Abstract

Diffusors are widely used optical components having numerous applications. They are commonly used to homogenize light beams and to create particular intensity distributions. The angular scattering profile of bulk scattering diffusing materials is determined by three bulk scattering parameters that are, however, not commonly available. This hampers an accurate implementation of bulk diffusors in ray tracing simulations. In this paper, the bulk scattering parameters of a concentration series of milk diluted with water were determined with the inverse adding–doubling method. Using these values as input, the macroscopic angular scattering profile was simulated using ray tracing software. The simulation results were compared to experimental data, and a good agreement between measured and simulated data was found. The method was also proven to be successful when applied to commercial diffusors.

© 2013 Optical Society of America

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References

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  1. Z. Sun, J. Chang, N. Zhao, W. Jin, and Y. Wang, “Research of diffusing plates for LCD backlights,” Optik 121, 760–764 (2010).
    [CrossRef]
  2. J.-H. Wang, S.-Y. Lien, J.-R. Ho, T.-K. Shih, C.-F. Chen, C.-C. Chen, and W.-T. Whang, “Optical diffusers based on silicone emulsions,” Opt. Mater. 32, 374–377 (2009).
    [CrossRef]
  3. C.-C. Sun, W.-T. Chien, I. Moreno, C.-T. Hsieh, M.-C. Lin, S.-L. Hsiao, and X.-H. Lee, “Calculating model of light transmission efficiency of diffusers attached to a lighting cavity,” Opt. Express 18, 6137–6148 (2010).
    [CrossRef]
  4. F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical considerations and nomenclature for reflectance,” Final Report (National Bureau of Standards, 1977).
  5. F. B. Leloup, S. Forment, P. Dutré, M. Pointer, and P. Hanselaer, “Design of an instrument for measuring the spectral bidirectional scatter distribution function,” Appl. Opt. 47, 5454–5467 (2008).
  6. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  7. J. F. Beek, P. Blokland, P. Posthumus, M. Aalders, J. W. Pickering, H. J. C. M. Sterenborg, and M. J. C. van Gemert, “In vitro double-integrating-sphere optical properties of tissues between 630 and 1064 nm,” Phys. Med. Biol. 42, 2255–2261 (1997).
    [CrossRef]
  8. J. W. Pickering, S. A. Prahl, N. van Wieringen, J. F. Beek, H. J. C. M. Sterenborg, and M. J. C. van Gemert, “Double-integrating-sphere system for measuring the optical properties of tissue,” Appl. Opt. 32, 399–410 (1993).
    [CrossRef]
  9. A. Kienle, M. S. Patterson, L. Ott, and R. Steiner, “Determination of the scattering coefficient and the anisotropy factor from laser Doppler spectra of liquids including blood,” Appl. Opt. 35, 3404–3412 (1996).
    [CrossRef]
  10. P. Minnis, K.-N. Liou, and Y. Takano, “Inference of cirrus cloud properties using satellite observed visible and infrared radiances. Part I: parameterization of radiance fields,” J. Atmos. Sci. 50, 1279–1304 (1993).
    [CrossRef]
  11. W. Saeys, M. A. Velazco-Roa, S. N. Thennadil, H. Ramon, and B. M. Nicolaï, “Optical properties of apple skin and flesh in the wavelength range from 350 to 2200 nm,” Appl. Opt. 47, 908–919 (2008).
    [CrossRef]
  12. S. A. Prahl, M. J. C. 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]
  13. R. Zhang, W. Verkruysse, B. Choi, J. A. Viator, B. Jung, L. O. Svaasand, G. Aguilar, and J. S. Nelson, “Determination of human skin optical properties from spectrophotometric measurements based on optimization by genetic algorithms,” J. Biomed. Opt. 10, 024030 (2005).
    [CrossRef]
  14. H. Karlsson, I. Fredriksson, M. Larsson, and T. Strömberg, “Inverse Monte Carlo for estimation of scattering and absorption in liquid optical phantoms,” Opt. Express 20, 12233–12246 (2012).
    [CrossRef]
  15. G. G. Stokes, “On the intensity of the light reflected from or transmitted through a pile of plates,” Proc. R. Soc. Lond. 11, 545–556 (1860).
    [CrossRef]
  16. W. J. Wiscombe, “On initialization, error and flux conservation in the doubling method,” J. Quant. Spectrosc. Radiat. Transfer 16, 637–658 (1976).
    [CrossRef]
  17. J. E. Hansen, “Radiative transfer by doubling very thin layers,” Astrophys. J. 155, 565–573 (1969).
    [CrossRef]
  18. L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
    [CrossRef]
  19. G. Yoon, S. A. Prahl, and A. J. Welch, “Accuracies of the diffusion approximation and its similarity relations for laser irradiated biological media,” Appl. Opt. 28, 2250–2255 (1989).
    [CrossRef]
  20. C.-C. Sun, T.-X. Lee, S.-H. Ma, Y.-L. Lee, and S.-M. Huang, “Precise optical modeling for LED lighting verified by cross correlation in the midfield region,” Opt. Lett. 31, 2193–2195 (2006).
    [CrossRef]
  21. I. Moreno and C.-C. Sun, “Modeling the radiation pattern of LEDs,” Opt. Express 16, 1808–1819 (2008).
    [CrossRef]

