Abstract

We have studied the performance of polytetrafluoroethylene integrating spheres in the ultraviolet (UV) region with wavelengths as short as 200  nm. Two techniques were used for this study; first, the spectral throughput of an integrating sphere irradiated by a deuterium lamp was analyzed by a monochromator. Second, a UV laser beam was directed into an integrating sphere, and spectrally dispersed laser induced fluorescence was studied. Significant absorption and fluorescence features were observed in the UV region and attributed to the contamination in the integrating sphere. We demonstrate that integrating spheres are easily contaminated by environmental pollutants such as polycyclic aromatic hydrocarbons emitted from engine exhaust. Baking of the contaminated integrating sphere can reverse some but not all of the effects caused by contaminants. The implications for using integrating spheres for UV measurement are discussed.

© Optical Society of America

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References

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  1. R. D. Saunders and W. R. Ott, "Spectral irradiance measurements: effect of UV-produced fluorescence in integrating spheres," Appl. Opt. 15, 827-827 (1976).
    [CrossRef] [PubMed]
  2. V. R. Weidner and J. J. Hsia, "Reflection properties of pressed polytetrafluoroethylene powder," J. Opt. Soc. Am. 71, 856-861 (1981).
    [CrossRef]
  3. 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]
  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 (1995/1996).
    [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. H. J. Kostkowski, Reliable Spectroradiometry (Spectroradiometry Consulting, 1997), Appendix B.
  9. P. Y. Barnes, M. E. Nadal, and E. A. Early, "Reflectance standards at ultraviolet wavelength," Proc. SPIE 3818, 9-14 (1999).
    [CrossRef]
  10. P. S. Shaw, U. Arp, H. Y. Yoon, R. D. Saunders, A. C. Parr, and K. R. Lykke, "A SURF beamline for synchrotron source-based absolute radiometry," Metrologia 40, S124-S127 (2003).
    [CrossRef]
  11. 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]
  12. S. W. Brown, G. P. Eppeldauer, and K. R. Lykke, "Facility for spectral irradiance and radiance responsivity calibrations using uniform sources," Appl. Opt. 45, 8218-8237 (2006).
    [CrossRef] [PubMed]
  13. S. W. Brown, B. C. Johnson, M. E. Feinholz, M. A. Yarbrough, S. J. Flora, K. R. Lykke, and D. K. Clark, "Stray-light correction algorithm for spectrographs," Metrologia 40, S81-S84 (2003).
    [CrossRef]
  14. 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]
  15. Certain commercial equipment, instruments, or materials are identified in this paper to foster understanding. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.
  16. See, for example, D. Cox, J. M. Key, M. S. Lai, J. R. Sutherland, M. R. Zahn, and J. M. Arrington, "On-line supercritical fluid extraction synchronous luminescence spectroscopy: a screening method for polycyclic aromatic hydrocarbons," J. Under. Chem. Res. 2, 39-42 (2005) and references therein.
  17. See, for example, M. L. Lee, M. V. Novotny, and K. D. Bartle, Analytical Chemistry of Polycyclic Aromatic Compounds (Academic, 1981).
  18. M. L. Lee, M. V. Novotny, and K. D. Bartle, Handbook of Polycyclic Aromatic Hydrocarbons, A. Bjørseth, ed. (Marcel Dekker, 1983).
  19. N. J. Turro, Molecular Photochemistry (Benjamin/Cummings, 1965).
  20. E. Clar, Polycyclic Hydrocarbons (Academic, 1964).
  21. R. A. Friedel and M. Orchin, Ultraviolet Spectra of Aromatic Compounds (Wiley, 1951).
  22. J. B. Birks, Photophysics of Aromatic Molecules (Wiley, 1970).

2007 (1)

2006 (2)

2005 (1)

See, for example, D. Cox, J. M. Key, M. S. Lai, J. R. Sutherland, M. R. Zahn, and J. M. Arrington, "On-line supercritical fluid extraction synchronous luminescence spectroscopy: a screening method for polycyclic aromatic hydrocarbons," J. Under. Chem. Res. 2, 39-42 (2005) and references therein.

