Abstract

Our recent study of the performance of integrating spheres shows prominent UV induced fluorescence features that are associated with contamination of the diffusing wall material by hydrocarbons. Because of multiple reflections of the radiation inside the integrating sphere, fluorescence is induced multiple times with each reflection of the incident radiation by the wall. Here, we report a simple theory on the fluorescence of integrating spheres developed from first principles. The results indicate a strong dependence of fluorescence on the reflectance of the diffusing material at both the excitation and fluorescence wavelengths as well as the geometry of the integrating sphere. Because of multiple reflection of the exciting radiation, a gain of more than an order of magnitude in fluorescence is possible compared with direct and single irradiation of a flat piece of the diffusing/fluorescing material. Applications of such fluorescence analysis for integrating spheres are discussed.

© 2008 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  4. C. J. Bruegge, A. E. Stiegman, R. A. Rainen, and A. W. Springsteen, “Use of Spectralon as a diffuse reflectance standard for in-flight calibration of earth-orbiting sensors,” Opt. Eng. 32, 805-814 (1993).
    [CrossRef]
  5. D. R. Gibbs, F. J. Duncan, R. P. Lambe, and T. M. Goodman, “Ageing of materials under intense UV radiation,” Metrologia 32, 601-607 (1995).
    [CrossRef]
  6. P. R. Spyak and C. Lansard, “Reflectance properties of pressed Algoflon F6: a replacement reflectance-standard material for Halon,” Appl. Opt. 36, 2963-2970 (1997).
    [CrossRef] [PubMed]
  7. W. Möller, K-P. Nikolaus, and A. Höpe, “Degradation of the diffuse reflectance of Spectralon under low-level irradiation,” Metrologia 40, S212-S215 (2003).
    [CrossRef]
  8. P. S. Shaw, Z. Li, U. Arp, and K. R. Lykke, “Ultraviolet characterization of integrating spheres,” Appl. Opt. 46, 5119-5128 (2007).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  11. Y. Ohno, “Integrating sphere simulation: application to total flux scale realization,” Appl. Opt. 33, 2637-2647 (1994).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  13. L. M. Hanssen, “Effects of non-Lambertian surfaces on integrating sphere measurements,” Appl. Opt. 35, 3597-3606(1996).
    [CrossRef] [PubMed]
  14. D. H. Alman and F. W. Billmeyer, “Integrating-sphere errors in the colorimetry of fluorescent materials,” Color Res. Appl. 1, 141-145 (1976).
  15. H. J. Kostkowski, Reliable Spectroradiometry (Spectroradiometry Consulting, 1997), Appendix B.1.
  16. “A guide to integrating sphere theory and applications,” http://www.labsphere.com/tecdocs.aspx.
  17. P. S. Shaw, U. Arp, R. D. Saunders, D. J. Shin, H. W. Yoon, C. E. Gibson, Z. Li, A. C. Parr, and K. R. Lykke, “Synchrotron radiation based irradiance calibration from 200 nm to 400 nm at SURF III,” Appl. Opt. 46, 25-35 (2007).
    [CrossRef]
  18. Y. Zong, S. W. Brown, B. C. Johnson, K. R. Lykke, and Y. Ohno, “Simple spectral stray light correction method for array spectroradiometers,” Appl. Opt. 45, 1111-1119 (2006).
    [CrossRef] [PubMed]
  19. F. Grum and G. W. Luckey, “Optical sphere paint and a working standard of reflectance,” Appl. Opt. 7, 2289-2294 (1968).
    [CrossRef] [PubMed]

2007 (2)

2006 (1)

2003 (1)

W. Möller, K-P. Nikolaus, and A. Höpe, “Degradation of the diffuse reflectance of Spectralon under low-level irradiation,” Metrologia 40, S212-S215 (2003).
[CrossRef]

1997 (1)

1996 (2)

1995 (1)

D. R. Gibbs, F. J. Duncan, R. P. Lambe, and T. M. Goodman, “Ageing of materials under intense UV radiation,” Metrologia 32, 601-607 (1995).
[CrossRef]

1994 (1)

1993 (2)

A. E. Stiegman, C. J. Bruegge, and A. W. Springsteen, “Ultraviolet stability and contamination analysis of Spectralon diffuse reflectance material,” Opt. Eng. 32, 799-804 (1993).
[CrossRef]

C. J. Bruegge, A. E. Stiegman, R. A. Rainen, and A. W. Springsteen, “Use of Spectralon as a diffuse reflectance standard for in-flight calibration of earth-orbiting sensors,” Opt. Eng. 32, 805-814 (1993).
[CrossRef]

1981 (1)

1976 (2)

R. D. Saunders and W. R. Ott, “Spectral irradiance measurements: effect of uv-produced fluorescence in integrating spheres,” Appl. Opt. 15, 827-828 (1976).
[CrossRef] [PubMed]

D. H. Alman and F. W. Billmeyer, “Integrating-sphere errors in the colorimetry of fluorescent materials,” Color Res. Appl. 1, 141-145 (1976).

