Abstract

The anomalous dispersion of an atomic line filter near a resonant transition is exploited for full-field frequency measurements. The influence of the line shape function on the dispersion in atomic vapors near resonance and the possibilities to increase sensitivity are discussed. From the model-calculated absorption of iodine vapor at frequency-doubled Nd:YAG laser wavelengths, the corresponding refractive index is obtained through the Kramers–Kronig relations. Both variables are used to assess the performance of a iodine vapor cell as a dispersive element in an interferometric setup for Doppler frequency shift detection. With good agreement, the predicted sensitivity of the setup is compared to an experimental calibration. Observed discrepancies are attributed to the assumption of a Gaussian line shape in the absorption model. The full-field Doppler frequency measurement capacity of the technique is demonstrated in a rotating disk experiment, and the measurement performance is assessed.

© 2009 Optical Society of America

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References

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  1. J. A. Gelbwachs, “Atomic resonance filters,” IEEE J. Quantum Electron. 24, 1266-1277 (1988).
    [Crossref]
  2. E. Hecht, Optics (Addison-Wesley, 1998).
  3. J. N. Forkey, W. R. Lempert, and R. B. Miles, “Corrected and calibrated I2 absorption model at frequency-doubled Nd:YAG laser wavelengths,” Appl. Opt. 36, 6729-6738 (1997).
    [Crossref]
  4. H. Komine, S. J. Brosnan, A. B. Litton, and E. A. Stappaerts, “Real-time Doppler global velocimetry,” in Proceedings of 29th AIAA Aerospace Sciences Meeting (American Institute of Aeronautics and Astronautics, 1991), paper AIAA-91-0337.
  5. J. M. Sirota and W. H. Christiansen, “Flow diagnostics by Resonant Holographic Interferometry,” in Proceedings of 21th AIAA Fluid Dynamics, Plasma Dynamics and Lasers Conference (American Institute of Aeronautics and Astronautics, 1990), paper AIAA-90-1550.
  6. A.-P. Tzannis, J. C. Lee, P. Beaud, H.-M. Frey, T. Greber, B. Mischler, P. P. Radi, and K. Boulouchos, “OH concentration measurements by resonant holographic interferometry and comparison with direct numerical simulations,” Flow Turb. Combust. 64, 183-196 (2000).
    [Crossref]
  7. T. J. McIntyre, A. I. Bishop, T. N. Eichmann, and H. Rubinsztein-Dunlop, “Enhanced flow visualization with near-resonant holographic interferometry,” Appl. Opt. 42, 4445-4451(2003).
    [Crossref] [PubMed]
  8. C. R. Schwarze, J. A. Gargas, J. H. Rentz, and M. Hercher, “Method for obtaining gas concentration with a phase-based metrology system,” Appl. Opt. 37, 3942-3947 (1998).
    [Crossref]
  9. K.-E. Peiponen, E. M. Vartiainen, and T. Asakura, Dispersion, Complex Analysis and Optical Spectroscopy (Springer, 1998).
  10. A. Thorne, U. Litzén, and S. Johansson, Spectrophysics (Springer, 1999).
  11. J. D. Posner, D. Dunn-Rankin, M. S. Brown, N. Brock, and P. A. DeBarber, “Resonant holographic interferometry for species concentration measurements with saturated anomalous dispersion,” Appl. Phys. B 78, 661-672 (2004).
    [Crossref]
  12. R. B. Miles, A. P. Yalin, Z. Tang, S. H. Zaidi, and J. N. Forkey, “Flow field imaging through sharp-edged atomic and molecular 'notch' filters,” Meas. Sci. Technol. 12, 442-451(2001).
    [Crossref]
  13. J. Tellinghuisen, “Transition strengths in the visible-infrared absorption spectrum of I2,” J. Chem. Phys. 76, 4736-4744(1982).
    [Crossref]
  14. S. Gerstenkorn and P. Luc, Atlas du Spectre d'Absorption de la Molecule d'Iode, 14800-20000 cm−1, Editions du CNRS(Laboratoire Aimé-Cotton CNRS II, 1978).
    [PubMed]
  15. A. Landolt and T. Rösgen, “Global Doppler frequency shift detection with near-resonant interferometry,” Exp. Fluids (to be published).
    [Crossref]
  16. J. F. Meyers, J. W. Lee, and R. J. Schwartz, “Characterization of measurement error sources in Doppler global velocimetry,” Meas. Sci. Technol. 12, 357-368 (2001).
    [Crossref]
  17. D. C. Ghiglia and L. A. Romero, “Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods,” J. Opt. Soc. Am. A 11, 107-117 (1994).
    [Crossref]