2003 (3)

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]

P. S. Shaw, U. Arp, H. Y. Yoon, R. D. Saunders, A. C. Parr, and K. R. Lykke, "A SURF beamline for synchrotron source-based absolute radiometry," Metrologia 40, S124-S127 (2003).
[CrossRef]

S. W. Brown, B. C. Johnson, M. E. Feinholz, M. A. Yarbrough, S. J. Flora, K. R. Lykke, and D. K. Clark, "Stray-light correction algorithm for spectrographs," Metrologia 40, S81-S84 (2003).
[CrossRef]

1999 (1)

P. Y. Barnes, M. E. Nadal, and E. A. Early, "Reflectance standards at ultraviolet wavelength," Proc. SPIE 3818, 9-14 (1999).
[CrossRef]

1997 (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 (1995/1996).
[CrossRef]

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]

1983 (1)

M. L. Lee, M. V. Novotny, and K. D. Bartle, Handbook of Polycyclic Aromatic Hydrocarbons, A. Bjørseth, ed. (Marcel Dekker, 1983).

1981 (2)

See, for example, M. L. Lee, M. V. Novotny, and K. D. Bartle, Analytical Chemistry of Polycyclic Aromatic Compounds (Academic, 1981).

V. R. Weidner and J. J. Hsia, "Reflection properties of pressed polytetrafluoroethylene powder," J. Opt. Soc. Am. 71, 856-861 (1981).
[CrossRef]

1976 (1)

1970 (1)

J. B. Birks, Photophysics of Aromatic Molecules (Wiley, 1970).

1965 (1)

N. J. Turro, Molecular Photochemistry (Benjamin/Cummings, 1965).

1964 (1)

E. Clar, Polycyclic Hydrocarbons (Academic, 1964).

1951 (1)

R. A. Friedel and M. Orchin, Ultraviolet Spectra of Aromatic Compounds (Wiley, 1951).

Arp, U.

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]

P. S. Shaw, U. Arp, H. Y. Yoon, R. D. Saunders, A. C. Parr, and K. R. Lykke, "A SURF beamline for synchrotron source-based absolute radiometry," Metrologia 40, S124-S127 (2003).
[CrossRef]

Barnes, P. Y.

P. Y. Barnes, M. E. Nadal, and E. A. Early, "Reflectance standards at ultraviolet wavelength," Proc. SPIE 3818, 9-14 (1999).
[CrossRef]

Bartle, K. D.

M. L. Lee, M. V. Novotny, and K. D. Bartle, Handbook of Polycyclic Aromatic Hydrocarbons, A. Bjørseth, ed. (Marcel Dekker, 1983).

Birks, J. B.

J. B. Birks, Photophysics of Aromatic Molecules (Wiley, 1970).

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]

Clar, E.

E. Clar, Polycyclic Hydrocarbons (Academic, 1964).

Clark, D. K.

S. W. Brown, B. C. Johnson, M. E. Feinholz, M. A. Yarbrough, S. J. Flora, K. R. Lykke, and D. K. Clark, "Stray-light correction algorithm for spectrographs," Metrologia 40, S81-S84 (2003).
[CrossRef]

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 (1995/1996).
[CrossRef]

Early, E. A.

P. Y. Barnes, M. E. Nadal, and E. A. Early, "Reflectance standards at ultraviolet wavelength," Proc. SPIE 3818, 9-14 (1999).
[CrossRef]

Eppeldauer, G. P.

Feinholz, M. E.

S. W. Brown, B. C. Johnson, M. E. Feinholz, M. A. Yarbrough, S. J. Flora, K. R. Lykke, and D. K. Clark, "Stray-light correction algorithm for spectrographs," Metrologia 40, S81-S84 (2003).
[CrossRef]

Flora, S. J.

S. W. Brown, B. C. Johnson, M. E. Feinholz, M. A. Yarbrough, S. J. Flora, K. R. Lykke, and D. K. Clark, "Stray-light correction algorithm for spectrographs," Metrologia 40, S81-S84 (2003).
[CrossRef]

Friedel, R. A.

R. A. Friedel and M. Orchin, Ultraviolet Spectra of Aromatic Compounds (Wiley, 1951).

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 (1995/1996).
[CrossRef]

Gibson, C. E.

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 (1995/1996).
[CrossRef]

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.

Johnson, B. C.

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]

S. W. Brown, B. C. Johnson, M. E. Feinholz, M. A. Yarbrough, S. J. Flora, K. R. Lykke, and D. K. Clark, "Stray-light correction algorithm for spectrographs," Metrologia 40, S81-S84 (2003).
[CrossRef]

Kostkowski, H. J.