1968 (1)

1967 (1)

1955 (1)

Alman, D. H.

D. H. Alman and F. W. Billmeyer, “Integrating-sphere errors in the colorimetry of fluorescent materials,” Color Res. Appl. 1, 141-145 (1976).

Arp, U.

Billmeyer, F. W.

D. H. Alman and F. W. Billmeyer, “Integrating-sphere errors in the colorimetry of fluorescent materials,” Color Res. Appl. 1, 141-145 (1976).

Brown, S. W.

Bruegge, C. J.

A. E. Stiegman, C. J. Bruegge, and A. W. Springsteen, “Ultraviolet stability and contamination analysis of Spectralon diffuse reflectance material,” Opt. Eng. 32, 799-804 (1993).
[CrossRef]

C. J. Bruegge, A. E. Stiegman, R. A. Rainen, and A. W. Springsteen, “Use of Spectralon as a diffuse reflectance standard for in-flight calibration of earth-orbiting sensors,” Opt. Eng. 32, 805-814 (1993).
[CrossRef]

Crowther, B. G.

Duncan, F. J.

D. R. Gibbs, F. J. Duncan, R. P. Lambe, and T. M. Goodman, “Ageing of materials under intense UV radiation,” Metrologia 32, 601-607 (1995).
[CrossRef]

Gibbs, D. R.

D. R. Gibbs, F. J. Duncan, R. P. Lambe, and T. M. Goodman, “Ageing of materials under intense UV radiation,” Metrologia 32, 601-607 (1995).
[CrossRef]

Gibson, C. E.

Goebel, D. G.

Goodman, T. M.

D. R. Gibbs, F. J. Duncan, R. P. Lambe, and T. M. Goodman, “Ageing of materials under intense UV radiation,” Metrologia 32, 601-607 (1995).
[CrossRef]

Grum, F.

Hanssen, L. M.

Höpe, A.

W. Möller, K-P. Nikolaus, and A. Höpe, “Degradation of the diffuse reflectance of Spectralon under low-level irradiation,” Metrologia 40, S212-S215 (2003).
[CrossRef]

Hsia, J. J.

Jacquez, J. A.

Johnson, B. C.

Kostkowski, H. J.

H. J. Kostkowski, Reliable Spectroradiometry (Spectroradiometry Consulting, 1997), Appendix B.1.

Kuppenheim, H. F.

Lambe, R. P.

D. R. Gibbs, F. J. Duncan, R. P. Lambe, and T. M. Goodman, “Ageing of materials under intense UV radiation,” Metrologia 32, 601-607 (1995).
[CrossRef]

Lansard, C.

Li, Z.

Luckey, G. W.

Lykke, K. R.

Möller, W.

W. Möller, K-P. Nikolaus, and A. Höpe, “Degradation of the diffuse reflectance of Spectralon under low-level irradiation,” Metrologia 40, S212-S215 (2003).
[CrossRef]

Nikolaus, K-P.

W. Möller, K-P. Nikolaus, and A. Höpe, “Degradation of the diffuse reflectance of Spectralon under low-level irradiation,” Metrologia 40, S212-S215 (2003).
[CrossRef]

Ohno, Y.

Ott, W. R.

Parr, A. C.

Rainen, R. A.

C. J. Bruegge, A. E. Stiegman, R. A. Rainen, and A. W. Springsteen, “Use of Spectralon as a diffuse reflectance standard for in-flight calibration of earth-orbiting sensors,” Opt. Eng. 32, 805-814 (1993).
[CrossRef]

Saunders, R. D.

Shaw, P. S.

Shin, D. J.

Springsteen, A. W.

C. J. Bruegge, A. E. Stiegman, R. A. Rainen, and A. W. Springsteen, “Use of Spectralon as a diffuse reflectance standard for in-flight calibration of earth-orbiting sensors,” Opt. Eng. 32, 805-814 (1993).
[CrossRef]

A. E. Stiegman, C. J. Bruegge, and A. W. Springsteen, “Ultraviolet stability and contamination analysis of Spectralon diffuse reflectance material,” Opt. Eng. 32, 799-804 (1993).
[CrossRef]

Spyak, P. R.

Stiegman, A. E.

