Abstract

Transparent refractive-index matched micro (TRIMM) particles have proved to be an excellent scattering component for use in translucent sheets. Measurements of hemispheric transmittance and reflectance versus angle of incidence, as well as angle-resolved studies of such translucent sheets, have been carried out to complement earlier published hemispheric reflectance and transmittance spectral measurements carried out at normal angle of incidence. Hemispheric values relative to angle of incidence are of interest for daylighting applications and building simulations, and angle-resolved measurements are vital for verifying that our modeling tools are reliable. Ray-tracing simulations based on Mie scattering for the individual TRIMM particles and angle-resolved measurements are in good agreement, indicating that the simulation method used is practical for the design of new scattering profiles by varying particle concentration or refractive index.

© 2005 Optical Society of America

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References

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  1. G. B. Smith, J. C. Jonsson, J. Franklin, “Spectral and global diffuse properties of high-performance translucent polymer sheets for energy efficient lighting and skylights,” Appl. Opt. 42, 3981–3991 (2003).
    [CrossRef] [PubMed]
  2. K. Grandin, A. Roos, “Evaluation of correction factors for transmittance measurements in single-beam integration spheres,” Appl. Opt. 33, 6098–6104 (1994).
    [CrossRef] [PubMed]
  3. P. Nostell, A. Roos, D. Rönnow, “Single-beam integrating sphere for reflectance and transmittance measurements versus angle of incidence in the solar wavelength range on diffuse and specular samples,” Rev. Sci. Instrum. 70, 2481–2494 (1999).
    [CrossRef]
  4. C. M. Sorensen, D. Fischbach, “Patterns in Mie scattering,” Opt. Commun. 173, 145–153 (2000).
    [CrossRef]
  5. C. M. Sorensen, D. Shi, “Patterns in the ripple structure of Mie scattering,” J. Opt. Soc. Am. A 19, 122–125 (2002).
    [CrossRef]
  6. C. Oh, C. M. Sorensen, “Scaling approach for the structure factor of a generalized system of scatterers,” J. Nanopart. Res. 1, 369–377 (1999).
    [CrossRef]
  7. J. C. Jonsson, A. Roos, G. B. Smith, “Light trapping in translucent samples and its effect on the hemispherical transmittance obtained by an integrating sphere,” in Optical Diagnostic Methods for Inorganic Materials III, L. M. Hanssen, ed., Proc. SPIE5192, 91–100 (2003).
    [CrossRef]
  8. G. B. Smith, D. C. Green, G. McCredie, M. Hossain, P. D. Swift, M. Luther, “Optical characterisation of materials and systems for daylighting,” Renew. Energy 22, 85–90 (2001).
    [CrossRef]
  9. J. C. Jonsson, G. B. Smith, G. A. Niklasson, “Experimental and Monte Carlo analysis of isotropic multiple Mie scattering,” Opt. Commun. 240, 9–17 (2004).
    [CrossRef]

2004

J. C. Jonsson, G. B. Smith, G. A. Niklasson, “Experimental and Monte Carlo analysis of isotropic multiple Mie scattering,” Opt. Commun. 240, 9–17 (2004).
[CrossRef]

2003

2002

2001

G. B. Smith, D. C. Green, G. McCredie, M. Hossain, P. D. Swift, M. Luther, “Optical characterisation of materials and systems for daylighting,” Renew. Energy 22, 85–90 (2001).
[CrossRef]

2000

C. M. Sorensen, D. Fischbach, “Patterns in Mie scattering,” Opt. Commun. 173, 145–153 (2000).
[CrossRef]

1999

C. Oh, C. M. Sorensen, “Scaling approach for the structure factor of a generalized system of scatterers,” J. Nanopart. Res. 1, 369–377 (1999).
[CrossRef]

P. Nostell, A. Roos, D. Rönnow, “Single-beam integrating sphere for reflectance and transmittance measurements versus angle of incidence in the solar wavelength range on diffuse and specular samples,” Rev. Sci. Instrum. 70, 2481–2494 (1999).
[CrossRef]

1994

Fischbach, D.

C. M. Sorensen, D. Fischbach, “Patterns in Mie scattering,” Opt. Commun. 173, 145–153 (2000).
[CrossRef]

Franklin, J.

Grandin, K.

Green, D. C.

G. B. Smith, D. C. Green, G. McCredie, M. Hossain, P. D. Swift, M. Luther, “Optical characterisation of materials and systems for daylighting,” Renew. Energy 22, 85–90 (2001).
[CrossRef]

Hossain, M.

G. B. Smith, D. C. Green, G. McCredie, M. Hossain, P. D. Swift, M. Luther, “Optical characterisation of materials and systems for daylighting,” Renew. Energy 22, 85–90 (2001).
[CrossRef]

Jonsson, J. C.