2004 (1)

J. D. Posner, D. Dunn-Rankin, M. S. Brown, N. Brock, and P. A. DeBarber, “Resonant holographic interferometry for species concentration measurements with saturated anomalous dispersion,” Appl. Phys. B 78, 661-672 (2004).
[Crossref]

2003 (1)

T. J. McIntyre, A. I. Bishop, T. N. Eichmann, and H. Rubinsztein-Dunlop, “Enhanced flow visualization with near-resonant holographic interferometry,” Appl. Opt. 42, 4445-4451(2003).
[Crossref] [PubMed]

2001 (2)

R. B. Miles, A. P. Yalin, Z. Tang, S. H. Zaidi, and J. N. Forkey, “Flow field imaging through sharp-edged atomic and molecular 'notch' filters,” Meas. Sci. Technol. 12, 442-451(2001).
[Crossref]

J. F. Meyers, J. W. Lee, and R. J. Schwartz, “Characterization of measurement error sources in Doppler global velocimetry,” Meas. Sci. Technol. 12, 357-368 (2001).
[Crossref]

2000 (1)

A.-P. Tzannis, J. C. Lee, P. Beaud, H.-M. Frey, T. Greber, B. Mischler, P. P. Radi, and K. Boulouchos, “OH concentration measurements by resonant holographic interferometry and comparison with direct numerical simulations,” Flow Turb. Combust. 64, 183-196 (2000).
[Crossref]

1999 (1)

A. Thorne, U. Litzén, and S. Johansson, Spectrophysics (Springer, 1999).

1998 (3)

C. R. Schwarze, J. A. Gargas, J. H. Rentz, and M. Hercher, “Method for obtaining gas concentration with a phase-based metrology system,” Appl. Opt. 37, 3942-3947 (1998).
[Crossref]

K.-E. Peiponen, E. M. Vartiainen, and T. Asakura, Dispersion, Complex Analysis and Optical Spectroscopy (Springer, 1998).

E. Hecht, Optics (Addison-Wesley, 1998).

1997 (1)

J. N. Forkey, W. R. Lempert, and R. B. Miles, “Corrected and calibrated I2 absorption model at frequency-doubled Nd:YAG laser wavelengths,” Appl. Opt. 36, 6729-6738 (1997).
[Crossref]

1994 (1)

D. C. Ghiglia and L. A. Romero, “Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods,” J. Opt. Soc. Am. A 11, 107-117 (1994).
[Crossref]

1991 (1)

H. Komine, S. J. Brosnan, A. B. Litton, and E. A. Stappaerts, “Real-time Doppler global velocimetry,” in Proceedings of 29th AIAA Aerospace Sciences Meeting (American Institute of Aeronautics and Astronautics, 1991), paper AIAA-91-0337.

1990 (1)

J. M. Sirota and W. H. Christiansen, “Flow diagnostics by Resonant Holographic Interferometry,” in Proceedings of 21th AIAA Fluid Dynamics, Plasma Dynamics and Lasers Conference (American Institute of Aeronautics and Astronautics, 1990), paper AIAA-90-1550.

