Abstract

A new method for absolute calibration of the detection efficiency of fluorescence collection systems is described for wavelengths covering the 180–2000-nm range. The radiation source for the technique is spontaneous Raman scattering in H2. An analytic expression is derived for the scattering cross section averaged over the solid angle of the fluorescence collection system. From this result, an optical system is calibrated at 845 nm, demonstrating that the technique is easy to use, is quick to implement, and gives accurate results.

© 1986 Optical Society of America

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  1. D. J. Bamford, L. E. Jusinski, W. K. Bischel, “Absolute Two-Photon Absorption and Three-Photon Ionization Cross Sections for Atomic Oxygen,” submitted to Phys. Rev. A. (1986).
    [CrossRef] [PubMed]
  2. K. D. Mielenz, Ed., Optical Radiation Measurements, Vol. 3, Measurement of Photoluminescence (Academic, New York, 1982).
  3. B. P. Stoicheff, “High Resolution Raman Spectroscopy of Gases IX. Spectra of H2, HD, D2,” Can. J. Phys. 35, 730 (1957).
    [CrossRef]
  4. J. V. Foltz, D. H. Rank, T. A. Wiggins, “Determinations of Some Hydrogen Molecular Constants,” J. Mol. Spectrosc. 21, 203 (1966).
    [CrossRef]
  5. P. J. Brannon, C. H. Church, C. W. Peters, “Electric Field Induced Spectra of Molecular Hydrogen, Deuterium and Deuterium Hydride,” J. Mol. Spectrosc. 27, 44 (1968).
    [CrossRef]
  6. A. L. Ford, J. C. Browne, “Rayleigh and Raman Cross Sections for the Hydrogen Molecule,” At. Data 5, 305 (1973);“Direct-Resolvent Operator Computations on the Hydrogen-Molecule Dynamic Polarizability, Rayleigh, and Raman Scattering,” Phys. Rev. A 7, 418 (1973).
    [CrossRef]
  7. W. M. Huo, NASA Ames RC, private communication.
  8. W. K. Bischel, G. Black, “Wavelength Dependence of Raman Scattering Cross Sections from 200–600 nm,” in Excimer Lasers 1983, C. K. Rhodes, H. Egger, H. Pummer, Eds. (American Institute of Physics, New York, 1983).
  9. W. M. Huo, R. L. Jaffe, “Ab Initio Calculation of the Third-Order Susceptibility of H2,” Phys. Rev. Lett. 47, 30 (1981).
    [CrossRef]
  10. W. Holzer, Y. Le Duff, K. Altmann, “J Dependence of the Depolarization Ratio of the Rotational Components of the Q Branch of the H2 and D2 Raman Band,” J. Chem. Phys. 58, 642 (1973);W. Holzer, Y. Le Duff, “The Depolarization Ratio of the Raman Bands of the Vibration of Diatomic Molecules,” in Advances in Raman Spectroscopy, Vol. 1, J. P. Mathieu, Ed. (Heyden and Sons, New York, 1973), pp. 109–114.
    [CrossRef]
  11. V. Wilke, W. Schmidt, “Tunable Coherent Radiation Source Covering a Spectral Range from 185 to 880 nm,” Appl. Phys. 18, 177 (1979);“Tunable UV-Radiation by Stimulated Raman Scattering in Hydrogen,” Appl. Phys. 16, 151 (1978).
    [CrossRef]
  12. D. J. Brink, D. Proch, “Efficient Tunable Ultraviolet Source Based on Stimulated Raman Scattering of an Excimer-Pumped Dye Laser,” Opt. Lett. 7, 494 (1982).
    [CrossRef] [PubMed]
  13. Landolt-Bornstein, Zahlenwerte und Funktionen Vol. II, Part 8, Optische Konstanten (Springer-Verlag, Berlin, 1962).
  14. H. W. Schrotter, H. W. Klockner, “Raman Scattering Cross Sections in Gases and Liquids,” in Raman Spectroscopy of Gases and Liquids, A. Weber, Ed. (Springer-Verlag, Berlin, 1979).
    [CrossRef]
  15. D. A. Long, Raman Spectroscopy (McGraw-Hill, New York, 1977).
  16. W. K. Bischel, B. E. Perry, D. R. Crosley, “Detection of Fluorescence from O and N Atoms Induced by Two-Photon Absorption,” Appl. Opt. 21, 1419 (1982);“Two-Photon Laser-Induced Fluorescence in Oxygen and Nitrogen Atoms,” Chem. Phys. Lett. 82, 85 (1981).
    [CrossRef] [PubMed]

