Abstract

The extension of a well-known inverse technique, inverse adding-doubling (IAD), is investigated for determining the volume scattering properties of diffusers for display and lighting applications. The luminance characteristics of volume scattering diffusers are vital for these applications. Through a simulation study, it is shown that fitting solely to the scattered (angular) intensity information with the extended IAD method, results in a volume scattering characterization that also reproduces the correct (spatial and angular) luminance characteristics for a wide range of samples. The gap between the simulation work and the experimental application of the investigated fitting procedure is bridged by considering the effect of experimental error in the scattered intensity distributions. This does not significantly alter the presented conclusions.

© 2016 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  6. 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]
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2016 (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]

2015 (2)

2014 (2)

2013 (2)

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 (3)

M. Kocifaj, H. Horvath, and M. Gangl, “Retrieval of aerosol aspect ratio from optical measurements in Vienna,” Atmos. Environ. 42(11), 2582–2592 (2008).
[Crossref]

F. B. Leloup, S. Forment, P. Dutré, M. R. Pointer, and P. Hanselaer, “Design of an instrument for measuring the spectral bidirectional scatter distribution function,” Appl. Opt. 47(29), 5454–5467 (2008).
[Crossref] [PubMed]

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(10), 1737–1754 (2008).
[Crossref] [PubMed]

2003 (1)

J.-G. Chang, C.-Y. Lin, C.-C. Hwang, and R.-J. Yang, “Optical design and analysis of LCD backlight units using ASAP,” Opt. Eng. Mag. 82, 75–89 (2003).

1994 (1)

D. Whitley, “A genetic algorithm tutorial,” Stat. Comput. 4(2), 65–85 (1994).
[Crossref]

1993 (2)

1988 (1)

1971 (1)

J. Hansen and J. Hovenier, “The doubling method applied to multiple scattering of polarized light,” J. Quant. Spectrosc. Radiat. Transfer 11(6), 809–812 (1971).
[Crossref]

Audenaert, J.

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, J.-G.

J.-G. Chang, C.-Y. Lin, C.-C. Hwang, and R.-J. Yang, “Optical design and analysis of LCD backlight units using ASAP,” Opt. Eng. Mag. 82, 75–89 (2003).

Chen, L.-S.

Choi, J.

J. Choi, K.-S. Hahn, H. Seo, and S.-C. Kim, “Design, analysis, and optimization of LCD backlight unit using ray tracing simulation,” in Proceedings of the International Conference Computational Science and Its Applications – ICCSA 2004, A. Laganá, M. L. Gavrilova, V. Kumar, Y. Mun, C. J. K. Tan, and O. Gervasi, eds. (Springer BerlinHeidelberg, 2004), pp. 837–846.
[Crossref]

Deconinck, G.

Durinck, G.

Dutré, P.

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(10), 1737–1754 (2008).
[Crossref] [PubMed]

Flynn, M. J.

D. S. Hirschorn, E. A. Krupinski, and M. J. Flynn, “PACS displays: how to select the right display technology,” J. Am. Coll. Radiol. 11(12), 1270–1276 (2014).
[Crossref]

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(10), 1737–1754 (2008).
[Crossref] [PubMed]

Forment, S.

Gangl, M.

M. Kocifaj, H. Horvath, and M. Gangl, “Retrieval of aerosol aspect ratio from optical measurements in Vienna,” Atmos. Environ. 42(11), 2582–2592 (2008).
[Crossref]

Hahn, K.-S.

J. Choi, K.-S. Hahn, H. Seo, and S.-C. Kim, “Design, analysis, and optimization of LCD backlight unit using ray tracing simulation,” in Proceedings of the International Conference Computational Science and Its Applications – ICCSA 2004, A. Laganá, M. L. Gavrilova, V. Kumar, Y. Mun, C. J. K. Tan, and O. Gervasi, eds. (Springer BerlinHeidelberg, 2004), pp. 837–846.
[Crossref]

Hanselaer, P.

Hansen, J.

J. Hansen and J. Hovenier, “The doubling method applied to multiple scattering of polarized light,” J. Quant. Spectrosc. Radiat. Transfer 11(6), 809–812 (1971).
[Crossref]

Hirschorn, D. S.

