Abstract

We discuss the use of time series of the jitter angle of multiple, small-aperture probe beams (the small-aperture beam technique, or SABT) as they emerge from a turbulent, optically active flow-field to quantify the time-varying optical path difference (OPD). The flow field studied is that for the transitionally turbulent region of a two-dimensional heated jet. Techniques to construct a complete time series of instantaneous realizations of the OPD are first applied to a numerically generated flow field and then to an experimental flow field. The SABT sensor’s measurement accuracy is assessed, and its application to flow fields that differ from the numerical heated jet is discussed.

© 1996 Optical Society of America

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  1. W. J. Smith, Modern Optical Engineering: The Design of Optical Systems (McGraw-Hill, New York, 1966), Chap. 3, pp. 49–71.
  2. G. W. Sutton, “Effects of turbulent fluctuations in an optically active fluid medium,” AIAA J. 7, 1737–1743 (1969).
    [CrossRef]
  3. V. I. Tatarski, Wave Propagation in a Turbulent Medium (Dover, New York, 1961), Chap. 6.
  4. R. K. Tyson, Principles of Adaptive Optics (Academic, San Diego, Calif., 1991), Chap. 8, pp. 257–260.
  5. J. W. Hardy, “Adaptive optics,” Sci. Am. 270, 60–65 (1994).
    [CrossRef]
  6. R. K. Tyson, “The status of astronomical adaptive optics systems,” O. E. Rep. 121, 11, 13 (1994).
  7. R. Q. Fugate, W. J. Wild, “Untwinkling the stars, part 1,” Sky Telescope 87(5), 20–31 (1994).
  8. R. Q. Fugate, W. J. Wild, “Untwinkling the stars, part 2,” Sky Telescope 87(6), 20–27 (1994).
  9. R. J. Hugo, E. J. Jumper, “Experimental measurement of a time-varying optical path difference using the small-aperture beam technique,” in Optical Diagnostics in Fluid and Thermal Flow, S. S. Cha, J. D. Trolinger, eds. Proc. SPIE2005, 116–128 (1993).
  10. R. J. Hugo, E. J. Jumper, G. Havener, S. A. Stepanek, “Time-resolved, aero-optical measurements of a wavefront aberrated by a compressible shear layer,” AIAA paper 95-1979 (American Institute of Aeronautics and Astronautics, New York, 1995).
  11. E. J. Jumper, R. J. Hugo, “Quantification of aero-optical phase distortion using the small-aperture beam technique,” AIAA J. 33, 2151–2157 (1995).
    [CrossRef]
  12. D. Malacara, Optical Shop Testing (Wiley, New York, 1978), Chap. 10, pp. 323–345.
  13. J. D. Trolinger, “Aero-optical characterization of aircraft optical turrets by holography, interferometry, and shadowgraph,” Vol. 80 of Progress in Astronautics and Aeronautics: Aero-Optical Phenomena, K. Gilbert, L. J. Otten, eds. (American Institute of Aeronautics and Astronautics, New York, 1982), pp. 200–217.
  14. D. Kelsall, “Optical ‘seeing’ through the atmosphere by an interferometric technique,” J. Opt. Soc. Am. 63, 1472–1484 (1973).
    [CrossRef]
  15. D. Kelsall, “Rapid interferometric technique for MTF measurements in the visible or infrared region,” Appl. Opt. 12, 1398–1399 (1973).
    [CrossRef] [PubMed]
  16. D. J. Wolters, “Aerodynamic effects on airborne optical systems,” MDC A2582 (McDonnell Douglas Corporation, St. Louis, 1973).
  17. W. J. Steinmetz, “Second moments of optical degradation due to a thin turbulent layer,” Vol. 80 of Progress in Astronautics and Aeronautics: Aero-Optical Phenomena, K. Gilbert, L. J. Otten, eds. (American Institute of Aeronautics and Astronautics, New York, 1982), pp. 78–100.
  18. W. C. Rose, D. A. Johnson, L. J. Otten, “Summary of ALL cycle II.5 aerodynamic shear- and boundary-layer measurements,” Vol. 80 of Progress in Astronautics and Aeronautics: Aero-Optical Phenomena, K. Gilbert, L. J. Otten, eds. (American Institute of Aeronautics and Astronautics, New York, 1982), pp. 294–305.
  19. K. G. Gilbert, “KC-135 aero-optical turbulent boundary-layer/shear-layer experiments,” Vol. 80 of Progress in Astronautics and Aeronautics: Aero-Optical Phenomena, K. Gilbert, L. J. Otten, eds. (American Institute of Aeronautics and Astronautics, New York, 1982), pp. 306–324.
  20. M. Malley, G. W. Sutton, N. Kincheloe, “Beam-jitter measurements of turbulent aero-optical path differences,” Appl. Opt. 31, 4440–4443 (1992).
    [CrossRef] [PubMed]
  21. D. R. Neal, T. J. O’Hern, J. R. Torczynski, M. E. Warren, R. Shul, T. S. McKechnie, “Wavefront sensors for optical diagnostics in fluid mechanics: application to heated flow, turbulence and droplet evaporation,” in Optical Diagnostics in Fluid and Thermal Flow, S. S. Cha, J. D. Trolinger, eds., Proc. SPIE2005, 194–203 (1993).
  22. L. McMackin, J. Wissler, N. Clark, E. Chen, K. Bishop, R. Pierson, B. Stavely, “Hartmann sensor and dynamic to-mographical analysis of organized structure in flow fields,” AIAA paper 94-2548 (American Institute of Aeronautics and Astronautics, New York, 1994).
  23. B. Masson, L. McMackin, J. Wissler, K. Bishop, “Study of a round jet using a Shack–Hartmann wavefront sensor,” AIAA paper 95-0644 (American Institute of Aeronautics and Astronautics, New York, 1995).
  24. G. Havener, F. Heltsley, “Design aspects and preliminary holographic-PIV measurements for a subsonic free shear layer flow channel,” AIAA paper 94-2550 (American Institute of Aeronautics and Astronautics, New York, 1994).
  25. M. V. Klein, Optics (Wiley, New York, 1970), Chap. 2, pp. 29–31.
  26. G. W. Sutton, ANSER, Suite 800, 1215 Jefferson Davis Highway, Arlington, Va. 22202 (personal communication, April1989).
  27. J. O. Hinze, Turbulence, 2nd ed. (McGraw-Hill, New York, 1975), Chap. 5, p. 420.
  28. J. B. Wissler, A. Roshko, “Transmission of thin light beams through turbulent mixing layers,” AIAA paper 92-0658 (American Institute of Aeronautics and Astronautics, New York, 1992).
  29. E. J. Jumper, R. J. Hugo, J. M. Cicchiello, “Turbulent-fluid-induced optical wavefront dynamics: near- and far-field implications,” AIAA paper 94-2547 (American Institute of Aeronautics and Astronautics, New York, 1994).
  30. R. J. Hugo, “Quantifying the spatio-temporal effects of optically-active turbulent flowfields on a coherent optical wave,” Ph.D. dissertation (University of Notre Dame, Notre Dame, Ind., 1995).
  31. J. S. Bendat, A. G. Piersol, Random Data—Analysis and Measurement Procedures, 2nd ed. (Wiley, New York, 1986), Chap. 12, pp. 425–483.
  32. A. Leonard, “Review: vortex methods for flow simulation,” J. Comput. Phys. 37, 289–335 (1980).
    [CrossRef]
  33. E. Acton, “A modelling of large eddies in an axisymmetric jet,” J. Fluid Mech. 98, 1–31 (1980).
    [CrossRef]