J. C. Jonsson, G. B. Smith, G. A. Niklasson, “Experimental and Monte Carlo analysis of isotropic multiple Mie scattering,” Opt. Commun. 240, 9–17 (2004).
[CrossRef]

G. B. Smith, J. C. Jonsson, J. Franklin, “Spectral and global diffuse properties of high-performance translucent polymer sheets for energy efficient lighting and skylights,” Appl. Opt. 42, 3981–3991 (2003).
[CrossRef] [PubMed]

J. C. Jonsson, A. Roos, G. B. Smith, “Light trapping in translucent samples and its effect on the hemispherical transmittance obtained by an integrating sphere,” in Optical Diagnostic Methods for Inorganic Materials III, L. M. Hanssen, ed., Proc. SPIE5192, 91–100 (2003).
[CrossRef]

Luther, M.

G. B. Smith, D. C. Green, G. McCredie, M. Hossain, P. D. Swift, M. Luther, “Optical characterisation of materials and systems for daylighting,” Renew. Energy 22, 85–90 (2001).
[CrossRef]

McCredie, G.

G. B. Smith, D. C. Green, G. McCredie, M. Hossain, P. D. Swift, M. Luther, “Optical characterisation of materials and systems for daylighting,” Renew. Energy 22, 85–90 (2001).
[CrossRef]

Niklasson, G. A.

J. C. Jonsson, G. B. Smith, G. A. Niklasson, “Experimental and Monte Carlo analysis of isotropic multiple Mie scattering,” Opt. Commun. 240, 9–17 (2004).
[CrossRef]

Nostell, P.

P. Nostell, A. Roos, D. Rönnow, “Single-beam integrating sphere for reflectance and transmittance measurements versus angle of incidence in the solar wavelength range on diffuse and specular samples,” Rev. Sci. Instrum. 70, 2481–2494 (1999).
[CrossRef]

Oh, C.

C. Oh, C. M. Sorensen, “Scaling approach for the structure factor of a generalized system of scatterers,” J. Nanopart. Res. 1, 369–377 (1999).
[CrossRef]

Rönnow, D.

P. Nostell, A. Roos, D. Rönnow, “Single-beam integrating sphere for reflectance and transmittance measurements versus angle of incidence in the solar wavelength range on diffuse and specular samples,” Rev. Sci. Instrum. 70, 2481–2494 (1999).
[CrossRef]

Roos, A.

P. Nostell, A. Roos, D. Rönnow, “Single-beam integrating sphere for reflectance and transmittance measurements versus angle of incidence in the solar wavelength range on diffuse and specular samples,” Rev. Sci. Instrum. 70, 2481–2494 (1999).
[CrossRef]

K. Grandin, A. Roos, “Evaluation of correction factors for transmittance measurements in single-beam integration spheres,” Appl. Opt. 33, 6098–6104 (1994).
[CrossRef] [PubMed]

J. C. Jonsson, A. Roos, G. B. Smith, “Light trapping in translucent samples and its effect on the hemispherical transmittance obtained by an integrating sphere,” in Optical Diagnostic Methods for Inorganic Materials III, L. M. Hanssen, ed., Proc. SPIE5192, 91–100 (2003).
[CrossRef]

Shi, D.

Smith, G. B.

J. C. Jonsson, G. B. Smith, G. A. Niklasson, “Experimental and Monte Carlo analysis of isotropic multiple Mie scattering,” Opt. Commun. 240, 9–17 (2004).
[CrossRef]

G. B. Smith, J. C. Jonsson, J. Franklin, “Spectral and global diffuse properties of high-performance translucent polymer sheets for energy efficient lighting and skylights,” Appl. Opt. 42, 3981–3991 (2003).
[CrossRef] [PubMed]

G. B. Smith, D. C. Green, G. McCredie, M. Hossain, P. D. Swift, M. Luther, “Optical characterisation of materials and systems for daylighting,” Renew. Energy 22, 85–90 (2001).
[CrossRef]

J. C. Jonsson, A. Roos, G. B. Smith, “Light trapping in translucent samples and its effect on the hemispherical transmittance obtained by an integrating sphere,” in Optical Diagnostic Methods for Inorganic Materials III, L. M. Hanssen, ed., Proc. SPIE5192, 91–100 (2003).
[CrossRef]

Sorensen, C. M.

C. M. Sorensen, D. Shi, “Patterns in the ripple structure of Mie scattering,” J. Opt. Soc. Am. A 19, 122–125 (2002).
[CrossRef]

C. M. Sorensen, D. Fischbach, “Patterns in Mie scattering,” Opt. Commun. 173, 145–153 (2000).
[CrossRef]

C. Oh, C. M. Sorensen, “Scaling approach for the structure factor of a generalized system of scatterers,” J. Nanopart. Res. 1, 369–377 (1999).
[CrossRef]

Swift, P. D.

G. B. Smith, D. C. Green, G. McCredie, M. Hossain, P. D. Swift, M. Luther, “Optical characterisation of materials and systems for daylighting,” Renew. Energy 22, 85–90 (2001).
[CrossRef]

Appl. Opt.

