Abstract

Bidirectional, angular resolved scatterometry was used to evaluate the feasibility of using rolled aluminum as reflectors in solar thermal collectors and solar cells. Two types of rolled aluminum with different surface roughnesses were investigated. The results show that the smoother of the two samples [rms height, (0.20 ± 0.02) µm] can be used as a nonimaging, concentrating reflector with moderate reflection losses compared with those of optically smooth aluminum reflectors. The sample with the rougher surface [rms height, (0.6 ± 0.1) µm] is not suitable as a concentrating element but can be used as planar reflectors. The orientation of the rolling grooves is then of importance for minimizing reflection losses in the system.

© 2001 Optical Society of America

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References

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  1. W. T. Welford, R. Winston, High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989).
  2. B. Perers, B. Karlsson, M. Bergkvist, “Intensity distribution in the collector plane from structured booster reflectors with rolling grooves and corrugation,” Sol. Energy 53, 215–226 (1994).
    [CrossRef]
  3. M. Rönnelid, B. Karlsson, “Optical properties of modified compound parabolic concentrators with linear corrugated reflectors,” Appl. Opt. 37, 5222–5226 (1998).
    [CrossRef]
  4. M. Rönnelid, B. Karlsson, “The use of corrugated booster reflectors for large solar collector fields,” Sol. Energy 65, 343–351 (1999).
    [CrossRef]
  5. P. Beckman, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, Oxford, 1963).
  6. J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering, 2nd ed. (Optical Society of America, Washington, D.C., 1999).
  7. J. C. Stover, Optical Scattering: Measurement and Analysis, 2nd ed. (McGraw-Hill, New York, 1995).
    [CrossRef]
  8. J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (Hilger, Bristol, U.K., 1991).
  9. E. L. Church, P. Z. Takacs, T. A. Leonard, “Prediction of BRDFs from surface profile measurements,” in Scatter from Optical Components, J. C. Stover, ed., Proc. SPIE1165, 136–150 (1989).
    [CrossRef]
  10. G. Palasantzas, “Roughness of spectrum and surface width of self-afine fractal surfaces via the K-correlation model,” Phys. Rev. 48, 14472–14478 (1993).
    [CrossRef]
  11. D. Rönnow, E. Veszelei, “Design review of an instrument for spectroscopic total integrated light scattering measurements in the visible wavelength region,” Rev. Sci. Instrum. 65, 327–334 (1994).
    [CrossRef]
  12. D. Rönnow, “Determination of interface roughness cross correlation of thin films from spectroscopic light scattering measurements,” J. Appl. Phys. 81, 3627–3636 (1997).
    [CrossRef]
  13. T. Lindström, A. Roos, “Reflectance and transmittance of anisotropically scattering samples in focusing Coblentz spheres,” Rev. Sci. Instrum. 71, 2270–2278 (2000).
    [CrossRef]
  14. P. Nostell, A. Roos, D. Rönnow, “Single-beam integrating sphere spectrophotometer 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]
  15. A. Roos, C. G. Ribbing, M. Bergkvist, “Anomalies in integrating sphere measurements on structured samples,” Appl. Opt. 27, 3828–3832 (1988).
    [CrossRef] [PubMed]
  16. J. M. Bennett, J. M. Elson, J. P. Rahn, “Angle-resolved scattering: comparison of theory and experiment,” in Thin Film Technologies I, J. Jacobsson, ed., Proc. SPIE401, 234–246 (1983).
    [CrossRef]
  17. P. Nostell, A. Roos, B. Karlsson, “Optical characterisation of solar reflecting surfaces,” in Optical Materials Technology for Energy Efficiency and Solar Conversion XV, C. M. Lampert, ed., Proc. SPIE3138, 163–172 (1997).
    [CrossRef]

2000 (1)

T. Lindström, A. Roos, “Reflectance and transmittance of anisotropically scattering samples in focusing Coblentz spheres,” Rev. Sci. Instrum. 71, 2270–2278 (2000).
[CrossRef]

1999 (2)

P. Nostell, A. Roos, D. Rönnow, “Single-beam integrating sphere spectrophotometer 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]

M. Rönnelid, B. Karlsson, “The use of corrugated booster reflectors for large solar collector fields,” Sol. Energy 65, 343–351 (1999).
[CrossRef]

1998 (1)

1997 (1)

D. Rönnow, “Determination of interface roughness cross correlation of thin films from spectroscopic light scattering measurements,” J. Appl. Phys. 81, 3627–3636 (1997).
[CrossRef]

1994 (2)

D. Rönnow, E. Veszelei, “Design review of an instrument for spectroscopic total integrated light scattering measurements in the visible wavelength region,” Rev. Sci. Instrum. 65, 327–334 (1994).
[CrossRef]

B. Perers, B. Karlsson, M. Bergkvist, “Intensity distribution in the collector plane from structured booster reflectors with rolling grooves and corrugation,” Sol. Energy 53, 215–226 (1994).
[CrossRef]

1993 (1)

G. Palasantzas, “Roughness of spectrum and surface width of self-afine fractal surfaces via the K-correlation model,” Phys. Rev. 48, 14472–14478 (1993).
[CrossRef]

1988 (1)

Beckman, P.

