Abstract

Analytical models of a spectral filter that contains iodine vapor and of the noise sources associated with charge-coupled-device (CCD) detector technology are combined with a planar Doppler velocimetry (PDV) signal analysis to evaluate the measurement capabilities of PDV for quantitative aerodynamic research and production wind-tunnel testing applications. The criteria for optimizing the filter cell and calibrating the frequency scale of its transmission function are described. The measurement uncertainty limits owing to scientific-grade CCD detector performance are then evaluated, and an analysis is developed of the scattering properties of aerosols suitable for aerodynamic flow seeding. The combined results predict that single-pulse PDV measurements with velocity measurement uncertainties as small as 2 m/s should be possible in aerodynamic test facilities for measurement distances of tens of meters.

© 1996 Optical Society of America

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References

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  1. H. Komine, S. J. Brosnan, A. B. Litton, E. A. Stappaerts, “Real-time, Doppler global velocimetry,” AIAA paper 91-0337, presented at the Twenty-Ninth Aerospace Sciences Meeting, Reno, Nev., 7–10 January 1991.
  2. J. F. Meyers, “Doppler global velocimetry. The next generation?,” Paper 92-3897, presented at the AIAA Seventeenth Aerospace Ground Testing Conference, Nashville, Tenn., 6–8 July 1992.
  3. J. F. Meyers, J. W. Lee, A. A. Cavone, “Three component Doppler global velocimeter measurements of the flow above a delta wing,” presented at the Sixth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 20–23 July 1992.
  4. J. W. Lee, J. F. Meyers, A. A. Cavone, K. E. Suzuki, “Doppler global velocimetry measurements of the vortical flow above an F/A-18,” Paper 93-0414, presented at the AIAA Thirty-First Aerospace Sciences Meeting and Exhibit, Reno, Nev., 11–14 January 1993.
  5. G. S. Elliott, M. Samimy, S. A. Arnette, “Molecular filter-based diagnostics in high speed flows,” Paper 93-0512, presented at the AIAA Thirty-First Aerospace Sciences Meeting and Exhibit, Reno, Nev., 11–14 January 1993.
  6. G. S. Elliott, M. Samimy, S. A. Arnette, “Details of a molecular filter-based velocimetry technique,” Paper 94-0490, presented at the AIAA Thirty-Second Aerospace Sciences Meeting and Exhibit, Reno, Nev., 10–13 January 1994.
  7. M. W. Smith, G. B. Northam, “Application of absorption filter-planar Doppler velocimetry to sonic and supersonic jets,” Paper 95-0299, presented at the AIAA Thirty-Third Aerospace Sciences Meeting and Exhibit, Reno, Nev., 9–12 January 1995.
  8. R. B. Bilhorn, J. V. Sweedler, P. M. Epperson, M. B. Denton, “Charge transfer device detectors for analytical optical spectroscopy—operation and characteristics,” Appl. Spectrosc. 41, 1114–1124 (1987).
    [CrossRef]
  9. Princeton Instruments Catalog of High Performance Cameras, Princeton Instruments, Inc., Princeton, N.J. (1994).
  10. C. Buil, CCD Astronomy: Construction and Use of an Astronomical CCD Camera (Willmann-Bell, Richmond, Va., 1991).
  11. S. Gerstenkorn, P. Luc, Atlas du Spectre d’ Absorption de la Molecule d’ Iode 14800–20000 cm−1 (Laboratorie Aime-Cotton, Centre National de la Recherche Scientifique, II-91405, Orsay, France, 1978).
  12. J. Tellinghuisen, “Transition strengths in the visible-infrared absorption spectrum of I2,” J. Chem. Phys. 76, 4736–4744 (1982).
    [CrossRef]
  13. The author is particularly grateful toJ. Forkey of the Department of Mechanical and Aerospace Engineering, Princeton University, for providing his iodine spectrum computer codes.
  14. R. B. Miles, J. N. Forkey, W. R. Lempert, “Filtered Rayleigh scattering measurements in supersonic/hypersonic facilities,” Paper 92-3894, presented at the Seventeenth AIAA Aerospace Ground Testing Conference, Nashville, Tenn., 6–8 July 1992.
  15. S. Gerstenkorn, P. Luc, Atlas du Spectre d’ Absorption de la Molecule d’ Iode 14800–20000 cm −1 (Laboratorie Aime-Cotton, Centre National de la Recherche Scientifique, II-91405, Orsay, France, 1986).
  16. P. Luc, “Molecular constants and Durham expansion parameters describing the B−X system of the iodine molecule,” J. Mol. Spectrosc. 80, 41–55 (1980).
    [CrossRef]
  17. S. Gerstenkorn, P. Luc, “Absolute iodine (I2) standards measured by means of Fourier transform spectroscopy,” Rev. Phys. Appl. 14, 791–794 (1979).
    [CrossRef]
  18. M. D. Levenson, A. L. Schawlow, “Hyperfine interactions in molecular iodine,” Phys. Rev. A 6, 10–20 (1972).
    [CrossRef]
  19. Private communication between P. Luc, J. Forkey. Similar Franck–Condon values may be found in J. Tellinghuisen, “Intensity factors for the I2B ↔ X band system,” Quant J. Spectrosc. Radiat. Transfer19, 149–161 (1978).
    [CrossRef]
  20. M. Glaser, “Identification of hyperfine structure components of the iodine molecule at 640 nm wavelength,” Opt. Commun. 54, 335–342 (1985).
    [CrossRef]
  21. A. Arie, R. L. Byer, “Laser heterodyne spectroscopy of 127I2 hyperfine structure near 532 nm,” J. Opt. Soc. Am. B 10, 1990–1997 (1993).
    [CrossRef]
  22. J. W. Pieterse, Spectra-Physics memorandum No. 88-1 (private communication, 12July1988).
  23. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in fortran (Cambridge U. Press, Cambridge, 1992).
  24. P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hil, New York, 1969), p. 59.
  25. L. E. Drain, The Laser Doppler Techniqu (Wiley, New York, 1980), pp. 182–190.
  26. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  27. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Optical Society of America, New York, 1983).
  28. W. W. Hunter, C. E. Nichols, eds., “Wind tunnel seeding systems for laser velocimeters,” NASA Conf. Pub. 2393 (NASA Langley Research Center, Hampton, Va.,, 1985).
  29. J. F. Meyers, “Generation of particles and seeding,” in Laser Velocimetry, von Karman Institute for Fluid Dynamics Lecture Series 1991-08 (von Karmann Institute for Fluid Dynamics, Rhode-Saint-Genes, Belgium, 1991).