D. S. Hirschorn, E. A. Krupinski, and M. J. Flynn, “PACS displays: how to select the right display technology,” J. Am. Coll. Radiol. 11(12), 1270–1276 (2014).
[Crossref]

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(11), 2582–2592 (2008).
[Crossref]

Hovenier, J.

J. Hansen and J. Hovenier, “The doubling method applied to multiple scattering of polarized light,” J. Quant. Spectrosc. Radiat. Transfer 11(6), 809–812 (1971).
[Crossref]

Huang, W.-C.

Hwang, C.-C.

J.-G. Chang, C.-Y. Lin, C.-C. Hwang, and R.-J. Yang, “Optical design and analysis of LCD backlight units using ASAP,” Opt. Eng. Mag. 82, 75–89 (2003).

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]

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(10), 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]

Kim, S.-C.

J. Choi, K.-S. Hahn, H. Seo, and S.-C. Kim, “Design, analysis, and optimization of LCD backlight unit using ray tracing simulation,” in Proceedings of the International Conference Computational Science and Its Applications – ICCSA 2004, A. Laganá, M. L. Gavrilova, V. Kumar, Y. Mun, C. J. K. Tan, and O. Gervasi, eds. (Springer BerlinHeidelberg, 2004), pp. 837–846.
[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(11), 2582–2592 (2008).
[Crossref]

Krupinski, E. A.

D. S. Hirschorn, E. A. Krupinski, and M. J. Flynn, “PACS displays: how to select the right display technology,” J. Am. Coll. Radiol. 11(12), 1270–1276 (2014).
[Crossref]

Leloup, F. B.

Leyre, S.

Lin, C.-Y.

J.-G. Chang, C.-Y. Lin, C.-C. Hwang, and R.-J. Yang, “Optical design and analysis of LCD backlight units using ASAP,” Opt. Eng. Mag. 82, 75–89 (2003).

Ma, S.-H.

Meuret, Y.

Moon, J.

Nocedal, J.

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

Oh, K.

Pointer, M. R.

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(4), 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]

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]

Seo, H.

J. Choi, K.-S. Hahn, H. Seo, and S.-C. Kim, “Design, analysis, and optimization of LCD backlight unit using ray tracing simulation,” in Proceedings of the International Conference Computational Science and Its Applications – ICCSA 2004, A. Laganá, M. L. Gavrilova, V. Kumar, Y. Mun, C. J. K. Tan, and O. Gervasi, eds. (Springer BerlinHeidelberg, 2004), pp. 837–846.
[Crossref]

Shepherd, A. P.

Steinke, J. M.

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(10), 1737–1754 (2008).
[Crossref] [PubMed]

Tuchin, V. V.

V. V. Tuchin, “Laser light scattering in biomedical diagnostics and therapy,” J. Laser Appl. 5(2), 43–60 (1993).
[Crossref]

van Gemert, M. J.

Welch, A. J.

Whitley, D.

D. Whitley, “A genetic algorithm tutorial,” Stat. Comput. 4(2), 65–85 (1994).
[Crossref]

Wright, S. J.

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

Yang, R.-J.

J.-G. Chang, C.-Y. Lin, C.-C. Hwang, and R.-J. Yang, “Optical design and analysis of LCD backlight units using ASAP,” Opt. Eng. Mag. 82, 75–89 (2003).

Appl. Opt. (5)

Atmos. Environ. (1)

M. Kocifaj, H. Horvath, and M. Gangl, “Retrieval of aerosol aspect ratio from optical measurements in Vienna,” Atmos. Environ. 42(11), 2582–2592 (2008).
[Crossref]

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(10), 1737–1754 (2008).
[Crossref] [PubMed]

J. Am. Coll. Radiol. (1)

D. S. Hirschorn, E. A. Krupinski, and M. J. Flynn, “PACS displays: how to select the right display technology,” J. Am. Coll. Radiol. 11(12), 1270–1276 (2014).
[Crossref]

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. Display Technol. (2)

J. Laser Appl. (1)

V. V. Tuchin, “Laser light scattering in biomedical diagnostics and therapy,” J. Laser Appl. 5(2), 43–60 (1993).
[Crossref]

J. Quant. Spectrosc. Radiat. Transfer (1)

J. Hansen and J. Hovenier, “The doubling method applied to multiple scattering of polarized light,” J. Quant. Spectrosc. Radiat. Transfer 11(6), 809–812 (1971).
[Crossref]

Opt. Eng. Mag. (1)

J.-G. Chang, C.-Y. Lin, C.-C. Hwang, and R.-J. Yang, “Optical design and analysis of LCD backlight units using ASAP,” Opt. Eng. Mag. 82, 75–89 (2003).