P. Beckman, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, Oxford, 1963).

Bennett, J. M.

J. M. Bennett, J. M. Elson, J. P. Rahn, “Angle-resolved scattering: comparison of theory and experiment,” in Thin Film Technologies I, J. Jacobsson, ed., Proc. SPIE401, 234–246 (1983).
[CrossRef]

J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering, 2nd ed. (Optical Society of America, Washington, D.C., 1999).

Bergkvist, M.

B. Perers, B. Karlsson, M. Bergkvist, “Intensity distribution in the collector plane from structured booster reflectors with rolling grooves and corrugation,” Sol. Energy 53, 215–226 (1994).
[CrossRef]

A. Roos, C. G. Ribbing, M. Bergkvist, “Anomalies in integrating sphere measurements on structured samples,” Appl. Opt. 27, 3828–3832 (1988).
[CrossRef] [PubMed]

Church, E. L.

E. L. Church, P. Z. Takacs, T. A. Leonard, “Prediction of BRDFs from surface profile measurements,” in Scatter from Optical Components, J. C. Stover, ed., Proc. SPIE1165, 136–150 (1989).
[CrossRef]

Elson, J. M.

J. M. Bennett, J. M. Elson, J. P. Rahn, “Angle-resolved scattering: comparison of theory and experiment,” in Thin Film Technologies I, J. Jacobsson, ed., Proc. SPIE401, 234–246 (1983).
[CrossRef]

Karlsson, B.

M. Rönnelid, B. Karlsson, “The use of corrugated booster reflectors for large solar collector fields,” Sol. Energy 65, 343–351 (1999).
[CrossRef]

M. Rönnelid, B. Karlsson, “Optical properties of modified compound parabolic concentrators with linear corrugated reflectors,” Appl. Opt. 37, 5222–5226 (1998).
[CrossRef]

B. Perers, B. Karlsson, M. Bergkvist, “Intensity distribution in the collector plane from structured booster reflectors with rolling grooves and corrugation,” Sol. Energy 53, 215–226 (1994).
[CrossRef]

P. Nostell, A. Roos, B. Karlsson, “Optical characterisation of solar reflecting surfaces,” in Optical Materials Technology for Energy Efficiency and Solar Conversion XV, C. M. Lampert, ed., Proc. SPIE3138, 163–172 (1997).
[CrossRef]

Leonard, T. A.

E. L. Church, P. Z. Takacs, T. A. Leonard, “Prediction of BRDFs from surface profile measurements,” in Scatter from Optical Components, J. C. Stover, ed., Proc. SPIE1165, 136–150 (1989).
[CrossRef]

Lindström, T.

T. Lindström, A. Roos, “Reflectance and transmittance of anisotropically scattering samples in focusing Coblentz spheres,” Rev. Sci. Instrum. 71, 2270–2278 (2000).
[CrossRef]

Mattsson, L.

J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering, 2nd ed. (Optical Society of America, Washington, D.C., 1999).

Nostell, P.

P. Nostell, A. Roos, D. Rönnow, “Single-beam integrating sphere spectrophotometer 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]

P. Nostell, A. Roos, B. Karlsson, “Optical characterisation of solar reflecting surfaces,” in Optical Materials Technology for Energy Efficiency and Solar Conversion XV, C. M. Lampert, ed., Proc. SPIE3138, 163–172 (1997).
[CrossRef]

Ogilvy, J. A.

J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (Hilger, Bristol, U.K., 1991).

Palasantzas, G.

G. Palasantzas, “Roughness of spectrum and surface width of self-afine fractal surfaces via the K-correlation model,” Phys. Rev. 48, 14472–14478 (1993).
[CrossRef]

Perers, B.

B. Perers, B. Karlsson, M. Bergkvist, “Intensity distribution in the collector plane from structured booster reflectors with rolling grooves and corrugation,” Sol. Energy 53, 215–226 (1994).
[CrossRef]

Rahn, J. P.

J. M. Bennett, J. M. Elson, J. P. Rahn, “Angle-resolved scattering: comparison of theory and experiment,” in Thin Film Technologies I, J. Jacobsson, ed., Proc. SPIE401, 234–246 (1983).
[CrossRef]

Ribbing, C. G.