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

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 (1995/1996).
[CrossRef]

Lansard, C.

Lee, M. L.

M. L. Lee, M. V. Novotny, and K. D. Bartle, Handbook of Polycyclic Aromatic Hydrocarbons, A. Bjørseth, ed. (Marcel Dekker, 1983).

Li, Z.

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]

Nadal, M. E.

P. Y. Barnes, M. E. Nadal, and E. A. Early, "Reflectance standards at ultraviolet wavelength," Proc. SPIE 3818, 9-14 (1999).
[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]

Novotny, M. V.

M. L. Lee, M. V. Novotny, and K. D. Bartle, Handbook of Polycyclic Aromatic Hydrocarbons, A. Bjørseth, ed. (Marcel Dekker, 1983).

Ohno, Y.

Orchin, M.

R. A. Friedel and M. Orchin, Ultraviolet Spectra of Aromatic Compounds (Wiley, 1951).

Ott, W. R.

Parr, A. C.

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]

P. S. Shaw, U. Arp, H. Y. Yoon, R. D. Saunders, A. C. Parr, and K. R. Lykke, "A SURF beamline for synchrotron source-based absolute radiometry," Metrologia 40, S124-S127 (2003).
[CrossRef]

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.

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]

P. S. Shaw, U. Arp, H. Y. Yoon, R. D. Saunders, A. C. Parr, and K. R. Lykke, "A SURF beamline for synchrotron source-based absolute radiometry," Metrologia 40, S124-S127 (2003).
[CrossRef]

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.

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]

Turro, N. J.

N. J. Turro, Molecular Photochemistry (Benjamin/Cummings, 1965).

Weidner, V. R.

Yarbrough, M. A.

S. W. Brown, B. C. Johnson, M. E. Feinholz, M. A. Yarbrough, S. J. Flora, K. R. Lykke, and D. K. Clark, "Stray-light correction algorithm for spectrographs," Metrologia 40, S81-S84 (2003).
[CrossRef]

Yoon, H. W.

Yoon, H. Y.

P. S. Shaw, U. Arp, H. Y. Yoon, R. D. Saunders, A. C. Parr, and K. R. Lykke, "A SURF beamline for synchrotron source-based absolute radiometry," Metrologia 40, S124-S127 (2003).
[CrossRef]

Zong, Y.

Appl. Opt. (5)

J. Opt. Soc. Am. (1)

J. Under. Chem. Res. (1)

See, for example, D. Cox, J. M. Key, M. S. Lai, J. R. Sutherland, M. R. Zahn, and J. M. Arrington, "On-line supercritical fluid extraction synchronous luminescence spectroscopy: a screening method for polycyclic aromatic hydrocarbons," J. Under. Chem. Res. 2, 39-42 (2005) and references therein.

Metrologia (4)

D. R. Gibbs, F. J. Duncan, R. P. Lambe, and T. M. Goodman, "Ageing of materials under intense UV radiation," Metrologia 32, 601-607 (1995/1996).
[CrossRef]

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]

P. S. Shaw, U. Arp, H. Y. Yoon, R. D. Saunders, A. C. Parr, and K. R. Lykke, "A SURF beamline for synchrotron source-based absolute radiometry," Metrologia 40, S124-S127 (2003).
[CrossRef]

S. W. Brown, B. C. Johnson, M. E. Feinholz, M. A. Yarbrough, S. J. Flora, K. R. Lykke, and D. K. Clark, "Stray-light correction algorithm for spectrographs," Metrologia 40, S81-S84 (2003).
[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]

Proc. SPIE (1)

P. Y. Barnes, M. E. Nadal, and E. A. Early, "Reflectance standards at ultraviolet wavelength," Proc. SPIE 3818, 9-14 (1999).
[CrossRef]

Other (8)

Certain commercial equipment, instruments, or materials are identified in this paper to foster understanding. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.

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

See, for example, M. L. Lee, M. V. Novotny, and K. D. Bartle, Analytical Chemistry of Polycyclic Aromatic Compounds (Academic, 1981).

M. L. Lee, M. V. Novotny, and K. D. Bartle, Handbook of Polycyclic Aromatic Hydrocarbons, A. Bjørseth, ed. (Marcel Dekker, 1983).