2012

2010

2009

J.-H. Wang, S.-Y. Lien, J.-R. Ho, T.-K. Shih, C.-F. Chen, C.-C. Chen, and W.-T. Whang, “Optical diffusers based on silicone emulsions,” Opt. Mater. 32, 374–377 (2009).
[CrossRef]

2008

2006

2005

R. Zhang, W. Verkruysse, B. Choi, J. A. Viator, B. Jung, L. O. Svaasand, G. Aguilar, and J. S. Nelson, “Determination of human skin optical properties from spectrophotometric measurements based on optimization by genetic algorithms,” J. Biomed. Opt. 10, 024030 (2005).
[CrossRef]

1997

J. F. Beek, P. Blokland, P. Posthumus, M. Aalders, J. W. Pickering, H. J. C. M. Sterenborg, and M. J. C. van Gemert, “In vitro double-integrating-sphere optical properties of tissues between 630 and 1064 nm,” Phys. Med. Biol. 42, 2255–2261 (1997).
[CrossRef]

1996

1993

1989

1976

W. J. Wiscombe, “On initialization, error and flux conservation in the doubling method,” J. Quant. Spectrosc. Radiat. Transfer 16, 637–658 (1976).
[CrossRef]

1969

J. E. Hansen, “Radiative transfer by doubling very thin layers,” Astrophys. J. 155, 565–573 (1969).
[CrossRef]

1941

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

1860

G. G. Stokes, “On the intensity of the light reflected from or transmitted through a pile of plates,” Proc. R. Soc. Lond. 11, 545–556 (1860).
[CrossRef]

Aalders, M.

J. F. Beek, P. Blokland, P. Posthumus, M. Aalders, J. W. Pickering, H. J. C. M. Sterenborg, and M. J. C. van Gemert, “In vitro double-integrating-sphere optical properties of tissues between 630 and 1064 nm,” Phys. Med. Biol. 42, 2255–2261 (1997).
[CrossRef]

Aguilar, G.

R. Zhang, W. Verkruysse, B. Choi, J. A. Viator, B. Jung, L. O. Svaasand, G. Aguilar, and J. S. Nelson, “Determination of human skin optical properties from spectrophotometric measurements based on optimization by genetic algorithms,” J. Biomed. Opt. 10, 024030 (2005).
[CrossRef]

Beek, J. F.

