Abstract

Volume scattering is an important effect in different fields, ranging from biology to lighting. Models for volume scattering usually rely on parameters that are estimated with inverse methods that iteratively fit simulations to experimental data. To obtain accurate estimates for these parameters, the scattered intensity distribution can be used in such fitting methods. However, it has been shown that for samples with long optical path lengths this type of data may result in poor parameter estimates. In this work, an inverse procedure is proposed that fits to scattered radiance distributions. By taking advantage of current generation graphics processing units, the method implemented is sufficiently efficient to allow performing an in-depth simulation study on the difference between using radiance or intensity distributions to estimate the volume scattering parameters of samples. This work shows that for samples with moderate optical path lengths, the intensity distribution contains sufficient information to accurately estimate the volume scattering properties. However, for longer optical path lengths, the descriptive power of the intensity distribution is not enough and radiance distribution based methods, such as the inverse method proposed, are better suited.

© 2017 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
  3. M. Kocifaj, H. Horvath, and M. Gangl, “Retrieval of aerosol aspect ratio from optical measurements in Vienna,” Atmos. Environ. 42, 2582–2592 (2008).
    [Crossref]
  4. S.-H. Ma, L.-S. Chen, and W.-C. Huang, “Effects of volume scattering diffusers on the color variation of white light LEDs,” J. Displ. Technol. 11, 13–21 (2015).
    [Crossref]
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    [Crossref] [PubMed]
  8. S. Leyre, Y. Meuret, G. Durinck, J. Hofkens, G. Deconinck, and P. Hanselaer, “Estimation of the effective phase function of bulk diffusing materials with the inverse adding-doubling method,” Appl. Opt. 53, 2117–2125 (2014).
    [Crossref] [PubMed]
  9. S. H. Shikder, M. Mourshed, and A. D. Price, “Luminaire position optimisation using radiance based simulation: a test case of a senior living room,” in Proceedings of the International Conference on Computing in Civil and Building Engineering (2010).
  10. R.-S. Chang, J.-Z. Tsai, T.-Y. Li, and H.-L. Liao, “Led backlight module by lightguide-diffusive component,” J. Displ. Technol. 8, 79–86 (2012).
    [Crossref]
  11. H. J. Kim and S. W. Kim, “Enhancement of physical and optical performances of polycarbonate-based diffusers for direct-lit LED backlight unit by incorporation of nanoclay platelets,” J. Appl. Polym. Sci. 133, 42973 (2016).
    [Crossref]
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    [Crossref] [PubMed]
  13. L. Wang, S. L. Jacques, and L. Zheng, “Mcml—monte carlo modeling of light transport in multi-layered tissues,” Computer methods and programs in biomedicine 47, 131–146 (1995).
    [Crossref]
  14. S. A. Prahl, “The adding-doubling method,” in “Optical-Thermal Response of Laser-Irradiated Tissue,” A. J. Welch and M. J. C. V. Gemert, eds. (SpringerUS, 1995), pp. 101–129.
    [Crossref]
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    [Crossref]
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    [Crossref]
  18. J. Nocedal and S. J. Wright, Numerical Optimization (Springer-Verlag, 2006).
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    [Crossref] [PubMed]

2016 (2)

H. J. Kim and S. W. Kim, “Enhancement of physical and optical performances of polycarbonate-based diffusers for direct-lit LED backlight unit by incorporation of nanoclay platelets,” J. Appl. Polym. Sci. 133, 42973 (2016).
[Crossref]

A. Correia, H. Cornelissen, S. Leyre, P. Hanselaer, and Y. Meuret, “Determination of volume scattering parameters that reproduce the luminance characteristics of diffusers,” Opt. Express 24, 11727 (2016).
[Crossref] [PubMed]

2015 (1)

S.-H. Ma, L.-S. Chen, and W.-C. Huang, “Effects of volume scattering diffusers on the color variation of white light LEDs,” J. Displ. Technol. 11, 13–21 (2015).
[Crossref]

2014 (1)

2012 (1)