Opt. Express (1)

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]

Stat. Comput. (1)

D. Whitley, “A genetic algorithm tutorial,” Stat. Comput. 4(2), 65–85 (1994).
[Crossref]

Other (3)

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

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]

J. Choi, K.-S. Hahn, H. Seo, and S.-C. Kim, “Design, analysis, and optimization of LCD backlight unit using ray tracing simulation,” in Proceedings of the International Conference Computational Science and Its Applications – ICCSA 2004, A. Laganá, M. L. Gavrilova, V. Kumar, Y. Mun, C. J. K. Tan, and O. Gervasi, eds. (Springer BerlinHeidelberg, 2004), pp. 837–846.
[Crossref]

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Figures (9)

Fig. 1
Fig. 1 Transmitted intensities simulated for a virtual sample and corresponding distorted transmitted intensity simulated using a (a) 1%, a (b) 5% and a (c) 10% standard deviation scaling factor S.
Fig. 2
Fig. 2 Absolute difference between original and fitted µs for the samples fitted (a) using Tc and (b) without using Tc.
Fig. 3
Fig. 3 Absolute difference between original and fitted µa for the samples fitted (a) with Tc and (b) without Tc.
Fig. 4
Fig. 4 Value of the RMSE between original and fitted phase functions for the fitting case (a) that included Tc and (b) without including Tc.
Fig. 5
Fig. 5 Luminance maps collected for the original {µs = 2.0 mm−1, d = 2.0 mm} sample. Each row shows the luminance map collected at altitude angles 70°, 28°, 7° for (a–c) an azimuth angle of 270° and for (d–f) an azimuth angle of 180°.
Fig. 6
Fig. 6 Differences computed with the NRMSE between the luminance characteristics of the 36 original and fitted virtual samples for the (a) Tc case and (b) no Tc case.
Fig. 7
Fig. 7 Luminance maps for {µs = 3.0 mm−1, d = 3.0 mm}. The first row (a–c) shows a luminance map of the (a) original sample, (b) the fitted sample and (c) a vertical cross section comparison for the Tc case. The second row (e–f) shows the same information for the fits without using Tc.
Fig. 8
Fig. 8 Luminance maps for {µs = 2.5 mm−1, d = 2.5 mm}. Each row shows a luminance map of the (a) original sample, (b) the fitted sample and (c) a vertical cross section comparison, with (a–c) for the fitting with Tc and (e–f) for the fitting without Tc.
Fig. 9
Fig. 9 Luminance deviations calculated with the NRMSE for (a–c) fits with Tc and (d–f) fits without Tc. Each column shows (a,d) the 1% error case, (b,e) the 5% error case and (c,f) the 10% error case.

Equations (7)

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

p HG ( θ ) = 1 4 π 1 g 2 ( 1 + g 2 2 g cos ( θ ) ) 1.5
p MTHG ( θ , g , w ) i = 1 N g w i p HG ( θ , g i ) with g i 0 , w i > 0 and i = 1 N g w i = 1
RMSE = t = 1 n [ I o ( θ ( t ) ) I f ( θ ( t ) ) ] 2 n
e A D = RMSE ( I T o ( θ ) , I T f ( θ ) ) + RMSE ( I R o ( θ ) , I R f ( θ ) )
T c = t 2 exp ( τ ) 1 r 2 exp ( 2 τ )
NRMSE = RMSE ( L o ( x , y ) , L f ( x , y ) ) max ( L o ( x , y ) ) min ( L o ( x , y ) )
I e ( θ ) = I o ( θ ) + S I o ( θ ) r N

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