Abstract

For most integrating sphere measurements, the difference in light distribution between a specular reference beam and a diffused sample beam can result in significant errors. The problem becomes especially pronounced in integrating spheres that include a port for reflectance or diffuse transmittance measurements. The port is included in many standard spectrophotometers to facilitate a multipurpose instrument, however, absorption around the port edge can result in a detected signal that is too low. The absorption effect is especially apparent for low-angle scattering samples, because a significant portion of the light is scattered directly onto that edge. In this paper, a method for more accurate transmittance measurements of low-angle light-scattering samples is presented. The method uses a standard integrating sphere spectrophotometer, and the problem with increased absorption around the port edge is addressed by introducing a diffuser between the sample and the integrating sphere during both reference and sample scan. This reduces the discrepancy between the two scans and spreads the scattered light over a greater portion of the sphere wall. The problem with multiple reflections between the sample and diffuser is successfully addressed using a correction factor. The method is tested for two patterned glass samples with low-angle scattering and in both cases the transmittance accuracy is significantly improved.

© 2011 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  6. I. Lindseth, A. Bardal, and R. Spooren, “Reflectance measurements of aluminium surfaces using integrating spheres,” Opt. Lasers Eng. 32, 419–435 (2000).
    [CrossRef]
  7. D. I. Milburn and K. G. T. Hollands, “The directional response error in integrating-sphere transmittance measurements at solar wavelengths,” Solar Energy 55, 85–91 (1995).
    [CrossRef]
  8. A. Roos, “Interpretation of integrating sphere signal output for nonideal transmitting samples,” Appl. Opt. 30, 468–474(1991).
    [CrossRef] [PubMed]
  9. D. K. Edwards, J. T. Gier, K. E. Nelson, and R. D. Roddick, “Integrating sphere for imperfectly diffuse samples,” J. Opt. Soc. Am. 51, 1279–1288 (1961).
    [CrossRef]
  10. F. Grum and R. J. Becherer, Optical Radiation Measurements (Academic, 1979).
  11. L. F. Costa, F. Grum, and T. E. Wightman, “Direct absorptance measurement of fluorescent and turbid samples in a 4π geometry,” Color Res. Appl. 1, 193–200 (1976).
  12. P. Nostell, A. Roos, and 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]

2000

I. Lindseth, A. Bardal, and R. Spooren, “Reflectance measurements of aluminium surfaces using integrating spheres,” Opt. Lasers Eng. 32, 419–435 (2000).
[CrossRef]

1999

P. Nostell, A. Roos, and 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]

1995

D. I. Milburn and K. G. T. Hollands, “The directional response error in integrating-sphere transmittance measurements at solar wavelengths,” Solar Energy 55, 85–91 (1995).
[CrossRef]

1991

1988

1986

F. J. J. Clarke and J. A. Compton, “Correction methods for integrating-sphere measurement of hemispherical reflectance,” Color Res. Appl. 11, 253–262 (1986).
[CrossRef]

1976

L. F. Costa, F. Grum, and T. E. Wightman, “Direct absorptance measurement of fluorescent and turbid samples in a 4π geometry,” Color Res. Appl. 1, 193–200 (1976).

1970

M. W. Finkel, “Integrating sphere theory,” Opt. Commun. 2, 25–28 (1970).
[CrossRef]

1967

1961

1955

Bardal, A.

I. Lindseth, A. Bardal, and R. Spooren, “Reflectance measurements of aluminium surfaces using integrating spheres,” Opt. Lasers Eng. 32, 419–435 (2000).
[CrossRef]

Becherer, R. J.

F. Grum and R. J. Becherer, Optical Radiation Measurements (Academic, 1979).

Bergkvist, M.

Clarke, F. J. J.

F. J. J. Clarke and J. A. Compton, “Correction methods for integrating-sphere measurement of hemispherical reflectance,” Color Res. Appl. 11, 253–262 (1986).
[CrossRef]

Compton, J. A.

F. J. J. Clarke and J. A. Compton, “Correction methods for integrating-sphere measurement of hemispherical reflectance,” Color Res. Appl. 11, 253–262 (1986).
[CrossRef]

Costa, L. F.

L. F. Costa, F. Grum, and T. E. Wightman, “Direct absorptance measurement of fluorescent and turbid samples in a 4π geometry,” Color Res. Appl. 1, 193–200 (1976).

Edwards, D. K.

Finkel, M. W.

M. W. Finkel, “Integrating sphere theory,” Opt. Commun. 2, 25–28 (1970).
[CrossRef]

Gier, J. T.

Goebel, D. O.

Grum, F.

L. F. Costa, F. Grum, and T. E. Wightman, “Direct absorptance measurement of fluorescent and turbid samples in a 4π geometry,” Color Res. Appl. 1, 193–200 (1976).

F. Grum and R. J. Becherer, Optical Radiation Measurements (Academic, 1979).

Hollands, K. G. T.

D. I. Milburn and K. G. T. Hollands, “The directional response error in integrating-sphere transmittance measurements at solar wavelengths,” Solar Energy 55, 85–91 (1995).
[CrossRef]

Jacquez, J. A.

Kuppenheim, H. F.

Lindseth, I.

I. Lindseth, A. Bardal, and R. Spooren, “Reflectance measurements of aluminium surfaces using integrating spheres,” Opt. Lasers Eng. 32, 419–435 (2000).
[CrossRef]

Milburn, D. I.

D. I. Milburn and K. G. T. Hollands, “The directional response error in integrating-sphere transmittance measurements at solar wavelengths,” Solar Energy 55, 85–91 (1995).
[CrossRef]

Nelson, K. E.