N. J. Turro, Molecular Photochemistry (Benjamin/Cummings, 1965).

E. Clar, Polycyclic Hydrocarbons (Academic, 1964).

R. A. Friedel and M. Orchin, Ultraviolet Spectra of Aromatic Compounds (Wiley, 1951).

J. B. Birks, Photophysics of Aromatic Molecules (Wiley, 1970).

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Figures (15)

Fig. 1
Fig. 1

Schematic diagram of the experimental setup for measurement of integrating sphere spectral throughput.

Fig. 2
Fig. 2

Spectral output with the deuterium lamp irradiating the monochromator entrance directly. This signal was used to normalize spectral outputs measured with integrating spheres to obtain the relative throughput of the integrating spheres as explained in the text.

Fig. 3
Fig. 3

Schematic diagram of the experimental setup for the LIF measurements on integrating spheres.

Fig. 4
Fig. 4

Typical line spread function of the spectrograph with the laser wavelength of 360   nm .

Fig. 5
Fig. 5

Relative throughput measured with (a) a freshly pressed PTFE integrating sphere, and (b)–(d) commercial sintered PTFE integrating spheres with (b) and (c) new from manufacturers when measured, while (d) had been used for UV radiometry prior to this measurement. All curves are normalized at 400 nm to 1. For easy viewing, there is an offset to each curve. The offsets are 0 for (a), 0.6 for (b), 0.8 for (c), and 1.1 for (d).

Fig. 6
Fig. 6

LIF measurements of (a) a pressed PTFE integrating sphere and (b)–(d) commercial sintered PTFE integrating spheres with the excitation laser tuned at 220   nm . All curves are normalized to 1 at the laser excitation wavelength of 220   nm . For easy viewing, there is an offset to each curve. The offsets are 0 for (a), 0.004 for (b), 0.008 for (c), and 0.012 for (d).

Fig. 7
Fig. 7

LIF measurements of a commercial sintered PTFE integrating sphere with the excitation laser tuned at (a) 210, (b) 220, (c) 240, (d) 266, (e) 293, and (f) 360 n m . For easy viewing, the peak of each curve at the wavelength of the excitation laser is normalized to a different value. The values are 10 7 for (a), 10 5 for (b), 10 3 for (c), 10 2 for (d), 10 1 for (e), and 1 for (f).

Fig. 8
Fig. 8

LIF measurements of a sintered PTFE integrating sphere before and after baking the integrating sphere 40 h in vacuum. For each graph, the top curves are before baking and the bottom curves are after baking. All curves are normalized to 1 at the corresponding laser excitation wavelengths.

Fig. 9
Fig. 9

LIF measurements of a sintered PTFE integrating sphere before and after baking the integrating sphere 40 h in vacuum. The top curve is before baking and the bottom curve is after baking.

Fig. 10
Fig. 10

LIF measurements of a pressed PTFE integrating sphere before and after baking the integrating sphere 40 h in vacuum. For each graph, the top curves are before baking and the bottom curves are after baking. All curves are normalized to 1 at the corresponding laser excitation wavelengths.

Fig. 11
Fig. 11

Relative throughput measurements of (a) a sintered PTFE integrating sphere before and after 65 h vacuum bake, (b) a sintered PTFE integrating sphere before and after 24 h air bake, and (c) a pressed PTFE integrating sphere before and after 40 h vacuum bake. Solid lines are before the bake, and open circles are after the bake.

Fig. 12
Fig. 12

Relative changes in throughput for pressed integrating spheres after 24 h vacuum bake and after 105 h air bake.

Fig. 13
Fig. 13

Relative change in throughput for pressed integrating spheres as a function of baking time in air for 206 and 396   nm .

Fig. 14
Fig. 14

LIF measurements of a sintered PTFE integrating sphere exposed to exhaust from a gasoline engine and from a diesel engine. Thin solid lines are before the exposure, thick solid lines are after the exposure. For gasoline exposure, dotted line is 19 h of baking in vacuum after exposure. For diesel exposure, dotted lines are baking for both 19 and 68 h.

Fig. 15
Fig. 15

Relative throughput measurements of a sintered PTFE integrating sphere before exposure, after exposure to gasoline engine exhaust, and after exposure to diesel engine exhaust.

Equations (1)

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Φ o u t = Φ i n r 2 A 2 [ 1 ( A 1 + A 2 ) ] 1 r [ 1 ( A 1 + A 2 ) ] ,

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