J. F. Beek, P. Blokland, P. Posthumus, M. Aalders, J. W. Pickering, H. J. C. M. Sterenborg, and M. J. C. van Gemert, “In vitro double-integrating-sphere optical properties of tissues between 630 and 1064 nm,” Phys. Med. Biol. 42, 2255–2261 (1997).
[CrossRef]

J. W. Pickering, S. A. Prahl, N. van Wieringen, J. F. Beek, H. J. C. M. Sterenborg, and M. J. C. van Gemert, “Double-integrating-sphere system for measuring the optical properties of tissue,” Appl. Opt. 32, 399–410 (1993).
[CrossRef]

Blokland, P.

J. F. Beek, P. Blokland, P. Posthumus, M. Aalders, J. W. Pickering, H. J. C. M. Sterenborg, and M. J. C. van Gemert, “In vitro double-integrating-sphere optical properties of tissues between 630 and 1064 nm,” Phys. Med. Biol. 42, 2255–2261 (1997).
[CrossRef]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Chang, J.

Z. Sun, J. Chang, N. Zhao, W. Jin, and Y. Wang, “Research of diffusing plates for LCD backlights,” Optik 121, 760–764 (2010).
[CrossRef]

Chen, C.-C.

J.-H. Wang, S.-Y. Lien, J.-R. Ho, T.-K. Shih, C.-F. Chen, C.-C. Chen, and W.-T. Whang, “Optical diffusers based on silicone emulsions,” Opt. Mater. 32, 374–377 (2009).
[CrossRef]

Chen, C.-F.

J.-H. Wang, S.-Y. Lien, J.-R. Ho, T.-K. Shih, C.-F. Chen, C.-C. Chen, and W.-T. Whang, “Optical diffusers based on silicone emulsions,” Opt. Mater. 32, 374–377 (2009).
[CrossRef]

Chien, W.-T.

Choi, B.

R. Zhang, W. Verkruysse, B. Choi, J. A. Viator, B. Jung, L. O. Svaasand, G. Aguilar, and J. S. Nelson, “Determination of human skin optical properties from spectrophotometric measurements based on optimization by genetic algorithms,” J. Biomed. Opt. 10, 024030 (2005).
[CrossRef]

Dutré, P.

Forment, S.

Fredriksson, I.

Ginsberg, I. W.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical considerations and nomenclature for reflectance,” Final Report (National Bureau of Standards, 1977).

Greenstein, J. L.

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Hanselaer, P.

Hansen, J. E.

J. E. Hansen, “Radiative transfer by doubling very thin layers,” Astrophys. J. 155, 565–573 (1969).
[CrossRef]

Henyey, L. G.

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Ho, J.-R.

J.-H. Wang, S.-Y. Lien, J.-R. Ho, T.-K. Shih, C.-F. Chen, C.-C. Chen, and W.-T. Whang, “Optical diffusers based on silicone emulsions,” Opt. Mater. 32, 374–377 (2009).
[CrossRef]

Hsia, J. J.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical considerations and nomenclature for reflectance,” Final Report (National Bureau of Standards, 1977).

Hsiao, S.-L.

Hsieh, C.-T.

Huang, S.-M.

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Jin, W.

Z. Sun, J. Chang, N. Zhao, W. Jin, and Y. Wang, “Research of diffusing plates for LCD backlights,” Optik 121, 760–764 (2010).
[CrossRef]

Jung, B.

R. Zhang, W. Verkruysse, B. Choi, J. A. Viator, B. Jung, L. O. Svaasand, G. Aguilar, and J. S. Nelson, “Determination of human skin optical properties from spectrophotometric measurements based on optimization by genetic algorithms,” J. Biomed. Opt. 10, 024030 (2005).
[CrossRef]

Karlsson, H.

Kienle, A.

Larsson, M.

Lee, T.-X.

Lee, X.-H.

Lee, Y.-L.

Leloup, F. B.

Lien, S.-Y.