Rönnelid, M.

M. Rönnelid, B. Karlsson, “The use of corrugated booster reflectors for large solar collector fields,” Sol. Energy 65, 343–351 (1999).
[CrossRef]

M. Rönnelid, B. Karlsson, “Optical properties of modified compound parabolic concentrators with linear corrugated reflectors,” Appl. Opt. 37, 5222–5226 (1998).
[CrossRef]

Rönnow, D.

P. Nostell, A. Roos, D. Rönnow, “Single-beam integrating sphere spectrophotometer 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]

D. Rönnow, “Determination of interface roughness cross correlation of thin films from spectroscopic light scattering measurements,” J. Appl. Phys. 81, 3627–3636 (1997).
[CrossRef]

D. Rönnow, E. Veszelei, “Design review of an instrument for spectroscopic total integrated light scattering measurements in the visible wavelength region,” Rev. Sci. Instrum. 65, 327–334 (1994).
[CrossRef]

Roos, A.

T. Lindström, A. Roos, “Reflectance and transmittance of anisotropically scattering samples in focusing Coblentz spheres,” Rev. Sci. Instrum. 71, 2270–2278 (2000).
[CrossRef]

P. Nostell, A. Roos, D. Rönnow, “Single-beam integrating sphere spectrophotometer 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]

A. Roos, C. G. Ribbing, M. Bergkvist, “Anomalies in integrating sphere measurements on structured samples,” Appl. Opt. 27, 3828–3832 (1988).
[CrossRef] [PubMed]

P. Nostell, A. Roos, B. Karlsson, “Optical characterisation of solar reflecting surfaces,” in Optical Materials Technology for Energy Efficiency and Solar Conversion XV, C. M. Lampert, ed., Proc. SPIE3138, 163–172 (1997).
[CrossRef]

Spizzichino, A.

P. Beckman, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, Oxford, 1963).

Stover, J. C.

J. C. Stover, Optical Scattering: Measurement and Analysis, 2nd ed. (McGraw-Hill, New York, 1995).
[CrossRef]

Takacs, P. Z.

E. L. Church, P. Z. Takacs, T. A. Leonard, “Prediction of BRDFs from surface profile measurements,” in Scatter from Optical Components, J. C. Stover, ed., Proc. SPIE1165, 136–150 (1989).
[CrossRef]

Veszelei, E.

D. Rönnow, E. Veszelei, “Design review of an instrument for spectroscopic total integrated light scattering measurements in the visible wavelength region,” Rev. Sci. Instrum. 65, 327–334 (1994).
[CrossRef]

Welford, W. T.

W. T. Welford, R. Winston, High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989).

Winston, R.

W. T. Welford, R. Winston, High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989).

Appl. Opt. (2)

J. Appl. Phys. (1)

D. Rönnow, “Determination of interface roughness cross correlation of thin films from spectroscopic light scattering measurements,” J. Appl. Phys. 81, 3627–3636 (1997).
[CrossRef]

Phys. Rev. (1)

G. Palasantzas, “Roughness of spectrum and surface width of self-afine fractal surfaces via the K-correlation model,” Phys. Rev. 48, 14472–14478 (1993).
[CrossRef]

Rev. Sci. Instrum. (3)

D. Rönnow, E. Veszelei, “Design review of an instrument for spectroscopic total integrated light scattering measurements in the visible wavelength region,” Rev. Sci. Instrum. 65, 327–334 (1994).
[CrossRef]

T. Lindström, A. Roos, “Reflectance and transmittance of anisotropically scattering samples in focusing Coblentz spheres,” Rev. Sci. Instrum. 71, 2270–2278 (2000).
[CrossRef]

P. Nostell, A. Roos, D. Rönnow, “Single-beam integrating sphere spectrophotometer 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]

Sol. Energy (2)

M. Rönnelid, B. Karlsson, “The use of corrugated booster reflectors for large solar collector fields,” Sol. Energy 65, 343–351 (1999).
[CrossRef]

B. Perers, B. Karlsson, M. Bergkvist, “Intensity distribution in the collector plane from structured booster reflectors with rolling grooves and corrugation,” Sol. Energy 53, 215–226 (1994).
[CrossRef]

Other (8)

J. M. Bennett, J. M. Elson, J. P. Rahn, “Angle-resolved scattering: comparison of theory and experiment,” in Thin Film Technologies I, J. Jacobsson, ed., Proc. SPIE401, 234–246 (1983).
[CrossRef]

P. Nostell, A. Roos, B. Karlsson, “Optical characterisation of solar reflecting surfaces,” in Optical Materials Technology for Energy Efficiency and Solar Conversion XV, C. M. Lampert, ed., Proc. SPIE3138, 163–172 (1997).
[CrossRef]

P. Beckman, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, Oxford, 1963).

J. M. Bennett, L. Mattsson, Introduction to Surface Roughness and Scattering, 2nd ed. (Optical Society of America, Washington, D.C., 1999).