R.-S. Chang, J.-Z. Tsai, T.-Y. Li, and H.-L. Liao, “Led backlight module by lightguide-diffusive component,” J. Displ. Technol. 8, 79–86 (2012).
[Crossref]

2011 (1)

2009 (1)

N. Honda, K. Ishii, A. Kimura, M. Sakai, and K. Awazu, “Determination of optical property changes by laser treatments using inverse adding-doubling method,” Proc. SPIE 7175, 71750Q (2009).
[Crossref]

2008 (2)

M. Kocifaj, H. Horvath, and M. Gangl, “Retrieval of aerosol aspect ratio from optical measurements in Vienna,” Atmos. Environ. 42, 2582–2592 (2008).
[Crossref]

A. Foi, M. Trimeche, V. Katkovnik, and K. Egiazarian, “Practical Poissonian-Gaussian noise modeling and fitting for single-image raw-data,” IEEE Trans. Image Process. 17, 1737–1754 (2008).
[Crossref] [PubMed]

2006 (2)

C. Audet and J. E. Dennis, “Mesh adaptive direct search algorithms for constrained optimization,” SIAM J. Optim. 17, 188–217 (2006).
[Crossref]

I. Turcu, “Effective phase function for light scattered by blood,” Appl. Opt. 45, 639–647 (2006).
[Crossref] [PubMed]

2001 (2)

A. Singhal, “Modern information retrieval: A brief overview,” IEEE Data Eng. Bull. 24, 35–43 (2001).

H.-M. Gutmann, “A radial basis function method for global optimization,” Journal of global optimization 19, 201–227 (2001).
[Crossref]

1995 (1)

L. Wang, S. L. Jacques, and L. Zheng, “Mcml—monte carlo modeling of light transport in multi-layered tissues,” Computer methods and programs in biomedicine 47, 131–146 (1995).
[Crossref]

1993 (2)

Audet, C.

C. Audet and J. E. Dennis, “Mesh adaptive direct search algorithms for constrained optimization,” SIAM J. Optim. 17, 188–217 (2006).
[Crossref]

Awazu, K.

N. Honda, K. Ishii, A. Kimura, M. Sakai, and K. Awazu, “Determination of optical property changes by laser treatments using inverse adding-doubling method,” Proc. SPIE 7175, 71750Q (2009).
[Crossref]

Chang, R.-S.

R.-S. Chang, J.-Z. Tsai, T.-Y. Li, and H.-L. Liao, “Led backlight module by lightguide-diffusive component,” J. Displ. Technol. 8, 79–86 (2012).
[Crossref]

Chen, L.-S.

S.-H. Ma, L.-S. Chen, and W.-C. Huang, “Effects of volume scattering diffusers on the color variation of white light LEDs,” J. Displ. Technol. 11, 13–21 (2015).
[Crossref]

Cornelissen, H.

Correia, A.

Deconinck, G.

Dennis, J. E.

C. Audet and J. E. Dennis, “Mesh adaptive direct search algorithms for constrained optimization,” SIAM J. Optim. 17, 188–217 (2006).
[Crossref]

Durinck, G.

Egiazarian, K.

A. Foi, M. Trimeche, V. Katkovnik, and K. Egiazarian, “Practical Poissonian-Gaussian noise modeling and fitting for single-image raw-data,” IEEE Trans. Image Process. 17, 1737–1754 (2008).
[Crossref] [PubMed]

Foi, A.

A. Foi, M. Trimeche, V. Katkovnik, and K. Egiazarian, “Practical Poissonian-Gaussian noise modeling and fitting for single-image raw-data,” IEEE Trans. Image Process. 17, 1737–1754 (2008).
[Crossref] [PubMed]

Gangl, M.

M. Kocifaj, H. Horvath, and M. Gangl, “Retrieval of aerosol aspect ratio from optical measurements in Vienna,” Atmos. Environ. 42, 2582–2592 (2008).
[Crossref]

Gutmann, H.-M.

H.-M. Gutmann, “A radial basis function method for global optimization,” Journal of global optimization 19, 201–227 (2001).
[Crossref]

Hanselaer, P.

Hofkens, J.

Honda, N.