J.-H. Wang, S.-Y. Lien, J.-R. Ho, T.-K. Shih, C.-F. Chen, C.-C. Chen, and W.-T. Whang, “Optical diffusers based on silicone emulsions,” Opt. Mater. 32, 374–377 (2009).
[CrossRef]

Limperis, T.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical considerations and nomenclature for reflectance,” Final Report (National Bureau of Standards, 1977).

Lin, M.-C.

Liou, K.-N.

P. Minnis, K.-N. Liou, and Y. Takano, “Inference of cirrus cloud properties using satellite observed visible and infrared radiances. Part I: parameterization of radiance fields,” J. Atmos. Sci. 50, 1279–1304 (1993).
[CrossRef]

Ma, S.-H.

Minnis, P.

P. Minnis, K.-N. Liou, and Y. Takano, “Inference of cirrus cloud properties using satellite observed visible and infrared radiances. Part I: parameterization of radiance fields,” J. Atmos. Sci. 50, 1279–1304 (1993).
[CrossRef]

Moreno, I.

Nelson, J. S.

R. Zhang, W. Verkruysse, B. Choi, J. A. Viator, B. Jung, L. O. Svaasand, G. Aguilar, and J. S. Nelson, “Determination of human skin optical properties from spectrophotometric measurements based on optimization by genetic algorithms,” J. Biomed. Opt. 10, 024030 (2005).
[CrossRef]

Nicodemus, F. E.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical considerations and nomenclature for reflectance,” Final Report (National Bureau of Standards, 1977).

Nicolaï, B. M.

Ott, L.

Patterson, M. S.

Pickering, J. W.

J. F. Beek, P. Blokland, P. Posthumus, M. Aalders, J. W. Pickering, H. J. C. M. Sterenborg, and M. J. C. van Gemert, “In vitro double-integrating-sphere optical properties of tissues between 630 and 1064 nm,” Phys. Med. Biol. 42, 2255–2261 (1997).
[CrossRef]

J. W. Pickering, S. A. Prahl, N. van Wieringen, J. F. Beek, H. J. C. M. Sterenborg, and M. J. C. van Gemert, “Double-integrating-sphere system for measuring the optical properties of tissue,” Appl. Opt. 32, 399–410 (1993).
[CrossRef]

Pointer, M.

Posthumus, P.

J. F. Beek, P. Blokland, P. Posthumus, M. Aalders, J. W. Pickering, H. J. C. M. Sterenborg, and M. J. C. van Gemert, “In vitro double-integrating-sphere optical properties of tissues between 630 and 1064 nm,” Phys. Med. Biol. 42, 2255–2261 (1997).
[CrossRef]

Prahl, S. A.

Ramon, H.

Richmond, J. C.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical considerations and nomenclature for reflectance,” Final Report (National Bureau of Standards, 1977).

Saeys, W.

Shih, T.-K.

J.-H. Wang, S.-Y. Lien, J.-R. Ho, T.-K. Shih, C.-F. Chen, C.-C. Chen, and W.-T. Whang, “Optical diffusers based on silicone emulsions,” Opt. Mater. 32, 374–377 (2009).
[CrossRef]

Steiner, R.

Sterenborg, H. J. C. M.

J. F. Beek, P. Blokland, P. Posthumus, M. Aalders, J. W. Pickering, H. J. C. M. Sterenborg, and M. J. C. van Gemert, “In vitro double-integrating-sphere optical properties of tissues between 630 and 1064 nm,” Phys. Med. Biol. 42, 2255–2261 (1997).
[CrossRef]

J. W. Pickering, S. A. Prahl, N. van Wieringen, J. F. Beek, H. J. C. M. Sterenborg, and M. J. C. van Gemert, “Double-integrating-sphere system for measuring the optical properties of tissue,” Appl. Opt. 32, 399–410 (1993).
[CrossRef]

Stokes, G. G.

G. G. Stokes, “On the intensity of the light reflected from or transmitted through a pile of plates,” Proc. R. Soc. Lond. 11, 545–556 (1860).
[CrossRef]

Strömberg, T.

Sun, C.-C.

Sun, Z.