1982

1981

W. M. Huo, R. L. Jaffe, “Ab Initio Calculation of the Third-Order Susceptibility of H2,” Phys. Rev. Lett. 47, 30 (1981).
[CrossRef]

1979

V. Wilke, W. Schmidt, “Tunable Coherent Radiation Source Covering a Spectral Range from 185 to 880 nm,” Appl. Phys. 18, 177 (1979);“Tunable UV-Radiation by Stimulated Raman Scattering in Hydrogen,” Appl. Phys. 16, 151 (1978).
[CrossRef]

1973

W. Holzer, Y. Le Duff, K. Altmann, “J Dependence of the Depolarization Ratio of the Rotational Components of the Q Branch of the H2 and D2 Raman Band,” J. Chem. Phys. 58, 642 (1973);W. Holzer, Y. Le Duff, “The Depolarization Ratio of the Raman Bands of the Vibration of Diatomic Molecules,” in Advances in Raman Spectroscopy, Vol. 1, J. P. Mathieu, Ed. (Heyden and Sons, New York, 1973), pp. 109–114.
[CrossRef]

A. L. Ford, J. C. Browne, “Rayleigh and Raman Cross Sections for the Hydrogen Molecule,” At. Data 5, 305 (1973);“Direct-Resolvent Operator Computations on the Hydrogen-Molecule Dynamic Polarizability, Rayleigh, and Raman Scattering,” Phys. Rev. A 7, 418 (1973).
[CrossRef]

1968

P. J. Brannon, C. H. Church, C. W. Peters, “Electric Field Induced Spectra of Molecular Hydrogen, Deuterium and Deuterium Hydride,” J. Mol. Spectrosc. 27, 44 (1968).
[CrossRef]

1966

J. V. Foltz, D. H. Rank, T. A. Wiggins, “Determinations of Some Hydrogen Molecular Constants,” J. Mol. Spectrosc. 21, 203 (1966).
[CrossRef]

1957

B. P. Stoicheff, “High Resolution Raman Spectroscopy of Gases IX. Spectra of H2, HD, D2,” Can. J. Phys. 35, 730 (1957).
[CrossRef]

Altmann, K.

W. Holzer, Y. Le Duff, K. Altmann, “J Dependence of the Depolarization Ratio of the Rotational Components of the Q Branch of the H2 and D2 Raman Band,” J. Chem. Phys. 58, 642 (1973);W. Holzer, Y. Le Duff, “The Depolarization Ratio of the Raman Bands of the Vibration of Diatomic Molecules,” in Advances in Raman Spectroscopy, Vol. 1, J. P. Mathieu, Ed. (Heyden and Sons, New York, 1973), pp. 109–114.
[CrossRef]

Bamford, D. J.

D. J. Bamford, L. E. Jusinski, W. K. Bischel, “Absolute Two-Photon Absorption and Three-Photon Ionization Cross Sections for Atomic Oxygen,” submitted to Phys. Rev. A. (1986).
[CrossRef] [PubMed]

Bischel, W. K.

W. K. Bischel, B. E. Perry, D. R. Crosley, “Detection of Fluorescence from O and N Atoms Induced by Two-Photon Absorption,” Appl. Opt. 21, 1419 (1982);“Two-Photon Laser-Induced Fluorescence in Oxygen and Nitrogen Atoms,” Chem. Phys. Lett. 82, 85 (1981).
[CrossRef] [PubMed]

D. J. Bamford, L. E. Jusinski, W. K. Bischel, “Absolute Two-Photon Absorption and Three-Photon Ionization Cross Sections for Atomic Oxygen,” submitted to Phys. Rev. A. (1986).
[CrossRef] [PubMed]

W. K. Bischel, G. Black, “Wavelength Dependence of Raman Scattering Cross Sections from 200–600 nm,” in Excimer Lasers 1983, C. K. Rhodes, H. Egger, H. Pummer, Eds. (American Institute of Physics, New York, 1983).

Black, G.

