,],
Δζ=[ΔϕΔsrΔre,mΔsσΔσm],
JTΔχT=JTJΔζT,
(JTJ+αI)ΔζT=JTΔχT,
Error function(normalized)=λj(μs(λj)oμs(λj)c)2λj(μs(λj)o)2.

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