1988 (1)

J. A. Gelbwachs, “Atomic resonance filters,” IEEE J. Quantum Electron. 24, 1266-1277 (1988).
[Crossref]

1982 (1)

J. Tellinghuisen, “Transition strengths in the visible-infrared absorption spectrum of I2,” J. Chem. Phys. 76, 4736-4744(1982).
[Crossref]

1978 (1)

S. Gerstenkorn and P. Luc, Atlas du Spectre d'Absorption de la Molecule d'Iode, 14800-20000 cm−1, Editions du CNRS(Laboratoire Aimé-Cotton CNRS II, 1978).
[PubMed]

Asakura, T.

K.-E. Peiponen, E. M. Vartiainen, and T. Asakura, Dispersion, Complex Analysis and Optical Spectroscopy (Springer, 1998).

Beaud, P.

A.-P. Tzannis, J. C. Lee, P. Beaud, H.-M. Frey, T. Greber, B. Mischler, P. P. Radi, and K. Boulouchos, “OH concentration measurements by resonant holographic interferometry and comparison with direct numerical simulations,” Flow Turb. Combust. 64, 183-196 (2000).
[Crossref]

Bishop, A. I.

T. J. McIntyre, A. I. Bishop, T. N. Eichmann, and H. Rubinsztein-Dunlop, “Enhanced flow visualization with near-resonant holographic interferometry,” Appl. Opt. 42, 4445-4451(2003).
[Crossref] [PubMed]

Boulouchos, K.

A.-P. Tzannis, J. C. Lee, P. Beaud, H.-M. Frey, T. Greber, B. Mischler, P. P. Radi, and K. Boulouchos, “OH concentration measurements by resonant holographic interferometry and comparison with direct numerical simulations,” Flow Turb. Combust. 64, 183-196 (2000).
[Crossref]

Brock, N.

J. D. Posner, D. Dunn-Rankin, M. S. Brown, N. Brock, and P. A. DeBarber, “Resonant holographic interferometry for species concentration measurements with saturated anomalous dispersion,” Appl. Phys. B 78, 661-672 (2004).
[Crossref]

Brosnan, S. J.

H. Komine, S. J. Brosnan, A. B. Litton, and E. A. Stappaerts, “Real-time Doppler global velocimetry,” in Proceedings of 29th AIAA Aerospace Sciences Meeting (American Institute of Aeronautics and Astronautics, 1991), paper AIAA-91-0337.

Brown, M. S.

J. D. Posner, D. Dunn-Rankin, M. S. Brown, N. Brock, and P. A. DeBarber, “Resonant holographic interferometry for species concentration measurements with saturated anomalous dispersion,” Appl. Phys. B 78, 661-672 (2004).
[Crossref]

Christiansen, W. H.

J. M. Sirota and W. H. Christiansen, “Flow diagnostics by Resonant Holographic Interferometry,” in Proceedings of 21th AIAA Fluid Dynamics, Plasma Dynamics and Lasers Conference (American Institute of Aeronautics and Astronautics, 1990), paper AIAA-90-1550.

DeBarber, P. A.

J. D. Posner, D. Dunn-Rankin, M. S. Brown, N. Brock, and P. A. DeBarber, “Resonant holographic interferometry for species concentration measurements with saturated anomalous dispersion,” Appl. Phys. B 78, 661-672 (2004).
[Crossref]

Dunn-Rankin, D.

J. D. Posner, D. Dunn-Rankin, M. S. Brown, N. Brock, and P. A. DeBarber, “Resonant holographic interferometry for species concentration measurements with saturated anomalous dispersion,” Appl. Phys. B 78, 661-672 (2004).
[Crossref]

Eichmann, T. N.

T. J. McIntyre, A. I. Bishop, T. N. Eichmann, and H. Rubinsztein-Dunlop, “Enhanced flow visualization with near-resonant holographic interferometry,” Appl. Opt. 42, 4445-4451(2003).
[Crossref] [PubMed]

Forkey, J. N.