1993 (1)

1987 (1)

1985 (1)

M. Glaser, “Identification of hyperfine structure components of the iodine molecule at 640 nm wavelength,” Opt. Commun. 54, 335–342 (1985).
[CrossRef]

1982 (1)

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

1980 (1)

P. Luc, “Molecular constants and Durham expansion parameters describing the B−X system of the iodine molecule,” J. Mol. Spectrosc. 80, 41–55 (1980).
[CrossRef]

1979 (1)

S. Gerstenkorn, P. Luc, “Absolute iodine (I2) standards measured by means of Fourier transform spectroscopy,” Rev. Phys. Appl. 14, 791–794 (1979).
[CrossRef]

1972 (1)

M. D. Levenson, A. L. Schawlow, “Hyperfine interactions in molecular iodine,” Phys. Rev. A 6, 10–20 (1972).
[CrossRef]

Arie, A.

Arnette, S. A.

G. S. Elliott, M. Samimy, S. A. Arnette, “Molecular filter-based diagnostics in high speed flows,” Paper 93-0512, presented at the AIAA Thirty-First Aerospace Sciences Meeting and Exhibit, Reno, Nev., 11–14 January 1993.

G. S. Elliott, M. Samimy, S. A. Arnette, “Details of a molecular filter-based velocimetry technique,” Paper 94-0490, presented at the AIAA Thirty-Second Aerospace Sciences Meeting and Exhibit, Reno, Nev., 10–13 January 1994.

Bevington, P. R.

P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hil, New York, 1969), p. 59.

Bilhorn, R. B.

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Optical Society of America, New York, 1983).

Brosnan, S. J.

H. Komine, S. J. Brosnan, A. B. Litton, E. A. Stappaerts, “Real-time, Doppler global velocimetry,” AIAA paper 91-0337, presented at the Twenty-Ninth Aerospace Sciences Meeting, Reno, Nev., 7–10 January 1991.

Buil, C.

C. Buil, CCD Astronomy: Construction and Use of an Astronomical CCD Camera (Willmann-Bell, Richmond, Va., 1991).

Byer, R. L.