W. K. Bischel, G. Black, “Wavelength Dependence of Raman Scattering Cross Sections from 200–600 nm,” in Excimer Lasers 1983, C. K. Rhodes, H. Egger, H. Pummer, Eds. (American Institute of Physics, New York, 1983).

Brannon, P. J.

P. J. Brannon, C. H. Church, C. W. Peters, “Electric Field Induced Spectra of Molecular Hydrogen, Deuterium and Deuterium Hydride,” J. Mol. Spectrosc. 27, 44 (1968).
[CrossRef]

Brink, D. J.

Browne, J. C.

A. L. Ford, J. C. Browne, “Rayleigh and Raman Cross Sections for the Hydrogen Molecule,” At. Data 5, 305 (1973);“Direct-Resolvent Operator Computations on the Hydrogen-Molecule Dynamic Polarizability, Rayleigh, and Raman Scattering,” Phys. Rev. A 7, 418 (1973).
[CrossRef]

Church, C. H.

P. J. Brannon, C. H. Church, C. W. Peters, “Electric Field Induced Spectra of Molecular Hydrogen, Deuterium and Deuterium Hydride,” J. Mol. Spectrosc. 27, 44 (1968).
[CrossRef]

Crosley, D. R.

Foltz, J. V.

J. V. Foltz, D. H. Rank, T. A. Wiggins, “Determinations of Some Hydrogen Molecular Constants,” J. Mol. Spectrosc. 21, 203 (1966).
[CrossRef]

Ford, A. L.

A. L. Ford, J. C. Browne, “Rayleigh and Raman Cross Sections for the Hydrogen Molecule,” At. Data 5, 305 (1973);“Direct-Resolvent Operator Computations on the Hydrogen-Molecule Dynamic Polarizability, Rayleigh, and Raman Scattering,” Phys. Rev. A 7, 418 (1973).
[CrossRef]

Holzer, W.

W. Holzer, Y. Le Duff, K. Altmann, “J Dependence of the Depolarization Ratio of the Rotational Components of the Q Branch of the H2 and D2 Raman Band,” J. Chem. Phys. 58, 642 (1973);W. Holzer, Y. Le Duff, “The Depolarization Ratio of the Raman Bands of the Vibration of Diatomic Molecules,” in Advances in Raman Spectroscopy, Vol. 1, J. P. Mathieu, Ed. (Heyden and Sons, New York, 1973), pp. 109–114.
[CrossRef]

Huo, W. M.

W. M. Huo, R. L. Jaffe, “Ab Initio Calculation of the Third-Order Susceptibility of H2,” Phys. Rev. Lett. 47, 30 (1981).
[CrossRef]

W. M. Huo, NASA Ames RC, private communication.

Jaffe, R. L.

W. M. Huo, R. L. Jaffe, “Ab Initio Calculation of the Third-Order Susceptibility of H2,” Phys. Rev. Lett. 47, 30 (1981).
[CrossRef]

Jusinski, L. E.

D. J. Bamford, L. E. Jusinski, W. K. Bischel, “Absolute Two-Photon Absorption and Three-Photon Ionization Cross Sections for Atomic Oxygen,” submitted to Phys. Rev. A. (1986).
[CrossRef] [PubMed]

Klockner, H. W.

H. W. Schrotter, H. W. Klockner, “Raman Scattering Cross Sections in Gases and Liquids,” in Raman Spectroscopy of Gases and Liquids, A. Weber, Ed. (Springer-Verlag, Berlin, 1979).
[CrossRef]

Le Duff, Y.

W. Holzer, Y. Le Duff, K. Altmann, “J Dependence of the Depolarization Ratio of the Rotational Components of the Q Branch of the H2 and D2 Raman Band,” J. Chem. Phys. 58, 642 (1973);W. Holzer, Y. Le Duff, “The Depolarization Ratio of the Raman Bands of the Vibration of Diatomic Molecules,” in Advances in Raman Spectroscopy, Vol. 1, J. P. Mathieu, Ed. (Heyden and Sons, New York, 1973), pp. 109–114.
[CrossRef]

Long, D. A.

D. A. Long, Raman Spectroscopy (McGraw-Hill, New York, 1977).

Perry, B. E.

Peters, C. W.