R. B. Miles, A. P. Yalin, Z. Tang, S. H. Zaidi, and J. N. Forkey, “Flow field imaging through sharp-edged atomic and molecular 'notch' filters,” Meas. Sci. Technol. 12, 442-451(2001).
[Crossref]

J. N. Forkey, W. R. Lempert, and R. B. Miles, “Corrected and calibrated I2 absorption model at frequency-doubled Nd:YAG laser wavelengths,” Appl. Opt. 36, 6729-6738 (1997).
[Crossref]

Frey, H.-M.

A.-P. Tzannis, J. C. Lee, P. Beaud, H.-M. Frey, T. Greber, B. Mischler, P. P. Radi, and K. Boulouchos, “OH concentration measurements by resonant holographic interferometry and comparison with direct numerical simulations,” Flow Turb. Combust. 64, 183-196 (2000).
[Crossref]

Gargas, J. A.

C. R. Schwarze, J. A. Gargas, J. H. Rentz, and M. Hercher, “Method for obtaining gas concentration with a phase-based metrology system,” Appl. Opt. 37, 3942-3947 (1998).
[Crossref]

Gelbwachs, J. A.

J. A. Gelbwachs, “Atomic resonance filters,” IEEE J. Quantum Electron. 24, 1266-1277 (1988).
[Crossref]

Gerstenkorn, S.

S. Gerstenkorn and P. Luc, Atlas du Spectre d'Absorption de la Molecule d'Iode, 14800-20000 cm−1, Editions du CNRS(Laboratoire Aimé-Cotton CNRS II, 1978).
[PubMed]

Ghiglia, D. C.

D. C. Ghiglia and L. A. Romero, “Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods,” J. Opt. Soc. Am. A 11, 107-117 (1994).
[Crossref]

Greber, T.

A.-P. Tzannis, J. C. Lee, P. Beaud, H.-M. Frey, T. Greber, B. Mischler, P. P. Radi, and K. Boulouchos, “OH concentration measurements by resonant holographic interferometry and comparison with direct numerical simulations,” Flow Turb. Combust. 64, 183-196 (2000).
[Crossref]

Hecht, E.

E. Hecht, Optics (Addison-Wesley, 1998).

Hercher, M.

C. R. Schwarze, J. A. Gargas, J. H. Rentz, and M. Hercher, “Method for obtaining gas concentration with a phase-based metrology system,” Appl. Opt. 37, 3942-3947 (1998).
[Crossref]

Johansson, S.

A. Thorne, U. Litzén, and S. Johansson, Spectrophysics (Springer, 1999).

Komine, H.

H. Komine, S. J. Brosnan, A. B. Litton, and E. A. Stappaerts, “Real-time Doppler global velocimetry,” in Proceedings of 29th AIAA Aerospace Sciences Meeting (American Institute of Aeronautics and Astronautics, 1991), paper AIAA-91-0337.

Landolt, A.

A. Landolt and T. Rösgen, “Global Doppler frequency shift detection with near-resonant interferometry,” Exp. Fluids (to be published).
[Crossref]

Lee, J. C.

A.-P. Tzannis, J. C. Lee, P. Beaud, H.-M. Frey, T. Greber, B. Mischler, P. P. Radi, and K. Boulouchos, “OH concentration measurements by resonant holographic interferometry and comparison with direct numerical simulations,” Flow Turb. Combust. 64, 183-196 (2000).
[Crossref]

Lee, J. W.

J. F. Meyers, J. W. Lee, and R. J. Schwartz, “Characterization of measurement error sources in Doppler global velocimetry,” Meas. Sci. Technol. 12, 357-368 (2001).
[Crossref]

Lempert, W. R.

J. N. Forkey, W. R. Lempert, and R. B. Miles, “Corrected and calibrated I2 absorption model at frequency-doubled Nd:YAG laser wavelengths,” Appl. Opt. 36, 6729-6738 (1997).
[Crossref]

Litton, A. B.