Cavone, A. A.

J. F. Meyers, J. W. Lee, A. A. Cavone, “Three component Doppler global velocimeter measurements of the flow above a delta wing,” presented at the Sixth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 20–23 July 1992.

J. W. Lee, J. F. Meyers, A. A. Cavone, K. E. Suzuki, “Doppler global velocimetry measurements of the vortical flow above an F/A-18,” Paper 93-0414, presented at the AIAA Thirty-First Aerospace Sciences Meeting and Exhibit, Reno, Nev., 11–14 January 1993.

Denton, M. B.

Drain, L. E.

L. E. Drain, The Laser Doppler Techniqu (Wiley, New York, 1980), pp. 182–190.

Elliott, G. S.

G. S. Elliott, M. Samimy, S. A. Arnette, “Molecular filter-based diagnostics in high speed flows,” Paper 93-0512, presented at the AIAA Thirty-First Aerospace Sciences Meeting and Exhibit, Reno, Nev., 11–14 January 1993.

G. S. Elliott, M. Samimy, S. A. Arnette, “Details of a molecular filter-based velocimetry technique,” Paper 94-0490, presented at the AIAA Thirty-Second Aerospace Sciences Meeting and Exhibit, Reno, Nev., 10–13 January 1994.

Epperson, P. M.

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in fortran (Cambridge U. Press, Cambridge, 1992).

Forkey, J.

Private communication between P. Luc, J. Forkey. Similar Franck–Condon values may be found in J. Tellinghuisen, “Intensity factors for the I2B ↔ X band system,” Quant J. Spectrosc. Radiat. Transfer19, 149–161 (1978).
[CrossRef]

The author is particularly grateful toJ. Forkey of the Department of Mechanical and Aerospace Engineering, Princeton University, for providing his iodine spectrum computer codes.

Forkey, J. N.

R. B. Miles, J. N. Forkey, W. R. Lempert, “Filtered Rayleigh scattering measurements in supersonic/hypersonic facilities,” Paper 92-3894, presented at the Seventeenth AIAA Aerospace Ground Testing Conference, Nashville, Tenn., 6–8 July 1992.

Gerstenkorn, S.

S. Gerstenkorn, P. Luc, “Absolute iodine (I2) standards measured by means of Fourier transform spectroscopy,” Rev. Phys. Appl. 14, 791–794 (1979).
[CrossRef]

S. Gerstenkorn, P. Luc, Atlas du Spectre d’ Absorption de la Molecule d’ Iode 14800–20000 cm −1 (Laboratorie Aime-Cotton, Centre National de la Recherche Scientifique, II-91405, Orsay, France, 1986).

S. Gerstenkorn, P. Luc, Atlas du Spectre d’ Absorption de la Molecule d’ Iode 14800–20000 cm−1 (Laboratorie Aime-Cotton, Centre National de la Recherche Scientifique, II-91405, Orsay, France, 1978).

Glaser, M.

M. Glaser, “Identification of hyperfine structure components of the iodine molecule at 640 nm wavelength,” Opt. Commun. 54, 335–342 (1985).
[CrossRef]

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Optical Society of America, New York, 1983).

Komine, H.

H. Komine, S. J. Brosnan, A. B. Litton, E. A. Stappaerts, “Real-time, Doppler global velocimetry,” AIAA paper 91-0337, presented at the Twenty-Ninth Aerospace Sciences Meeting, Reno, Nev., 7–10 January 1991.

Lee, J. W.

J. F. Meyers, J. W. Lee, A. A. Cavone, “Three component Doppler global velocimeter measurements of the flow above a delta wing,” presented at the Sixth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 20–23 July 1992.

J. W. Lee, J. F. Meyers, A. A. Cavone, K. E. Suzuki, “Doppler global velocimetry measurements of the vortical flow above an F/A-18,” Paper 93-0414, presented at the AIAA Thirty-First Aerospace Sciences Meeting and Exhibit, Reno, Nev., 11–14 January 1993.

Lempert, W. R.

R. B. Miles, J. N. Forkey, W. R. Lempert, “Filtered Rayleigh scattering measurements in supersonic/hypersonic facilities,” Paper 92-3894, presented at the Seventeenth AIAA Aerospace Ground Testing Conference, Nashville, Tenn., 6–8 July 1992.

Levenson, M. D.