P. J. Brannon, C. H. Church, C. W. Peters, “Electric Field Induced Spectra of Molecular Hydrogen, Deuterium and Deuterium Hydride,” J. Mol. Spectrosc. 27, 44 (1968).
[CrossRef]

Proch, D.

Rank, D. H.

J. V. Foltz, D. H. Rank, T. A. Wiggins, “Determinations of Some Hydrogen Molecular Constants,” J. Mol. Spectrosc. 21, 203 (1966).
[CrossRef]

Schmidt, W.

V. Wilke, W. Schmidt, “Tunable Coherent Radiation Source Covering a Spectral Range from 185 to 880 nm,” Appl. Phys. 18, 177 (1979);“Tunable UV-Radiation by Stimulated Raman Scattering in Hydrogen,” Appl. Phys. 16, 151 (1978).
[CrossRef]

Schrotter, H. W.

H. W. Schrotter, H. W. Klockner, “Raman Scattering Cross Sections in Gases and Liquids,” in Raman Spectroscopy of Gases and Liquids, A. Weber, Ed. (Springer-Verlag, Berlin, 1979).
[CrossRef]

Stoicheff, B. P.

B. P. Stoicheff, “High Resolution Raman Spectroscopy of Gases IX. Spectra of H2, HD, D2,” Can. J. Phys. 35, 730 (1957).
[CrossRef]

Wiggins, T. A.

J. V. Foltz, D. H. Rank, T. A. Wiggins, “Determinations of Some Hydrogen Molecular Constants,” J. Mol. Spectrosc. 21, 203 (1966).
[CrossRef]

Wilke, V.

V. Wilke, W. Schmidt, “Tunable Coherent Radiation Source Covering a Spectral Range from 185 to 880 nm,” Appl. Phys. 18, 177 (1979);“Tunable UV-Radiation by Stimulated Raman Scattering in Hydrogen,” Appl. Phys. 16, 151 (1978).
[CrossRef]

Appl. Opt.

Appl. Phys.

V. Wilke, W. Schmidt, “Tunable Coherent Radiation Source Covering a Spectral Range from 185 to 880 nm,” Appl. Phys. 18, 177 (1979);“Tunable UV-Radiation by Stimulated Raman Scattering in Hydrogen,” Appl. Phys. 16, 151 (1978).
[CrossRef]

At. Data

A. L. Ford, J. C. Browne, “Rayleigh and Raman Cross Sections for the Hydrogen Molecule,” At. Data 5, 305 (1973);“Direct-Resolvent Operator Computations on the Hydrogen-Molecule Dynamic Polarizability, Rayleigh, and Raman Scattering,” Phys. Rev. A 7, 418 (1973).
[CrossRef]

Can. J. Phys.

B. P. Stoicheff, “High Resolution Raman Spectroscopy of Gases IX. Spectra of H2, HD, D2,” Can. J. Phys. 35, 730 (1957).
[CrossRef]

J. Chem. Phys.

W. Holzer, Y. Le Duff, K. Altmann, “J Dependence of the Depolarization Ratio of the Rotational Components of the Q Branch of the H2 and D2 Raman Band,” J. Chem. Phys. 58, 642 (1973);W. Holzer, Y. Le Duff, “The Depolarization Ratio of the Raman Bands of the Vibration of Diatomic Molecules,” in Advances in Raman Spectroscopy, Vol. 1, J. P. Mathieu, Ed. (Heyden and Sons, New York, 1973), pp. 109–114.
[CrossRef]

J. Mol. Spectrosc.

J. V. Foltz, D. H. Rank, T. A. Wiggins, “Determinations of Some Hydrogen Molecular Constants,” J. Mol. Spectrosc. 21, 203 (1966).
[CrossRef]

P. J. Brannon, C. H. Church, C. W. Peters, “Electric Field Induced Spectra of Molecular Hydrogen, Deuterium and Deuterium Hydride,” J. Mol. Spectrosc. 27, 44 (1968).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

W. M. Huo, R. L. Jaffe, “Ab Initio Calculation of the Third-Order Susceptibility of H2,” Phys. Rev. Lett. 47, 30 (1981).
[CrossRef]

Other

W. M. Huo, NASA Ames RC, private communication.

W. K. Bischel, G. Black, “Wavelength Dependence of Raman Scattering Cross Sections from 200–600 nm,” in Excimer Lasers 1983, C. K. Rhodes, H. Egger, H. Pummer, Eds. (American Institute of Physics, New York, 1983).