H. Komine, S. J. Brosnan, A. B. Litton, and E. A. Stappaerts, “Real-time Doppler global velocimetry,” in Proceedings of 29th AIAA Aerospace Sciences Meeting (American Institute of Aeronautics and Astronautics, 1991), paper AIAA-91-0337.

Litzén, U.

A. Thorne, U. Litzén, and S. Johansson, Spectrophysics (Springer, 1999).

Luc, P.

S. Gerstenkorn and P. Luc, Atlas du Spectre d'Absorption de la Molecule d'Iode, 14800-20000 cm−1, Editions du CNRS(Laboratoire Aimé-Cotton CNRS II, 1978).
[PubMed]

McIntyre, T. J.

T. J. McIntyre, A. I. Bishop, T. N. Eichmann, and H. Rubinsztein-Dunlop, “Enhanced flow visualization with near-resonant holographic interferometry,” Appl. Opt. 42, 4445-4451(2003).
[Crossref] [PubMed]

Meyers, J. F.

J. F. Meyers, J. W. Lee, and R. J. Schwartz, “Characterization of measurement error sources in Doppler global velocimetry,” Meas. Sci. Technol. 12, 357-368 (2001).
[Crossref]

Miles, R. B.

R. B. Miles, A. P. Yalin, Z. Tang, S. H. Zaidi, and J. N. Forkey, “Flow field imaging through sharp-edged atomic and molecular 'notch' filters,” Meas. Sci. Technol. 12, 442-451(2001).
[Crossref]

J. N. Forkey, W. R. Lempert, and R. B. Miles, “Corrected and calibrated I2 absorption model at frequency-doubled Nd:YAG laser wavelengths,” Appl. Opt. 36, 6729-6738 (1997).
[Crossref]

Mischler, B.

A.-P. Tzannis, J. C. Lee, P. Beaud, H.-M. Frey, T. Greber, B. Mischler, P. P. Radi, and K. Boulouchos, “OH concentration measurements by resonant holographic interferometry and comparison with direct numerical simulations,” Flow Turb. Combust. 64, 183-196 (2000).
[Crossref]

Peiponen, K.-E.

K.-E. Peiponen, E. M. Vartiainen, and T. Asakura, Dispersion, Complex Analysis and Optical Spectroscopy (Springer, 1998).

Posner, J. D.

J. D. Posner, D. Dunn-Rankin, M. S. Brown, N. Brock, and P. A. DeBarber, “Resonant holographic interferometry for species concentration measurements with saturated anomalous dispersion,” Appl. Phys. B 78, 661-672 (2004).
[Crossref]

Radi, P. P.

A.-P. Tzannis, J. C. Lee, P. Beaud, H.-M. Frey, T. Greber, B. Mischler, P. P. Radi, and K. Boulouchos, “OH concentration measurements by resonant holographic interferometry and comparison with direct numerical simulations,” Flow Turb. Combust. 64, 183-196 (2000).
[Crossref]

Rentz, J. H.

C. R. Schwarze, J. A. Gargas, J. H. Rentz, and M. Hercher, “Method for obtaining gas concentration with a phase-based metrology system,” Appl. Opt. 37, 3942-3947 (1998).
[Crossref]

Romero, L. A.

D. C. Ghiglia and L. A. Romero, “Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods,” J. Opt. Soc. Am. A 11, 107-117 (1994).
[Crossref]

Rösgen, T.

A. Landolt and T. Rösgen, “Global Doppler frequency shift detection with near-resonant interferometry,” Exp. Fluids (to be published).
[Crossref]

Rubinsztein-Dunlop, H.

T. J. McIntyre, A. I. Bishop, T. N. Eichmann, and H. Rubinsztein-Dunlop, “Enhanced flow visualization with near-resonant holographic interferometry,” Appl. Opt. 42, 4445-4451(2003).
[Crossref] [PubMed]

Schwartz, R. J.