Z. Sun, J. Chang, N. Zhao, W. Jin, and Y. Wang, “Research of diffusing plates for LCD backlights,” Optik 121, 760–764 (2010).
[CrossRef]

Svaasand, L. O.

R. Zhang, W. Verkruysse, B. Choi, J. A. Viator, B. Jung, L. O. Svaasand, G. Aguilar, and J. S. Nelson, “Determination of human skin optical properties from spectrophotometric measurements based on optimization by genetic algorithms,” J. Biomed. Opt. 10, 024030 (2005).
[CrossRef]

Takano, Y.

P. Minnis, K.-N. Liou, and Y. Takano, “Inference of cirrus cloud properties using satellite observed visible and infrared radiances. Part I: parameterization of radiance fields,” J. Atmos. Sci. 50, 1279–1304 (1993).
[CrossRef]

Thennadil, S. N.

van Gemert, M. J. C.

van Wieringen, N.

Velazco-Roa, M. A.

Verkruysse, W.

R. Zhang, W. Verkruysse, B. Choi, J. A. Viator, B. Jung, L. O. Svaasand, G. Aguilar, and J. S. Nelson, “Determination of human skin optical properties from spectrophotometric measurements based on optimization by genetic algorithms,” J. Biomed. Opt. 10, 024030 (2005).
[CrossRef]

Viator, J. A.

R. Zhang, W. Verkruysse, B. Choi, J. A. Viator, B. Jung, L. O. Svaasand, G. Aguilar, and J. S. Nelson, “Determination of human skin optical properties from spectrophotometric measurements based on optimization by genetic algorithms,” J. Biomed. Opt. 10, 024030 (2005).
[CrossRef]

Wang, J.-H.

J.-H. Wang, S.-Y. Lien, J.-R. Ho, T.-K. Shih, C.-F. Chen, C.-C. Chen, and W.-T. Whang, “Optical diffusers based on silicone emulsions,” Opt. Mater. 32, 374–377 (2009).
[CrossRef]

Wang, Y.

Z. Sun, J. Chang, N. Zhao, W. Jin, and Y. Wang, “Research of diffusing plates for LCD backlights,” Optik 121, 760–764 (2010).
[CrossRef]

Welch, A. J.

Whang, W.-T.

J.-H. Wang, S.-Y. Lien, J.-R. Ho, T.-K. Shih, C.-F. Chen, C.-C. Chen, and W.-T. Whang, “Optical diffusers based on silicone emulsions,” Opt. Mater. 32, 374–377 (2009).
[CrossRef]

Wiscombe, W. J.

W. J. Wiscombe, “On initialization, error and flux conservation in the doubling method,” J. Quant. Spectrosc. Radiat. Transfer 16, 637–658 (1976).
[CrossRef]

Yoon, G.

Zhang, R.

R. Zhang, W. Verkruysse, B. Choi, J. A. Viator, B. Jung, L. O. Svaasand, G. Aguilar, and J. S. Nelson, “Determination of human skin optical properties from spectrophotometric measurements based on optimization by genetic algorithms,” J. Biomed. Opt. 10, 024030 (2005).
[CrossRef]

Zhao, N.

Z. Sun, J. Chang, N. Zhao, W. Jin, and Y. Wang, “Research of diffusing plates for LCD backlights,” Optik 121, 760–764 (2010).
[CrossRef]

Appl. Opt.

Astrophys. J.

J. E. Hansen, “Radiative transfer by doubling very thin layers,” Astrophys. J. 155, 565–573 (1969).
[CrossRef]

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

J. Atmos. Sci.

P. Minnis, K.-N. Liou, and Y. Takano, “Inference of cirrus cloud properties using satellite observed visible and infrared radiances. Part I: parameterization of radiance fields,” J. Atmos. Sci. 50, 1279–1304 (1993).
[CrossRef]

J. Biomed. Opt.

R. Zhang, W. Verkruysse, B. Choi, J. A. Viator, B. Jung, L. O. Svaasand, G. Aguilar, and J. S. Nelson, “Determination of human skin optical properties from spectrophotometric measurements based on optimization by genetic algorithms,” J. Biomed. Opt. 10, 024030 (2005).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer

W. J. Wiscombe, “On initialization, error and flux conservation in the doubling method,” J. Quant. Spectrosc. Radiat. Transfer 16, 637–658 (1976).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Mater.