M. D. Levenson, A. L. Schawlow, “Hyperfine interactions in molecular iodine,” Phys. Rev. A 6, 10–20 (1972).
[CrossRef]

Litton, A. B.

H. Komine, S. J. Brosnan, A. B. Litton, E. A. Stappaerts, “Real-time, Doppler global velocimetry,” AIAA paper 91-0337, presented at the Twenty-Ninth Aerospace Sciences Meeting, Reno, Nev., 7–10 January 1991.

Luc, P.

P. Luc, “Molecular constants and Durham expansion parameters describing the B−X system of the iodine molecule,” J. Mol. Spectrosc. 80, 41–55 (1980).
[CrossRef]

S. Gerstenkorn, P. Luc, “Absolute iodine (I2) standards measured by means of Fourier transform spectroscopy,” Rev. Phys. Appl. 14, 791–794 (1979).
[CrossRef]

Private communication between P. Luc, J. Forkey. Similar Franck–Condon values may be found in J. Tellinghuisen, “Intensity factors for the I2B ↔ X band system,” Quant J. Spectrosc. Radiat. Transfer19, 149–161 (1978).
[CrossRef]

S. Gerstenkorn, P. Luc, Atlas du Spectre d’ Absorption de la Molecule d’ Iode 14800–20000 cm −1 (Laboratorie Aime-Cotton, Centre National de la Recherche Scientifique, II-91405, Orsay, France, 1986).

S. Gerstenkorn, P. Luc, Atlas du Spectre d’ Absorption de la Molecule d’ Iode 14800–20000 cm−1 (Laboratorie Aime-Cotton, Centre National de la Recherche Scientifique, II-91405, Orsay, France, 1978).

Meyers, J. F.

J. F. Meyers, “Doppler global velocimetry. The next generation?,” Paper 92-3897, presented at the AIAA Seventeenth Aerospace Ground Testing Conference, Nashville, Tenn., 6–8 July 1992.

J. F. Meyers, J. W. Lee, A. A. Cavone, “Three component Doppler global velocimeter measurements of the flow above a delta wing,” presented at the Sixth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 20–23 July 1992.

J. W. Lee, J. F. Meyers, A. A. Cavone, K. E. Suzuki, “Doppler global velocimetry measurements of the vortical flow above an F/A-18,” Paper 93-0414, presented at the AIAA Thirty-First Aerospace Sciences Meeting and Exhibit, Reno, Nev., 11–14 January 1993.

J. F. Meyers, “Generation of particles and seeding,” in Laser Velocimetry, von Karman Institute for Fluid Dynamics Lecture Series 1991-08 (von Karmann Institute for Fluid Dynamics, Rhode-Saint-Genes, Belgium, 1991).

Miles, R. B.

R. B. Miles, J. N. Forkey, W. R. Lempert, “Filtered Rayleigh scattering measurements in supersonic/hypersonic facilities,” Paper 92-3894, presented at the Seventeenth AIAA Aerospace Ground Testing Conference, Nashville, Tenn., 6–8 July 1992.

Northam, G. B.

M. W. Smith, G. B. Northam, “Application of absorption filter-planar Doppler velocimetry to sonic and supersonic jets,” Paper 95-0299, presented at the AIAA Thirty-Third Aerospace Sciences Meeting and Exhibit, Reno, Nev., 9–12 January 1995.

Pieterse, J. W.

J. W. Pieterse, Spectra-Physics memorandum No. 88-1 (private communication, 12July1988).

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in fortran (Cambridge U. Press, Cambridge, 1992).

Samimy, M.

G. S. Elliott, M. Samimy, S. A. Arnette, “Details of a molecular filter-based velocimetry technique,” Paper 94-0490, presented at the AIAA Thirty-Second Aerospace Sciences Meeting and Exhibit, Reno, Nev., 10–13 January 1994.

G. S. Elliott, M. Samimy, S. A. Arnette, “Molecular filter-based diagnostics in high speed flows,” Paper 93-0512, presented at the AIAA Thirty-First Aerospace Sciences Meeting and Exhibit, Reno, Nev., 11–14 January 1993.

Schawlow, A. L.

M. D. Levenson, A. L. Schawlow, “Hyperfine interactions in molecular iodine,” Phys. Rev. A 6, 10–20 (1972).
[CrossRef]

Smith, M. W.