J. F. Meyers, J. W. Lee, and R. J. Schwartz, “Characterization of measurement error sources in Doppler global velocimetry,” Meas. Sci. Technol. 12, 357-368 (2001).
[Crossref]

Schwarze, C. R.

C. R. Schwarze, J. A. Gargas, J. H. Rentz, and M. Hercher, “Method for obtaining gas concentration with a phase-based metrology system,” Appl. Opt. 37, 3942-3947 (1998).
[Crossref]

Sirota, J. M.

J. M. Sirota and W. H. Christiansen, “Flow diagnostics by Resonant Holographic Interferometry,” in Proceedings of 21th AIAA Fluid Dynamics, Plasma Dynamics and Lasers Conference (American Institute of Aeronautics and Astronautics, 1990), paper AIAA-90-1550.

Stappaerts, E. A.

H. Komine, S. J. Brosnan, A. B. Litton, and E. A. Stappaerts, “Real-time Doppler global velocimetry,” in Proceedings of 29th AIAA Aerospace Sciences Meeting (American Institute of Aeronautics and Astronautics, 1991), paper AIAA-91-0337.

Tang, Z.

R. B. Miles, A. P. Yalin, Z. Tang, S. H. Zaidi, and J. N. Forkey, “Flow field imaging through sharp-edged atomic and molecular 'notch' filters,” Meas. Sci. Technol. 12, 442-451(2001).
[Crossref]

Tellinghuisen, J.

J. Tellinghuisen, “Transition strengths in the visible-infrared absorption spectrum of I2,” J. Chem. Phys. 76, 4736-4744(1982).
[Crossref]

Thorne, A.

A. Thorne, U. Litzén, and S. Johansson, Spectrophysics (Springer, 1999).

Tzannis, A.-P.

A.-P. Tzannis, J. C. Lee, P. Beaud, H.-M. Frey, T. Greber, B. Mischler, P. P. Radi, and K. Boulouchos, “OH concentration measurements by resonant holographic interferometry and comparison with direct numerical simulations,” Flow Turb. Combust. 64, 183-196 (2000).
[Crossref]

Vartiainen, E. M.

K.-E. Peiponen, E. M. Vartiainen, and T. Asakura, Dispersion, Complex Analysis and Optical Spectroscopy (Springer, 1998).

Yalin, A. P.

R. B. Miles, A. P. Yalin, Z. Tang, S. H. Zaidi, and J. N. Forkey, “Flow field imaging through sharp-edged atomic and molecular 'notch' filters,” Meas. Sci. Technol. 12, 442-451(2001).
[Crossref]

Zaidi, S. H.

R. B. Miles, A. P. Yalin, Z. Tang, S. H. Zaidi, and J. N. Forkey, “Flow field imaging through sharp-edged atomic and molecular 'notch' filters,” Meas. Sci. Technol. 12, 442-451(2001).
[Crossref]

Appl. Opt. (3)

J. N. Forkey, W. R. Lempert, and R. B. Miles, “Corrected and calibrated I2 absorption model at frequency-doubled Nd:YAG laser wavelengths,” Appl. Opt. 36, 6729-6738 (1997).
[Crossref]

T. J. McIntyre, A. I. Bishop, T. N. Eichmann, and H. Rubinsztein-Dunlop, “Enhanced flow visualization with near-resonant holographic interferometry,” Appl. Opt. 42, 4445-4451(2003).
[Crossref] [PubMed]

C. R. Schwarze, J. A. Gargas, J. H. Rentz, and M. Hercher, “Method for obtaining gas concentration with a phase-based metrology system,” Appl. Opt. 37, 3942-3947 (1998).
[Crossref]

Appl. Phys. B (1)