J. Nanopart. Res.

C. Oh, C. M. Sorensen, “Scaling approach for the structure factor of a generalized system of scatterers,” J. Nanopart. Res. 1, 369–377 (1999).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

J. C. Jonsson, G. B. Smith, G. A. Niklasson, “Experimental and Monte Carlo analysis of isotropic multiple Mie scattering,” Opt. Commun. 240, 9–17 (2004).
[CrossRef]

C. M. Sorensen, D. Fischbach, “Patterns in Mie scattering,” Opt. Commun. 173, 145–153 (2000).
[CrossRef]

Renew. Energy

G. B. Smith, D. C. Green, G. McCredie, M. Hossain, P. D. Swift, M. Luther, “Optical characterisation of materials and systems for daylighting,” Renew. Energy 22, 85–90 (2001).
[CrossRef]

Rev. Sci. Instrum.

P. Nostell, A. Roos, D. Rönnow, “Single-beam integrating sphere for reflectance and transmittance measurements versus angle of incidence in the solar wavelength range on diffuse and specular samples,” Rev. Sci. Instrum. 70, 2481–2494 (1999).
[CrossRef]

Other

J. C. Jonsson, A. Roos, G. B. Smith, “Light trapping in translucent samples and its effect on the hemispherical transmittance obtained by an integrating sphere,” in Optical Diagnostic Methods for Inorganic Materials III, L. M. Hanssen, ed., Proc. SPIE5192, 91–100 (2003).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Top-view schematic of the integrating spheres used for hemispheric measurements of scattering samples at oblique angles of incidence. (a) In the transmittance sphere, both sample and sphere rotate about an axis through the entrance port. (b) For the reflectance sphere, the sample (lighter shading) and the sample holder (darker shading) rotate, but the sphere is fixed. Both figures show the angle of incidence, θ, which is measured with respect to the surface normal.

Fig. 2
Fig. 2

Schematic of the goniometer setup used for angle-resolved scattering measurements. Angle of incidence α is defined as the angle between the incident light and the sample normal (dashed line). Scattering angle θ is also defined relative to the surface normal. The sample normal corresponds to θ = 0°. Positive angles are given by the clockwise direction; negative angles correspond to angles in the counterclockwise direction from the surface normal.

Fig. 3
Fig. 3

Flowchart describing the ray-tracing simulation.

Fig. 4
Fig. 4

Micrograph of the N77 sample, showing the smearing of surface particles and an indication of a size distribution among the TRIMM particles. The full scale is 100 µm (10 µm per minor tick).

Fig. 5
Fig. 5

(a), (b) Hemispheric reflectance (thinner curves) and transmittance (thicker curves) values for several angles of incidence of the N73 samples of thicknesses 1 and 3 mm, respectively. (c), (d) 1 − TtotRtot, which corresponds to absorption and side loss of the transmittance measurements.

Fig. 6
Fig. 6

(a), (b) Hemispheric reflectance (thinner curves) and transmittance (thicker curves) values for several angles of incidence of the N77 samples of thicknesses 1 and 3 mm, respectively. (c), (d) 1 − TtotRtot, which corresponds to absorption and side loss of the transmittance measurements.

Fig. 7
Fig. 7

Hemispheric transmittance and reflectance versus angle of incidence for 500 nm. The solid curves indicate the calculated reflectance for a clear PMMA sample to emphasize the increased effect of scattering with increasing angle of incidence. The large difference between N73D3 and N77D1 indicates that side loss is higher for thicker samples.

Fig. 8
Fig. 8

Experimental results for goniometer measurements of the scattering profiles versus angle of incidence for (a) N73, 1 mm; (b) N73, 3 mm; (c) N77, 1 mm; and (d) N77, 3 mm.

Fig. 9
Fig. 9

(a) Comparison of ray-tracing simulation and measured scattering intensities for a normal angle of incidence for all four samples. (b) Crossover regions for three of the simulated scattering intensities versus qR. Linear fits for low and high qR regions are shown. Values for the 1-mm N77 sample have been left out because of their similarity to those of the 3-mm N73 sample.

Equations (6)

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T m = S s S r = [ 1 R w ( 1 f s ) ] { T d + T s [ R w ( 1 x f s ) + x f s R s ] } [ 1 R w ( 1 f s ) f s R s ] R w ( 1 x f s ) ,
T tot = S s S r [ 1 R w ( 1 f s ) f s R s ] R w ( 1 x f s ) [ 1 R w ( 1 f s ) ] { C + ( 1 C ) [ R w ( 1 x f s ) + x f s R s ] } .
R tot = R w ( S s / S r ) + R sp [ 1 R w ( 1 A 2 cos θ ) R h ( 1 f ) A 2 cos θ ] 1 + R sp f A 2 cos θ T tot 2 R h ,
I ( q R ) 0 q R < 1 , I ( q R ) 2 1 < q R < ρ , I ( q R ) 2 ρ < q R ,
θ new = across ( cos θ sin Δ θ + sin Δ θ cos Δ ϕ ) ,
ϕ new = arcsin sin Δ ϕ sin Δ θ sin θ new .

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