J.-H. Wang, S.-Y. Lien, J.-R. Ho, T.-K. Shih, C.-F. Chen, C.-C. Chen, and W.-T. Whang, “Optical diffusers based on silicone emulsions,” Opt. Mater. 32, 374–377 (2009).
[CrossRef]

Optik

Z. Sun, J. Chang, N. Zhao, W. Jin, and Y. Wang, “Research of diffusing plates for LCD backlights,” Optik 121, 760–764 (2010).
[CrossRef]

Phys. Med. Biol.

J. F. Beek, P. Blokland, P. Posthumus, M. Aalders, J. W. Pickering, H. J. C. M. Sterenborg, and M. J. C. van Gemert, “In vitro double-integrating-sphere optical properties of tissues between 630 and 1064 nm,” Phys. Med. Biol. 42, 2255–2261 (1997).
[CrossRef]

Proc. R. Soc. Lond.

G. G. Stokes, “On the intensity of the light reflected from or transmitted through a pile of plates,” Proc. R. Soc. Lond. 11, 545–556 (1860).
[CrossRef]

Other

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical considerations and nomenclature for reflectance,” Final Report (National Bureau of Standards, 1977).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

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Figures (4)

Fig. 1.
Fig. 1.

Schematic representation of the BSDF setup: (1) Xe source, (2) collimating mirror, (3) ND filter wheel, (4) sample, and (5) detector head.

Fig. 2.
Fig. 2.

Measured (marks) and simulated (curves) scattered intensities in reflection (left) and transmission (right) of a diluted milk series in a cuvette with thickness 1.1 mm at 550 nm.

Fig. 3.
Fig. 3.

Measured (marks) and simulated (curves) scattered intensities in reflection (left) and transmission (right) of a diluted milk series in a cuvette with thickness 2 mm at 550 nm.

Fig. 4.
Fig. 4.

Scattered intensities of the two commercial diffusors, blue for WN297 and red for WH02 at 550 nm. The solid, dashed, and dotted curves denote the simulated scattered intensities for the three different combinations of μs and g given in Table 3. The marks are the measured values (Δ for WH02 and for WN297). The deviations between the average simulated values and the individual simulation results for each combination of μs and g are shown separately below the figure.

Tables (3)

Tables Icon

Table 1. Measured Reflectance, Transmittance, and Regular Transmittance of the Diffusing Materials

Tables Icon

Table 2. Bulk Scattering Properties of the Diffusing Materials Determined with the IAD Method

Tables Icon

Table 3. Bulk Scattering Parameters Used for the Simulations of the Two Commercial Diffusers

Equations (9)

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

s.L(r,s)=(μa+μs)L(r,s)+μs4πp(s,s)L(r,s)dΩ.
Treg=(1r)2eτ1r2e2.τ.
pHG(θ)=14π1g2(1+g22gcos(θ))3/2.
μs=μs(1g).
T=2πΦi0π/2Is(θ)sin(θ)dθ+Treg,
R=2πΦiπ/2πIs(θ)sin(θ)dθ+Rreg.
Is(0°)=Is(θ1)cos(θ1)+(Is(θ1)cos(θ1)Is(θ2)cos(θ2))θ1(θ1θ2).
Treg=Φs(0°)Is(0°)ΩrecΦi.
NCC=θ=0°90°[(Im(θ)I¯m)(Is(θ)I¯s)]θ=0°90°[(Im(θ)I¯m)2]θ=0°90°[(Is(θ)I¯s)2].

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