J. D. Posner, D. Dunn-Rankin, M. S. Brown, N. Brock, and P. A. DeBarber, “Resonant holographic interferometry for species concentration measurements with saturated anomalous dispersion,” Appl. Phys. B 78, 661-672 (2004).
[Crossref]

Exp. Fluids (1)

A. Landolt and T. Rösgen, “Global Doppler frequency shift detection with near-resonant interferometry,” Exp. Fluids (to be published).
[Crossref]

Flow Turb. Combust. (1)

A.-P. Tzannis, J. C. Lee, P. Beaud, H.-M. Frey, T. Greber, B. Mischler, P. P. Radi, and K. Boulouchos, “OH concentration measurements by resonant holographic interferometry and comparison with direct numerical simulations,” Flow Turb. Combust. 64, 183-196 (2000).
[Crossref]

IEEE J. Quantum Electron. (1)

J. A. Gelbwachs, “Atomic resonance filters,” IEEE J. Quantum Electron. 24, 1266-1277 (1988).
[Crossref]

J. Chem. Phys. (1)

J. Tellinghuisen, “Transition strengths in the visible-infrared absorption spectrum of I2,” J. Chem. Phys. 76, 4736-4744(1982).
[Crossref]

J. Opt. Soc. Am. A (1)

D. C. Ghiglia and L. A. Romero, “Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods,” J. Opt. Soc. Am. A 11, 107-117 (1994).
[Crossref]

Meas. Sci. Technol. (2)

J. F. Meyers, J. W. Lee, and R. J. Schwartz, “Characterization of measurement error sources in Doppler global velocimetry,” Meas. Sci. Technol. 12, 357-368 (2001).
[Crossref]

R. B. Miles, A. P. Yalin, Z. Tang, S. H. Zaidi, and J. N. Forkey, “Flow field imaging through sharp-edged atomic and molecular 'notch' filters,” Meas. Sci. Technol. 12, 442-451(2001).
[Crossref]

Other (6)

S. Gerstenkorn and P. Luc, Atlas du Spectre d'Absorption de la Molecule d'Iode, 14800-20000 cm−1, Editions du CNRS(Laboratoire Aimé-Cotton CNRS II, 1978).
[PubMed]

E. Hecht, Optics (Addison-Wesley, 1998).

H. Komine, S. J. Brosnan, A. B. Litton, and E. A. Stappaerts, “Real-time Doppler global velocimetry,” in Proceedings of 29th AIAA Aerospace Sciences Meeting (American Institute of Aeronautics and Astronautics, 1991), paper AIAA-91-0337.

J. M. Sirota and W. H. Christiansen, “Flow diagnostics by Resonant Holographic Interferometry,” in Proceedings of 21th AIAA Fluid Dynamics, Plasma Dynamics and Lasers Conference (American Institute of Aeronautics and Astronautics, 1990), paper AIAA-90-1550.

K.-E. Peiponen, E. M. Vartiainen, and T. Asakura, Dispersion, Complex Analysis and Optical Spectroscopy (Springer, 1998).

A. Thorne, U. Litzén, and S. Johansson, Spectrophysics (Springer, 1999).

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Figures (9)

Fig. 1
Fig. 1

Characteristics of Gaussian (solid line) and Lorentzian (broken line) broadened lines, respectively. From top to bottom: Absorption coefficient α, refractive index n, the derivative of the refractive index relative with respect to ω and the ratio of the derivative of the refractive index to the absorption (normalized to the respective values at ω 2 , 3 ). The FWHM and the points where the changes in refractive index are maximal for a Gaussian are marked on the abscissa.

Fig. 2
Fig. 2

Comparison of the predicted (broken line) and the measured normalized transmission profiles for the iodine cell used.

Fig. 3
Fig. 3

Model prediction of transmission, absorption coefficient, refractive index and gradient of refractive index for the I 2 vapor cell used (line numbering in accordance with [14]).