C. J. Bruegge, A. E. Stiegman, R. A. Rainen, and A. W. Springsteen, “Use of Spectralon as a diffuse reflectance standard for in-flight calibration of earth-orbiting sensors,” Opt. Eng. 32, 805-814 (1993).
[CrossRef]

A. E. Stiegman, C. J. Bruegge, and A. W. Springsteen, “Ultraviolet stability and contamination analysis of Spectralon diffuse reflectance material,” Opt. Eng. 32, 799-804 (1993).
[CrossRef]

Weidner, V. R.

Yoon, H. W.

Zong, Y.

Appl. Opt. (10)

R. D. Saunders and W. R. Ott, “Spectral irradiance measurements: effect of uv-produced fluorescence in integrating spheres,” Appl. Opt. 15, 827-828 (1976).
[CrossRef] [PubMed]

P. R. Spyak and C. Lansard, “Reflectance properties of pressed Algoflon F6: a replacement reflectance-standard material for Halon,” Appl. Opt. 36, 2963-2970 (1997).
[CrossRef] [PubMed]

P. S. Shaw, Z. Li, U. Arp, and K. R. Lykke, “Ultraviolet characterization of integrating spheres,” Appl. Opt. 46, 5119-5128 (2007).
[CrossRef] [PubMed]

D. G. Goebel, “Generalized integrating-sphere theory,” Appl. Opt. 6, 125-128 (1967).
[CrossRef] [PubMed]

Y. Ohno, “Integrating sphere simulation: application to total flux scale realization,” Appl. Opt. 33, 2637-2647 (1994).
[CrossRef] [PubMed]

B. G. Crowther, “Computer modeling of integrating spheres,” Appl. Opt. 35, 5880-5886 (1996).
[CrossRef] [PubMed]

L. M. Hanssen, “Effects of non-Lambertian surfaces on integrating sphere measurements,” Appl. Opt. 35, 3597-3606(1996).
[CrossRef] [PubMed]

P. S. Shaw, U. Arp, R. D. Saunders, D. J. Shin, H. W. Yoon, C. E. Gibson, Z. Li, A. C. Parr, and K. R. Lykke, “Synchrotron radiation based irradiance calibration from 200 nm to 400 nm at SURF III,” Appl. Opt. 46, 25-35 (2007).
[CrossRef]

Y. Zong, S. W. Brown, B. C. Johnson, K. R. Lykke, and Y. Ohno, “Simple spectral stray light correction method for array spectroradiometers,” Appl. Opt. 45, 1111-1119 (2006).
[CrossRef] [PubMed]

F. Grum and G. W. Luckey, “Optical sphere paint and a working standard of reflectance,” Appl. Opt. 7, 2289-2294 (1968).
[CrossRef] [PubMed]

Color Res. Appl. (1)

D. H. Alman and F. W. Billmeyer, “Integrating-sphere errors in the colorimetry of fluorescent materials,” Color Res. Appl. 1, 141-145 (1976).

J. Opt. Soc. Am. (2)

Metrologia (2)

W. Möller, K-P. Nikolaus, and A. Höpe, “Degradation of the diffuse reflectance of Spectralon under low-level irradiation,” Metrologia 40, S212-S215 (2003).
[CrossRef]

D. R. Gibbs, F. J. Duncan, R. P. Lambe, and T. M. Goodman, “Ageing of materials under intense UV radiation,” Metrologia 32, 601-607 (1995).
[CrossRef]

Opt. Eng. (2)

A. E. Stiegman, C. J. Bruegge, and A. W. Springsteen, “Ultraviolet stability and contamination analysis of Spectralon diffuse reflectance material,” Opt. Eng. 32, 799-804 (1993).
[CrossRef]

C. J. Bruegge, A. E. Stiegman, R. A. Rainen, and A. W. Springsteen, “Use of Spectralon as a diffuse reflectance standard for in-flight calibration of earth-orbiting sensors,” Opt. Eng. 32, 805-814 (1993).
[CrossRef]

Other (2)

H. J. Kostkowski, Reliable Spectroradiometry (Spectroradiometry Consulting, 1997), Appendix B.1.

“A guide to integrating sphere theory and applications,” http://www.labsphere.com/tecdocs.aspx.

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Figures (7)

Fig. 1
Fig. 1

Measured throughput of a pressed PTFE integrating sphere using monochromatic light versus polychromatic light from a deuterium lamp.

Fig. 2
Fig. 2

Fluorescence process inside an integrating sphere. The solid blue lines are the incident and subsequently reflected beams, whereas the excited fluorescence beams are represented by dotted red lines.

Fig. 3
Fig. 3

Throughput of an integrating sphere plotted against the reflectance for A r = 0.2 % , 1%, and 5% with α = 1 .