N. Honda, K. Ishii, A. Kimura, M. Sakai, and K. Awazu, “Determination of optical property changes by laser treatments using inverse adding-doubling method,” Proc. SPIE 7175, 71750Q (2009).
[Crossref]

Horvath, H.

M. Kocifaj, H. Horvath, and M. Gangl, “Retrieval of aerosol aspect ratio from optical measurements in Vienna,” Atmos. Environ. 42, 2582–2592 (2008).
[Crossref]

Huang, W.-C.

S.-H. Ma, L.-S. Chen, and W.-C. Huang, “Effects of volume scattering diffusers on the color variation of white light LEDs,” J. Displ. Technol. 11, 13–21 (2015).
[Crossref]

Ishii, K.

N. Honda, K. Ishii, A. Kimura, M. Sakai, and K. Awazu, “Determination of optical property changes by laser treatments using inverse adding-doubling method,” Proc. SPIE 7175, 71750Q (2009).
[Crossref]

Jacques, S. L.

L. Wang, S. L. Jacques, and L. Zheng, “Mcml—monte carlo modeling of light transport in multi-layered tissues,” Computer methods and programs in biomedicine 47, 131–146 (1995).
[Crossref]

Katkovnik, V.

A. Foi, M. Trimeche, V. Katkovnik, and K. Egiazarian, “Practical Poissonian-Gaussian noise modeling and fitting for single-image raw-data,” IEEE Trans. Image Process. 17, 1737–1754 (2008).
[Crossref] [PubMed]

Kim, H. J.

H. J. Kim and S. W. Kim, “Enhancement of physical and optical performances of polycarbonate-based diffusers for direct-lit LED backlight unit by incorporation of nanoclay platelets,” J. Appl. Polym. Sci. 133, 42973 (2016).
[Crossref]

Kim, S. W.

H. J. Kim and S. W. Kim, “Enhancement of physical and optical performances of polycarbonate-based diffusers for direct-lit LED backlight unit by incorporation of nanoclay platelets,” J. Appl. Polym. Sci. 133, 42973 (2016).
[Crossref]

Kimura, A.

N. Honda, K. Ishii, A. Kimura, M. Sakai, and K. Awazu, “Determination of optical property changes by laser treatments using inverse adding-doubling method,” Proc. SPIE 7175, 71750Q (2009).
[Crossref]

Kocifaj, M.

M. Kocifaj, H. Horvath, and M. Gangl, “Retrieval of aerosol aspect ratio from optical measurements in Vienna,” Atmos. Environ. 42, 2582–2592 (2008).
[Crossref]

Leyre, S.

Li, T.-Y.

R.-S. Chang, J.-Z. Tsai, T.-Y. Li, and H.-L. Liao, “Led backlight module by lightguide-diffusive component,” J. Displ. Technol. 8, 79–86 (2012).
[Crossref]

Liao, H.-L.

R.-S. Chang, J.-Z. Tsai, T.-Y. Li, and H.-L. Liao, “Led backlight module by lightguide-diffusive component,” J. Displ. Technol. 8, 79–86 (2012).
[Crossref]

Ma, S.-H.

S.-H. Ma, L.-S. Chen, and W.-C. Huang, “Effects of volume scattering diffusers on the color variation of white light LEDs,” J. Displ. Technol. 11, 13–21 (2015).
[Crossref]

McKee, D.

Meuret, Y.

Mourshed, M.

S. H. Shikder, M. Mourshed, and A. D. Price, “Luminaire position optimisation using radiance based simulation: a test case of a senior living room,” in Proceedings of the International Conference on Computing in Civil and Building Engineering (2010).

Nocedal, J.

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

Piskozub, J.

Prahl, S. A.

S. A. Prahl, M. J. van Gemert, and A. J. Welch, “Determining the optical properties of turbid media by using the adding-doubling method,” Appl. Opt. 32, 559–568 (1993).
[Crossref] [PubMed]

S. A. Prahl, “The adding-doubling method,” in “Optical-Thermal Response of Laser-Irradiated Tissue,” A. J. Welch and M. J. C. V. Gemert, eds. (SpringerUS, 1995), pp. 101–129.
[Crossref]

Price, A. D.