1995 (1)

E. J. Jumper, R. J. Hugo, “Quantification of aero-optical phase distortion using the small-aperture beam technique,” AIAA J. 33, 2151–2157 (1995).
[CrossRef]

1994 (4)

J. W. Hardy, “Adaptive optics,” Sci. Am. 270, 60–65 (1994).
[CrossRef]

R. K. Tyson, “The status of astronomical adaptive optics systems,” O. E. Rep. 121, 11, 13 (1994).

R. Q. Fugate, W. J. Wild, “Untwinkling the stars, part 1,” Sky Telescope 87(5), 20–31 (1994).

R. Q. Fugate, W. J. Wild, “Untwinkling the stars, part 2,” Sky Telescope 87(6), 20–27 (1994).

1992 (1)

1980 (2)

A. Leonard, “Review: vortex methods for flow simulation,” J. Comput. Phys. 37, 289–335 (1980).
[CrossRef]

E. Acton, “A modelling of large eddies in an axisymmetric jet,” J. Fluid Mech. 98, 1–31 (1980).
[CrossRef]

1973 (2)

1969 (1)

G. W. Sutton, “Effects of turbulent fluctuations in an optically active fluid medium,” AIAA J. 7, 1737–1743 (1969).
[CrossRef]

Acton, E.

E. Acton, “A modelling of large eddies in an axisymmetric jet,” J. Fluid Mech. 98, 1–31 (1980).
[CrossRef]

Bendat, J. S.

J. S. Bendat, A. G. Piersol, Random Data—Analysis and Measurement Procedures, 2nd ed. (Wiley, New York, 1986), Chap. 12, pp. 425–483.

Bishop, K.

B. Masson, L. McMackin, J. Wissler, K. Bishop, “Study of a round jet using a Shack–Hartmann wavefront sensor,” AIAA paper 95-0644 (American Institute of Aeronautics and Astronautics, New York, 1995).

L. McMackin, J. Wissler, N. Clark, E. Chen, K. Bishop, R. Pierson, B. Stavely, “Hartmann sensor and dynamic to-mographical analysis of organized structure in flow fields,” AIAA paper 94-2548 (American Institute of Aeronautics and Astronautics, New York, 1994).

Chen, E.