J. C. Stover, Optical Scattering: Measurement and Analysis, 2nd ed. (McGraw-Hill, New York, 1995).
[CrossRef]

J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (Hilger, Bristol, U.K., 1991).

E. L. Church, P. Z. Takacs, T. A. Leonard, “Prediction of BRDFs from surface profile measurements,” in Scatter from Optical Components, J. C. Stover, ed., Proc. SPIE1165, 136–150 (1989).
[CrossRef]

W. T. Welford, R. Winston, High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989).

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Figures (12)

Fig. 1
Fig. 1

Light-optical micrographs of (a) sheet aluminum and (b) aluminum foil samples.

Fig. 2
Fig. 2

Line profiles of the sheet aluminum sample taken with an interference fringe microscope working in the white-light vertical scanning interferometry mode.

Fig. 3
Fig. 3

Line profiles for the aluminum foil sample taken with an interference fringe microscope working in the white-light vertical scanning interferometry mode.

Fig. 4
Fig. 4

One-dimensional average PSD taken along line profiles perpendicular to the rolling grooves for the sheet with a rms height of 0.6 µm and the foil sample with a rms height of 0.2 µm.

Fig. 5
Fig. 5

Schematic drawing of the ARS measurement equipment. P i , incident beam; P s , scattered intensity, P 0 the specular component. Angles θ and ϕ are the in- and out-of-plane scattering angles, respectively.

Fig. 6
Fig. 6

Scattering distribution of sheet aluminum as a function of angle in the incidence plane θ and angle out of the plane ϕ, for p-polarized 0.633-µm He–Ne laser light at incidence angle 60°. Note that the intensity has been normalized to the maximum intensity (i.e., the intensity in the specular direction) and that the intensity (Int.) scale is logarithmic. The specular direction has the angles θ = ϕ = 0. (a) Parallel grooves, (b) perpendicular grooves with respect to the plane of the incident light.

Fig. 7
Fig. 7

Reflectance versus wavelength for sheet aluminum as measured in the TIS instrument: R d , diffuse reflectance; R t , total reflectance. Also indicated are the measurements performed with black screens that limit the scattering to smaller angular intervals. The ranges of the angular intervals are indicated.

Fig. 8
Fig. 8

Reflectance versus wavelength for the aluminum foil as measured by the TIS instrument. R d , diffuse reflectance; R t , total reflectance. Also indicated are the measurements performed with black screens that limit the scattering to smaller angular intervals. The ranges of the angular intervals are indicated.

Fig. 9
Fig. 9

Reflectance spectra of the sheet and the foil samples in the wavelength range 0.3–2.5 µm at 5° and 60° angles of incidence. The near-normal reflectance of the sheet after etching is also indicated.

Fig. 10
Fig. 10

Fraction of total scattered radiation in angular intervals about the specular direction, calculated by summarizing of measured ARS data for the sheet and the foil samples. Also indicated are data points obtained from TIS measurements at 0.630 µm with the black screens.

Fig. 11
Fig. 11

Two examples of the scattering pattern from p-polarized light with a 60° incidence angle on the rolled aluminum sheet sample. (a) Grooves parallel and (b) grooves perpendicular to the incident plane. The chosen five angular regions for which the relative scattered intensity is summed up are indicated.

Fig. 12
Fig. 12

Distribution of specular and scattered power in the scatterband from the surface of the sheet sample from p-polarized light at a 60° angle of incidence. Each bar represents the scattered radiation in steps of 2° along the scatterband. For the parallel alignment of the grooves to the incident plane, the abscissa represents ϕ, and for the perpendicular alignment of the grooves to the incident plane the abscissa represents θ. The change of abscissa variable is due to the change in orientation of the scatterband when the plane of incidence is changed with respect to the incident plane, as is clearly seen in Fig. 11.

Tables (1)

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Table 1 Division of Scattered Radiation into Various Angular Regionsa

Equations (5)

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

PSDf=d0Nj=1N |Zj exp-i2πfj-1d0|2,
ΔΩi,j=Δϕi,jΔθi,j cos ϕi,j,
Δϕi,j=0.5|ϕi+1,j-ϕi-1,j|,
Δθi,j=0.5|θi,j-1-θi,j+1|.
Xp,q=k,ln Psk,lΩk,lΩk,lΩp,qi,jm Psi,jΩi,j,

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