M. W. Smith, G. B. Northam, “Application of absorption filter-planar Doppler velocimetry to sonic and supersonic jets,” Paper 95-0299, presented at the AIAA Thirty-Third Aerospace Sciences Meeting and Exhibit, Reno, Nev., 9–12 January 1995.

Stappaerts, E. A.

H. Komine, S. J. Brosnan, A. B. Litton, E. A. Stappaerts, “Real-time, Doppler global velocimetry,” AIAA paper 91-0337, presented at the Twenty-Ninth Aerospace Sciences Meeting, Reno, Nev., 7–10 January 1991.

Suzuki, K. E.

J. W. Lee, J. F. Meyers, A. A. Cavone, K. E. Suzuki, “Doppler global velocimetry measurements of the vortical flow above an F/A-18,” Paper 93-0414, presented at the AIAA Thirty-First Aerospace Sciences Meeting and Exhibit, Reno, Nev., 11–14 January 1993.

Sweedler, J. V.

Tellinghuisen, J.

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

Private communication between P. Luc, J. Forkey. Similar Franck–Condon values may be found in J. Tellinghuisen, “Intensity factors for the I2B ↔ X band system,” Quant J. Spectrosc. Radiat. Transfer19, 149–161 (1978).
[CrossRef]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in fortran (Cambridge U. Press, Cambridge, 1992).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in fortran (Cambridge U. Press, Cambridge, 1992).

Appl. Spectrosc. (1)

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. Mol. Spectrosc. (1)

P. Luc, “Molecular constants and Durham expansion parameters describing the B−X system of the iodine molecule,” J. Mol. Spectrosc. 80, 41–55 (1980).
[CrossRef]

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

Opt. Commun. (1)

M. Glaser, “Identification of hyperfine structure components of the iodine molecule at 640 nm wavelength,” Opt. Commun. 54, 335–342 (1985).
[CrossRef]

Phys. Rev. A (1)

M. D. Levenson, A. L. Schawlow, “Hyperfine interactions in molecular iodine,” Phys. Rev. A 6, 10–20 (1972).
[CrossRef]

Rev. Phys. Appl. (1)

S. Gerstenkorn, P. Luc, “Absolute iodine (I2) standards measured by means of Fourier transform spectroscopy,” Rev. Phys. Appl. 14, 791–794 (1979).
[CrossRef]

Other (22)

Private communication between P. Luc, J. Forkey. Similar Franck–Condon values may be found in J. Tellinghuisen, “Intensity factors for the I2B ↔ X band system,” Quant J. Spectrosc. Radiat. Transfer19, 149–161 (1978).
[CrossRef]

The author is particularly grateful toJ. Forkey of the Department of Mechanical and Aerospace Engineering, Princeton University, for providing his iodine spectrum computer codes.

R. B. Miles, J. N. Forkey, W. R. Lempert, “Filtered Rayleigh scattering measurements in supersonic/hypersonic facilities,” Paper 92-3894, presented at the Seventeenth AIAA Aerospace Ground Testing Conference, Nashville, Tenn., 6–8 July 1992.

S. Gerstenkorn, P. Luc, Atlas du Spectre d’ Absorption de la Molecule d’ Iode 14800–20000 cm −1 (Laboratorie Aime-Cotton, Centre National de la Recherche Scientifique, II-91405, Orsay, France, 1986).

Princeton Instruments Catalog of High Performance Cameras, Princeton Instruments, Inc., Princeton, N.J. (1994).

C. Buil, CCD Astronomy: Construction and Use of an Astronomical CCD Camera (Willmann-Bell, Richmond, Va., 1991).

S. Gerstenkorn, P. Luc, Atlas du Spectre d’ Absorption de la Molecule d’ Iode 14800–20000 cm−1 (Laboratorie Aime-Cotton, Centre National de la Recherche Scientifique, II-91405, Orsay, France, 1978).

H. Komine, S. J. Brosnan, A. B. Litton, E. A. Stappaerts, “Real-time, Doppler global velocimetry,” AIAA paper 91-0337, presented at the Twenty-Ninth Aerospace Sciences Meeting, Reno, Nev., 7–10 January 1991.

J. F. Meyers, “Doppler global velocimetry. The next generation?,” Paper 92-3897, presented at the AIAA Seventeenth Aerospace Ground Testing Conference, Nashville, Tenn., 6–8 July 1992.

J. F. Meyers, J. W. Lee, A. A. Cavone, “Three component Doppler global velocimeter measurements of the flow above a delta wing,” presented at the Sixth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 20–23 July 1992.