Fig. 4
Fig. 4

Fluorescence gain as a function of the reflectance at both wavelengths of λ 0 and λ f calculated for an integrating sphere with A r = 1 % .

Fig. 5
Fig. 5

Throughput of an integrating sphere as a function of A r for values of the reflectance of 0.97, 0.98, and 0.99.

Fig. 6
Fig. 6

Fluorescence gain of an integrating sphere as a function of A r for ρ ( λ f ) = 0.99 and ρ ( λ 0 ) = 0.99 , 0.98, and 0.97.

Fig. 7
Fig. 7

Relative fluorescence yield of an integrating sphere normalized by fluorescence yield f ( λ f , λ 0 ) as a function of A r for ρ ( λ 0 ) = 0.99 and ρ ( λ f ) = 0.99 , 0.98, and 0.97.

Tables (1)

Tables Icon

Table 1 Flux Analysis of Incident and Fluorescence Radiation Inside an Integrating Sphere for Each Reflection a

Equations (15)

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Φ out ( λ 0 ) = n = 1 [ Φ in ( λ 0 ) ρ ( λ 0 ) n ( 1 A r ) n 1 α A r ] ,
Φ out ( λ 0 ) = Φ in ( λ 0 ) ρ ( λ 0 ) α A r n = 0 [ ρ ( λ 0 ) ( 1 A r ) ] n .
Φ out ( λ 0 ) Φ in ( λ 0 ) = ρ ( λ 0 ) α A r 1 ρ ( λ 0 ) ( 1 A r ) .
Ψ out ( λ 0 ) = n = 1 [ f ( λ f , λ ) 0 Φ in ( λ 0 ) ρ ( λ 0 ) n 1 ( 1 A r ) n 1 · ρ ( λ f ) α A r 1 ρ ( λ f ) ( 1 A r ) ] ,
Ψ out ( λ f ) Φ in ( λ 0 ) = f ( λ f , λ 0 ) ρ ( λ f ) α A r 1 ρ ( λ f ) ( 1 A r ) n = 0 [ ρ ( λ 0 ) n ( 1 A r ) n ] ,
Ψ out ( λ f ) Φ in ( λ 0 ) = f ( λ f , λ 0 ) ρ ( λ f ) α A r [ ( 1 ρ ( λ f ) ( 1 A r ) ] [ 1 ρ ( λ 0 ) ( 1 A r ) ] .
κ = ρ ( λ f ) α A r [ 1 ρ ( λ f ) ( 1 A r ) ] [ ( 1 ρ ( λ 0 ) ( 1 A r ) ] .
Φ out ( λ 0 ) = n = 2 [ Φ in ( λ 0 ) ρ ( λ 0 ) n ( 1 A r ) n 1 α A r ] ,
Φ out ( λ 0 ) Φ in ( λ 0 ) = ρ ( λ 0 ) 2 α A r ( 1 A r ) 1 ρ ( λ 0 ) ( 1 A r ) .
Ψ 1 , out ( λ 0 ) = f ( λ f , λ ) 0 Φ in ( λ 0 ) · ρ ( λ f ) α A r ( 1 A r ) 1 ρ ( λ f ) ( 1 A r ) .
Ψ out ( λ 0 ) = Ψ 1 , out ( λ 0 ) + n = 2 [ f ( λ f , λ ) 0 Φ in ( λ 0 ) ρ ( λ 0 ) n 1 ( 1 A r ) n 1 · ρ ( λ f ) α A r 1 ρ ( λ f ) ( 1 A r ) ] .
Ψ out ( λ f ) Φ in ( λ 0 ) = f ( λ f , λ ) 0 ρ ( λ f ) α A r 1 ρ ( λ f ) ( 1 A r ) { ρ ( λ f ) ( 1 A r ) + n = 1 [ ρ ( λ 0 ) n ( 1 A r ) n ] } ,
Ψ out ( λ f ) Φ in ( λ 0 ) = f ( λ f , λ 0 ) ρ ( λ f ) α A r ( 1 A r ) [ 1 ρ ( λ f ) ( 1 A r ) ] [ 1 ρ ( λ 0 ) ( 1 A r ) ] [ 1 + ρ ( λ 0 ) A r ] .
A r = ( 1 ρ ( λ f ) ) ( 1 ρ ( λ 0 ) ) ρ ( λ f ) ρ ( λ 0 ) .
Ψ out ( λ f ) Φ in ( λ 0 ) / Φ out ( λ 0 ) Φ in ( λ 0 ) = f ( λ f , λ 0 ) ρ ( λ f ) ρ ( λ 0 ) 1 ( 1 ρ ( λ f ) ( 1 A r ) ) .

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