Fig. 4
Fig. 4

Cell transmission and associated gradient of the refractive index for line no. 1111 at vapor pressures of 0.20 (dotted line), 1.03 (dot and dash), 4.26 (broken line), and 14.93 (solid line) Torr, and 100 ° C cell temperature, including background absorption.

Fig. 5
Fig. 5

Gradient of the refractive index relative to absorption (normalized to the value at ω 2 , 3 ) without (broken line) and with background absorption (solid line).

Fig. 6
Fig. 6

Imaging Michelson interferometer (highlighted in gray) with a dispersive vapor cell D1. M1 and M2 are the end mirrors, and BS1 is a nonpolarizing beam splitter cube. The lenses L1, L2, and L3 form an image of the disk on both mirrors and on the CCD sensor. The frequency monitoring system consists of a second vapor cell D2 and a nonpolarizing beam splitter BS2 that directs 1% of the beam energy from the holographic beam sampler HBS onto the two fast photodiodes PD1 and PD2. TQ1 and TQ2 are the temperature control units for the vapor cells 1 and 2, respectively.

Fig. 7
Fig. 7

Measured (filled circles), and least-squares fitted (solid line) sensitivity and its theoretical prediction (broken line), (top). The relative deviation of each measurement point from the fitted curve and their combined RMS value (broken line), (bottom).

Fig. 8
Fig. 8

Raw fringe image with the disk rotating (left) and the measured Doppler frequency shift distribution (right).

Fig. 9
Fig. 9

Measured azimuthal disk velocity (solid line) compared to the calculated value (broken line), the discrepancy between the two data sets (center), and the RMS of individual images (bottom).

Equations (16)

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

N = n i k .
n ( ω ) 1 = 2 π P 0 ω k ( ω ) ω 2 ω 2 d ω , k ( ω ) = 2 ω π P 0 n ( ω ) 1 ω 2 ω 2 d ω ,
I = I 0 e α 0 V ( ω ) l ,
L ( ω ) = ( Δ ω L / 2 ) 2 ( ω ω 0 ) 2 + ( Δ ω L / 2 ) 2 ,
α ( ω ) = α 0 L ( ω ) = α 0 ( Δ ω L / 2 ) 2 ( ω ω 0 ) 2 + ( Δ ω L / 2 ) 2 .
n L ( ω ) 1 = α 0 c Δ ω L 4 ω 0 ( ω 0 ω ) ( ω ω 0 ) 2 + ( Δ ω L / 2 ) 2 ,
ω 1 , 2 , 3 = ω 0 , ω 0 ± 3 2 Δ ω L , n L ( ω 1 , 2 , 3 ) ω = α 0 c ω 0 Δ ω L ( 1 , 1 8 , 1 8 ) .
G ( w ) = exp ( ( ω 0 ω ) 2 ln 2 ( Δ ω G / 2 ) 2 ) ,
Δ ω G = 2 ω 0 c 2 k B T ln 2 m ,
H [ e x 2 ] = e x 2 erfi ( x ) ,
k ( ω ) = α 0 c 2 ω exp ( ( ω 0 ω ) 2 ln 2 ( Δ ω G / 2 ) 2 ) .
n G ( ω ) 1 = α 0 c 2 ω exp ( ( ω 0 ω ) 2 ln 2 ( Δ ω G / 2 ) 2 ) erfi ( 2 ln 2 ( ω ω 0 ) Δ ω 0 ) .
ω 1 , 2 , 3 = ω 0 , ω 0 ± 1.502 2 ln 2 Δ ω G , n G ( ω 1 , 2 , 3 ) ω = α 0 c ω 0 Δ ω G 2 ln 2 ( 1 π , 0.161 , 0.161 ) .
Δ ν = ν 0 o l c · V ,
Δ ϕ ω = 2 l c [ ω ( n ( ω ) 1 ) ω + ( n ( ω ) 1 ) ] + 2 L c .
Δ ϕ ω | max , Gauss = 0.161 c π 2 k B l α 0 ω 0 m T .

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