J. W. Lee, J. F. Meyers, A. A. Cavone, K. E. Suzuki, “Doppler global velocimetry measurements of the vortical flow above an F/A-18,” Paper 93-0414, presented at the AIAA Thirty-First Aerospace Sciences Meeting and Exhibit, Reno, Nev., 11–14 January 1993.

G. S. Elliott, M. Samimy, S. A. Arnette, “Molecular filter-based diagnostics in high speed flows,” Paper 93-0512, presented at the AIAA Thirty-First Aerospace Sciences Meeting and Exhibit, Reno, Nev., 11–14 January 1993.

G. S. Elliott, M. Samimy, S. A. Arnette, “Details of a molecular filter-based velocimetry technique,” Paper 94-0490, presented at the AIAA Thirty-Second Aerospace Sciences Meeting and Exhibit, Reno, Nev., 10–13 January 1994.

M. W. Smith, G. B. Northam, “Application of absorption filter-planar Doppler velocimetry to sonic and supersonic jets,” Paper 95-0299, presented at the AIAA Thirty-Third Aerospace Sciences Meeting and Exhibit, Reno, Nev., 9–12 January 1995.

J. W. Pieterse, Spectra-Physics memorandum No. 88-1 (private communication, 12July1988).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in fortran (Cambridge U. Press, Cambridge, 1992).

P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hil, New York, 1969), p. 59.

L. E. Drain, The Laser Doppler Techniqu (Wiley, New York, 1980), pp. 182–190.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Optical Society of America, New York, 1983).

W. W. Hunter, C. E. Nichols, eds., “Wind tunnel seeding systems for laser velocimeters,” NASA Conf. Pub. 2393 (NASA Langley Research Center, Hampton, Va.,, 1985).

J. F. Meyers, “Generation of particles and seeding,” in Laser Velocimetry, von Karman Institute for Fluid Dynamics Lecture Series 1991-08 (von Karmann Institute for Fluid Dynamics, Rhode-Saint-Genes, Belgium, 1991).

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Figures (19)

Fig. 1
Fig. 1

PDV configuration for the measurement of one velocity component in the direction S.

Fig. 2
Fig. 2

PDV vector geometry.

Fig. 3
Fig. 3

Comparison of an experimental and a fitted response function. The experimental data show the effects of a 20-MHz laser frequency modulation.

Fig. 4
Fig. 4

Comparison of an experimental spectral scan with the spectral model. The line numbers are those assigned to selected features in Ref. 11.

Fig. 5
Fig. 5

Comparison of transmission slopes over the laser tuning range for a cell body temperature of 100 °C, a stem temperature of 30 °C, and a path length of 15.24 cm.

Fig. 6
Fig. 6

Effect of cell stem temperature on the transmission of the blue side of line 1109 for a body temperature of 100 °C and a path length of 15.24 cm.

Fig. 7
Fig. 7

Effect of cell stem temperature on the transmission spectral slope of the blue side of line 1109 for a body temperature of 100 °C and a path length of 15.24 cm.

Fig. 8
Fig. 8

Effect of cell body temperature on the transmission of the blue side of line 1109 for a stem temperature of 45 °C and a path length of 15.24 cm.

Fig. 9
Fig. 9

Optical arrangement for the rotating wheel experiments. F.P., Fabry–Perot.

Fig. 10
Fig. 10

Comparison of PDV measurements of surface speeds on a rotating wheel with actual speeds. The error bars correspond to the rms uncertainty at each speed. They are compared with the expected uncertainty associated with 12-bit digital errors.

Fig. 11
Fig. 11

Effect of unfiltered signal level S 2 (photoelectrons) on the single-pulse Doppler-shift rms uncertainties for a CCD detector with 16-bit digital resolution (G AD = 10 electrons/count), well depth Dw = 500,000 electrons, readout noise σRO = 18 electrons, accumulated dark charge S DC = 1 electron, unfiltered laser signal S 4 = 400,000 photoelectrons (S 4/Dw = 0.8), and laser filtered− unfiltered signal ratio S 34 =0.5.

Fig. 12
Fig. 12

Effect of laser signal ratio on the single-pulse Doppler-shift rms uncertainties for S 2 = 250,000 photoelectrons. Other CCD array conditions are the same as given for Fig. 11.