D. J. Bamford, L. E. Jusinski, W. K. Bischel, “Absolute Two-Photon Absorption and Three-Photon Ionization Cross Sections for Atomic Oxygen,” submitted to Phys. Rev. A. (1986).
[CrossRef] [PubMed]

K. D. Mielenz, Ed., Optical Radiation Measurements, Vol. 3, Measurement of Photoluminescence (Academic, New York, 1982).

Landolt-Bornstein, Zahlenwerte und Funktionen Vol. II, Part 8, Optische Konstanten (Springer-Verlag, Berlin, 1962).

H. W. Schrotter, H. W. Klockner, “Raman Scattering Cross Sections in Gases and Liquids,” in Raman Spectroscopy of Gases and Liquids, A. Weber, Ed. (Springer-Verlag, Berlin, 1979).
[CrossRef]

D. A. Long, Raman Spectroscopy (McGraw-Hill, New York, 1977).

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Figures (6)

Fig. 1
Fig. 1

Overall schematic of the apparatus for the calibration of a fluorescence collection system using Raman scattering in H2.

Fig. 2
Fig. 2

Coordinate system to describe the scattering process. A lens with radius a and focal length f is located along the z axis. The laser propagates along the x axis with its polarization vector P making an angle β0 with the z axis. The vector O is the generalized observation direction defined by an angle θ with respect to the z axis and an angle ϕ with respect to the x axis.

Fig. 3
Fig. 3

Raman signal as a function of translating the laser beam along the three orthogonal axes for our optical system. (a) Translation along the z and y axis giving the depth of focus (z axis) of the optical system of ∼7.5 mm and a height (y axis) of ∼2.5 mm. Translation along the y axis is equivalent to translation along the x axis for a cylindrically symmetric optical system. (b) Translation along the x axis (see text) determining the effective length viewed by the optical system of L = 4.0 mm.

Fig. 4
Fig. 4

Raman signal as a function of laser energy and H2 pressure demonstrating linearity in both parameters. The slope equal to 0.35 mV/(mJ Torr) is used in Eq. (1) to calibrate the system.

Fig. 5
Fig. 5

Normalized averaged scattering cross section, Eq. (11), as a function of β0 for f/Nos. of collection systems of 0.40, 0.70, 0.90, and 10. The squares are the experimental measurements. Although the collection lens has a nominal f/No. of 0.70, the f/0.9 curve gives the best fit to the data.

Fig. 6
Fig. 6

Normalized average scattering cross section, Eq. (11), as a function of the angular aperture θ0 of the optical system for two depolarization ratios corresponding to scattering from H2 (ρ = 0.016) and a completely depolarized band (ρ = 0.75).

Tables (1)

Tables Icon

Table I Quantities Involved in Eq. (1)

Equations (14)

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S = E 0 N 0 h ν s σ ¯ Ω ( β 0 , θ 0 ) D ,
L = P ( x ) d x ,
Ω 0 = 0 θ 0 0 2 π sin θ d θ d ϕ ,
Ω 0 = 2 π ( 1 cos θ 0 ) .
σ Ω ( 90 ° ) = A ν s 4 ( ν i 2 ν p 2 ) 2 ,
σ Ω ( β ) = σ Ω ( 90 ° ) ( A + B sin 2 β ) ,
cos β = O P .
O = x ̂ sin θ cos ϕ + ŷ sin θ sin ϕ + z ̂ cos θ
P = ŷ sin β 0 + z ̂ cos β 0 .
sin 2 β = 1 ( sin θ sin ϕ sin β 0 + cos θ cos β 0 ) 2 .
R = σ ¯ Ω ( β 0 , θ 0 ) σ Ω ( 90 ° ) = 1 Ω 0 θ 0 0 2 π ( A + B sin 2 β ) sin θ d θ d ϕ ,
R = 1 B 3 ( 1 cos θ 0 ) [ sin 2 β 0 ( 1 cos θ 0 ½ cos θ 0 sin 2 θ 0 ) + cos 2 β 0 ( 1 cos 3 θ 0 ) ] .
N = ( 4 π / D ) S ,
σ ¯ Ω ( β 0 θ 0 )

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