S. H. Shikder, M. Mourshed, and A. D. Price, “Luminaire position optimisation using radiance based simulation: a test case of a senior living room,” in Proceedings of the International Conference on Computing in Civil and Building Engineering (2010).

Sakai, M.

N. Honda, K. Ishii, A. Kimura, M. Sakai, and K. Awazu, “Determination of optical property changes by laser treatments using inverse adding-doubling method,” Proc. SPIE 7175, 71750Q (2009).
[Crossref]

Shikder, S. H.

S. H. Shikder, M. Mourshed, and A. D. Price, “Luminaire position optimisation using radiance based simulation: a test case of a senior living room,” in Proceedings of the International Conference on Computing in Civil and Building Engineering (2010).

Singhal, A.

A. Singhal, “Modern information retrieval: A brief overview,” IEEE Data Eng. Bull. 24, 35–43 (2001).

Trimeche, M.

A. Foi, M. Trimeche, V. Katkovnik, and K. Egiazarian, “Practical Poissonian-Gaussian noise modeling and fitting for single-image raw-data,” IEEE Trans. Image Process. 17, 1737–1754 (2008).
[Crossref] [PubMed]

Tsai, J.-Z.

R.-S. Chang, J.-Z. Tsai, T.-Y. Li, and H.-L. Liao, “Led backlight module by lightguide-diffusive component,” J. Displ. Technol. 8, 79–86 (2012).
[Crossref]

Tuchin, V. V.

V. V. Tuchin, “Laser light scattering in biomedical diagnostics and therapy,” J. Laser Appl. 5, 43–60 (1993).
[Crossref]

Turcu, I.

van Gemert, M. J.

Wang, L.

L. Wang, S. L. Jacques, and L. Zheng, “Mcml—monte carlo modeling of light transport in multi-layered tissues,” Computer methods and programs in biomedicine 47, 131–146 (1995).
[Crossref]

Welch, A. J.

Wright, S. J.

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

Zheng, L.

L. Wang, S. L. Jacques, and L. Zheng, “Mcml—monte carlo modeling of light transport in multi-layered tissues,” Computer methods and programs in biomedicine 47, 131–146 (1995).
[Crossref]

Appl. Opt. (3)

Atmos. Environ. (1)

M. Kocifaj, H. Horvath, and M. Gangl, “Retrieval of aerosol aspect ratio from optical measurements in Vienna,” Atmos. Environ. 42, 2582–2592 (2008).
[Crossref]

Computer methods and programs in biomedicine (1)

L. Wang, S. L. Jacques, and L. Zheng, “Mcml—monte carlo modeling of light transport in multi-layered tissues,” Computer methods and programs in biomedicine 47, 131–146 (1995).
[Crossref]

IEEE Data Eng. Bull. (1)

A. Singhal, “Modern information retrieval: A brief overview,” IEEE Data Eng. Bull. 24, 35–43 (2001).

IEEE Trans. Image Process. (1)

A. Foi, M. Trimeche, V. Katkovnik, and K. Egiazarian, “Practical Poissonian-Gaussian noise modeling and fitting for single-image raw-data,” IEEE Trans. Image Process. 17, 1737–1754 (2008).
[Crossref] [PubMed]

J. Appl. Polym. Sci. (1)

H. J. Kim and S. W. Kim, “Enhancement of physical and optical performances of polycarbonate-based diffusers for direct-lit LED backlight unit by incorporation of nanoclay platelets,” J. Appl. Polym. Sci. 133, 42973 (2016).
[Crossref]

J. Displ. Technol. (2)

R.-S. Chang, J.-Z. Tsai, T.-Y. Li, and H.-L. Liao, “Led backlight module by lightguide-diffusive component,” J. Displ. Technol. 8, 79–86 (2012).
[Crossref]

S.-H. Ma, L.-S. Chen, and W.-C. Huang, “Effects of volume scattering diffusers on the color variation of white light LEDs,” J. Displ. Technol. 11, 13–21 (2015).
[Crossref]