Fig. 13
Fig. 13

Effect of digital resolution on the single-pulse Doppler-shift rms uncertainties for S 2 = 100,000 photoelectrons. Other CCD array conditions are the same as given for Fig. 11. The A/D gain values [electrons/count (e/cnt)] corresponding to each value of N-bit are indicated.

Fig. 14
Fig. 14

PDV light sheet and collection optics geometry.

Fig. 15
Fig. 15

Scattering efficiencies for absorbing and nonabsorbing homogeneous spheres obtained using log-normal size distributions with Δr/r 0 = 0.5. Light wavelength λ0 = 532 nm.

Fig. 16
Fig. 16

Extinction efficiencies for absorbing and nonabsorbing homogeneous spheres obtained using log-normal size distributions with Δr/r 0 = 0.5. Light wavelength λ0 = 532 nm.

Fig. 17
Fig. 17

Angular scattering function for absorbing spheres (n = 1.5 + i1.0) in p-polarized light at λ0 = 532 nm for a log-normal particle distribution with r 0 = 0.5 μm and Δr/r 0 = 0.5.

Fig. 18
Fig. 18

Angular scattering function for absorbing spheres (n = 1.5 + i1.0) in s-polarized light at λ0 = 532 nm for a log-normal particle distribution with r 0 = 0.5 μm and Δr/r0 = 0.5.

Fig. 19
Fig. 19

Observation ranges that give the specified photoelectron signal for a constant ratio of laser sheet height to range, Δy/R = 0.1. Laser pulse energy E 0 = 300 mJ/pulse, A pix = 25 μm × 25 μm, f # = 1.4, ηqe = 0.3. Data are limited to aerosol transmissions for D ext > 50 cm.

Equations (22)

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Δ ν = ν 0 c ( a ^ l ^ ) V ,
V  cos Ω = ( λ 0 2  sin  ϕ 2 ) Δ ν ,
S 1 = G 1 T ( ν D ) E 0 , S 2 = G 2 E 0 , S 3 = G 3 T ( ν 0 ) E 0 , S 4 = G 4 E 0 ,
S 12 = S 1 / S 2 = G 12 T ( ν D ) , S 34 = S 3 / S 4 = G 34 T ( ν 0 ) ,
ν D ν = ζ D [ S 12 ] , ν 0 ν = ζ 0 [ S 34 ] ,
Δ ν = ζ D [ S 12 ] ζ 0 [ S 34 ] .
T ( ν ) = exp [ ( α ν + α nr ) N I 2 L path ] ,
Δ ν S 12 / G 12 S 34 / G 34 ( d T / d ν ) ν ,
σ u 2 = i σ i 2 ( u x i ) 2 .
σ Δ ν 2 = σ 12 2 ( ν S 12 ) ν D 2 + σ 34 2 ( ν S 34 ) ν 0 2 ,
σ 12 2 = ( S 1 / S 2 ) 2 ( σ 1 2 S 1 2 + σ 2 2 S 2 2 )
σ i 2 = σ RO 2 + S i + B i + S DC G AD 2 .
E scat = E 0 Δ y Δ z X scat N part V FOV Ω c θ pol ( α , Ψ ) × exp ( N part X ext C path ) ,
θ p = f s ( α ) cos 2 Ψ + f p ( α ) sin 2 Ψ , θ s = f s ( α ) sin 2 Ψ + f p ( α ) cos 2 Ψ .
V FOV = A pix ( R / F L ) 2 Δ z sin  α  cos  ψ .
Ω c = π 4 ( F L / R ) 2 f # 2 .
S 2 = η QE E scat h ν 0 = η QE E 0 h ν 0 π 4 ( X scat X ext ) H pol ( α , Ψ )    × A pix f # 2 Δ y D ext exp ( C path D ext ) ,
H pol ( α , Ψ ) = [ θ pol ( α , Ψ ) sinαcosΨ ] .
D F ( r ) = C 0 exp { C 1 [ ln ( r / r 0 ) ] 2 } ,
0 D F ( r ) d r = 1 .
P D ( x , r 0 , Δ r r 0 ) = ( ln   2 / π ) 1 / 2 r 0 Δ x × exp { ln   2 [ ( Δ x 2   ln   2 ) 2 + ( x Δ x ) 2 ] } .
X scat ( r 0 , Δ r r 0 ) = 0 P D ( r , r 0 , Δ r r 0 ) X s ( r ) d r ,

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