Nostell, P.

P. Nostell, A. Roos, and 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]

Ribbing, C.-G.

Roddick, R. D.

Rönnow, D.

P. Nostell, A. Roos, and 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]

Roos, A.

P. Nostell, A. Roos, and 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, “Interpretation of integrating sphere signal output for nonideal transmitting samples,” Appl. Opt. 30, 468–474(1991).
[CrossRef] [PubMed]

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

Spooren, R.

I. Lindseth, A. Bardal, and R. Spooren, “Reflectance measurements of aluminium surfaces using integrating spheres,” Opt. Lasers Eng. 32, 419–435 (2000).
[CrossRef]

Wightman, T. E.

L. F. Costa, F. Grum, and T. E. Wightman, “Direct absorptance measurement of fluorescent and turbid samples in a 4π geometry,” Color Res. Appl. 1, 193–200 (1976).

Appl. Opt.

Color Res. Appl.

F. J. J. Clarke and J. A. Compton, “Correction methods for integrating-sphere measurement of hemispherical reflectance,” Color Res. Appl. 11, 253–262 (1986).
[CrossRef]

L. F. Costa, F. Grum, and T. E. Wightman, “Direct absorptance measurement of fluorescent and turbid samples in a 4π geometry,” Color Res. Appl. 1, 193–200 (1976).

J. Opt. Soc. Am.

Opt. Commun.

M. W. Finkel, “Integrating sphere theory,” Opt. Commun. 2, 25–28 (1970).
[CrossRef]

Opt. Lasers Eng.

I. Lindseth, A. Bardal, and R. Spooren, “Reflectance measurements of aluminium surfaces using integrating spheres,” Opt. Lasers Eng. 32, 419–435 (2000).
[CrossRef]

Rev. Sci. Instrum.

P. Nostell, A. Roos, and 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]

Solar Energy

D. I. Milburn and K. G. T. Hollands, “The directional response error in integrating-sphere transmittance measurements at solar wavelengths,” Solar Energy 55, 85–91 (1995).
[CrossRef]

Other

F. Grum and R. J. Becherer, Optical Radiation Measurements (Academic, 1979).

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Figures (10)

Fig. 1
Fig. 1

Detected light intensities, normalized to the highest intensity, for different positions of the light spot on the specular transmittance exit port.

Fig. 2
Fig. 2

Side view of the integrating sphere that illustrates the position of the sample and the diffuser for the two scans that are required to determine the correction coefficient k exp . When the signal S 1 is detected the distance between the clear glass and the diffuser is sufficient to reduce all contributions from multiple reflections. During the second scan multiple reflections contribute to the detected signal S 2 .

Fig. 3
Fig. 3

Transmitted scattering image when light from a laser pointer is incident upon the smooth front side, in (a) for the Pyramidal sample and in (b) for the Peel sample.

Fig. 4
Fig. 4

The bidirectional transmittance distribution function (BTDF) in (a) for the Pyramidal sample and in (b) for the Peel sample. The BTDF was determined using a goniophotometer.

Fig. 5
Fig. 5

Transmittance and reflectance of the diffuser at normal angle of incidence with the smooth side (side f) and the scattering side (side b) facing the beam. The diffuser has a high diffuse transmittance and a low reflectance. The total reflectance when the scattering side (side b) faces the beam is especially low and entirely diffuse.

Fig. 6
Fig. 6

In-plane scattering of the two patterned glass samples and the effect when a diffuser is introduced between the sample the and the detector. In (a) at 550 nm and in (b) at 1500 nm . At both wavelengths the diffuser helps to spread out and homogenize the detected signal.

Fig. 7
Fig. 7

Transmittance of the diffuser when it is positioned at distance d from the integrating sphere port. The relatively constant intensity reduction over the wavelength range indicates that the scattering distribution of the diffuser is sufficiently wavelength independent.

Fig. 8
Fig. 8

Transmittance of the two light-scattering samples Pyramidal and Peel. The transmittance has been determined using standard measurements, i.e., measured without a diffuser, in the Tsphere and L900 instruments. The discrepancy between the two instruments is addressed with the proposed measurement method.

Fig. 9
Fig. 9

Transmittance of a low-iron clear glass sample determined using the proposed method and standard measurements. The spectra labeled Tsphere and L900 are standard measurements, i.e., measured without a diffuser, in the respective instruments. The subscripts Uncorr, Corr1, and Corr2 indicate uncorrected transmittance, transmittance corrected for multiple reflections according to Eq. (3), and transmittance corrected for multiple reflections and non-normal-incidence angles according to Eq. (4), respectively.

Fig. 10
Fig. 10

Transmittance of the (a) Pyramidal and (b) Peel samples using the proposed method and standard measurements. The spectra labeled Tsphere and L900 are standard measurements, i.e., measured without a diffuser, in the respective instruments. The subscripts Uncorr, Corr1, and Corr2 indicate uncorrected transmittance, transmittance corrected for multiple reflections according to Eq. (3), and transmittance corrected for multiple reflections and non-normal-incidence angles according to Eq. (4), respectively.

Equations (6)

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T = T s T d + T s R d R s T d + T s ( R d R s ) 2 T d + = m = 0 T s T d ( R s R d ) m = T s T d 1 R s R d ,
T s = T ( 1 R s R d ) T d .
T s , Corr 1 = S T ( 1 R s R d ) .
T s , Corr 2 = S T ( 1 k exp R s R d ) .
S 1 = S 2 ( 1 k exp R cg R d ) ,
k exp = ( 1 S 1 S 2 ) R cg R d .

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