J. Laser Appl. (1)

V. V. Tuchin, “Laser light scattering in biomedical diagnostics and therapy,” J. Laser Appl. 5, 43–60 (1993).
[Crossref]

Journal of global optimization (1)

H.-M. Gutmann, “A radial basis function method for global optimization,” Journal of global optimization 19, 201–227 (2001).
[Crossref]

Opt. Express (2)

Proc. SPIE (1)

N. Honda, K. Ishii, A. Kimura, M. Sakai, and K. Awazu, “Determination of optical property changes by laser treatments using inverse adding-doubling method,” Proc. SPIE 7175, 71750Q (2009).
[Crossref]

SIAM J. Optim. (1)

C. Audet and J. E. Dennis, “Mesh adaptive direct search algorithms for constrained optimization,” SIAM J. Optim. 17, 188–217 (2006).
[Crossref]

Other (3)

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

S. H. Shikder, M. Mourshed, and A. D. Price, “Luminaire position optimisation using radiance based simulation: a test case of a senior living room,” in Proceedings of the International Conference on Computing in Civil and Building Engineering (2010).

S. A. Prahl, “The adding-doubling method,” in “Optical-Thermal Response of Laser-Irradiated Tissue,” A. J. Welch and M. J. C. V. Gemert, eds. (SpringerUS, 1995), pp. 101–129.
[Crossref]

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Figures (9)

Fig. 1
Fig. 1

Cosine distance between the radiance distribution of samples simulated with LightTools and with the GPU ray-tracer. Left and right inserts show cross-sections (images) of the radiance distributions simulated with LightTools (top) and the GPU ray-tracer (bottom) for two specific samples.

Fig. 2
Fig. 2

Time taken over amount of rays traced for both the LightTools ray-tracer and the GPU ray-tracer for a long optical path length sample shown in (a) a logarithmic scale and (b) a linear scale. Results shown are the average of 5 runs, including all overheads, using a workstation with an Intel Xeon Processor E5-2630 v3 CPU and a NVIDIA Titan X (Maxwell) GPU.

Fig. 3
Fig. 3

Cross-sections of the objective function domain calculated for a short optical path length sample. The three cross-sections intersect at the set of volume scattering parameters of the objective sample.

Fig. 4
Fig. 4

Radiance based objective function cross-sections perpendicular to the (a,d) μa axis, (b,e) the μs axis and (c,f) the g axis. The red cross indicates the true solution and correspond to a sample with (a–c) a short optical path length and (d–f) a long optical path length.

Fig. 5
Fig. 5

Radiance based objective function cross-sections for the long optical path length sample. The cross-sections were calculated by tracing (a) 226 rays, (b) 228 rays and (c) 230 rays.

Fig. 6
Fig. 6

Signal before and after adding artificial noise for a sample with μs = 31.40 mm−1, μa = 6.60 mm−1 and g = 0.89. In (a) the reflected and transmitted intensity are shown, with the noisy versions in black, while a cross-section of the transmitted radiance distribution is shown (b) before adding noise and (c) after adding noise.

Fig. 7
Fig. 7

Error analysis of the results from the inverse Monte Carlo method. In (a) the average cosine distance between original and fitted radiance distribution is shown, while in (b) the average percent error between original and estimated volume scattering parameters is presented.

Fig. 8
Fig. 8

Intensity based objective function cross-sections perpendicular to the (a,d) μa axis, (b,e) the μs axis and (c,f) the g axis. The red cross indicates the true solution and correspond to a sample with a (a–c) short optical path length and (d–f) a long optical path length.

Fig. 9
Fig. 9

Objective function cross-sections perpendicular to the (a,d) μa axis, (b,e) the μs axis and (c,f) the g axis. The cross-sections were calculated using (a–c) radiance distributions and (d–f) intensity distributions. The red cross indicates the real solution and correspond to a sample with μs = 33.69 mm−1, μa = 7.30 mm−1 and g = 0.89.

Equations (2)

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C D ( x , y ) = 1 π arccos ( i n x i y i i n x i 2 i n y i 2 )
S = S + r n S . f P + f G

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