L. McMackin, J. Wissler, N. Clark, E. Chen, K. Bishop, R. Pierson, B. Stavely, “Hartmann sensor and dynamic to-mographical analysis of organized structure in flow fields,” AIAA paper 94-2548 (American Institute of Aeronautics and Astronautics, New York, 1994).

Cicchiello, J. M.

E. J. Jumper, R. J. Hugo, J. M. Cicchiello, “Turbulent-fluid-induced optical wavefront dynamics: near- and far-field implications,” AIAA paper 94-2547 (American Institute of Aeronautics and Astronautics, New York, 1994).

Clark, N.

L. McMackin, J. Wissler, N. Clark, E. Chen, K. Bishop, R. Pierson, B. Stavely, “Hartmann sensor and dynamic to-mographical analysis of organized structure in flow fields,” AIAA paper 94-2548 (American Institute of Aeronautics and Astronautics, New York, 1994).

Fugate, R. Q.

R. Q. Fugate, W. J. Wild, “Untwinkling the stars, part 1,” Sky Telescope 87(5), 20–31 (1994).

R. Q. Fugate, W. J. Wild, “Untwinkling the stars, part 2,” Sky Telescope 87(6), 20–27 (1994).

Gilbert, K. G.

K. G. Gilbert, “KC-135 aero-optical turbulent boundary-layer/shear-layer experiments,” Vol. 80 of Progress in Astronautics and Aeronautics: Aero-Optical Phenomena, K. Gilbert, L. J. Otten, eds. (American Institute of Aeronautics and Astronautics, New York, 1982), pp. 306–324.

Hardy, J. W.

J. W. Hardy, “Adaptive optics,” Sci. Am. 270, 60–65 (1994).
[CrossRef]

Havener, G.

G. Havener, F. Heltsley, “Design aspects and preliminary holographic-PIV measurements for a subsonic free shear layer flow channel,” AIAA paper 94-2550 (American Institute of Aeronautics and Astronautics, New York, 1994).

R. J. Hugo, E. J. Jumper, G. Havener, S. A. Stepanek, “Time-resolved, aero-optical measurements of a wavefront aberrated by a compressible shear layer,” AIAA paper 95-1979 (American Institute of Aeronautics and Astronautics, New York, 1995).

Heltsley, F.

G. Havener, F. Heltsley, “Design aspects and preliminary holographic-PIV measurements for a subsonic free shear layer flow channel,” AIAA paper 94-2550 (American Institute of Aeronautics and Astronautics, New York, 1994).

Hinze, J. O.

J. O. Hinze, Turbulence, 2nd ed. (McGraw-Hill, New York, 1975), Chap. 5, p. 420.

Hugo, R. J.

E. J. Jumper, R. J. Hugo, “Quantification of aero-optical phase distortion using the small-aperture beam technique,” AIAA J. 33, 2151–2157 (1995).
[CrossRef]

E. J. Jumper, R. J. Hugo, J. M. Cicchiello, “Turbulent-fluid-induced optical wavefront dynamics: near- and far-field implications,” AIAA paper 94-2547 (American Institute of Aeronautics and Astronautics, New York, 1994).

R. J. Hugo, E. J. Jumper, “Experimental measurement of a time-varying optical path difference using the small-aperture beam technique,” in Optical Diagnostics in Fluid and Thermal Flow, S. S. Cha, J. D. Trolinger, eds. Proc. SPIE2005, 116–128 (1993).

R. J. Hugo, “Quantifying the spatio-temporal effects of optically-active turbulent flowfields on a coherent optical wave,” Ph.D. dissertation (University of Notre Dame, Notre Dame, Ind., 1995).

R. J. Hugo, E. J. Jumper, G. Havener, S. A. Stepanek, “Time-resolved, aero-optical measurements of a wavefront aberrated by a compressible shear layer,” AIAA paper 95-1979 (American Institute of Aeronautics and Astronautics, New York, 1995).

Johnson, D. A.

W. C. Rose, D. A. Johnson, L. J. Otten, “Summary of ALL cycle II.5 aerodynamic shear- and boundary-layer measurements,” Vol. 80 of Progress in Astronautics and Aeronautics: Aero-Optical Phenomena, K. Gilbert, L. J. Otten, eds. (American Institute of Aeronautics and Astronautics, New York, 1982), pp. 294–305.

Jumper, E. J.

E. J. Jumper, R. J. Hugo, “Quantification of aero-optical phase distortion using the small-aperture beam technique,” AIAA J. 33, 2151–2157 (1995).
[CrossRef]

E. J. Jumper, R. J. Hugo, J. M. Cicchiello, “Turbulent-fluid-induced optical wavefront dynamics: near- and far-field implications,” AIAA paper 94-2547 (American Institute of Aeronautics and Astronautics, New York, 1994).

R. J. Hugo, E. J. Jumper, “Experimental measurement of a time-varying optical path difference using the small-aperture beam technique,” in Optical Diagnostics in Fluid and Thermal Flow, S. S. Cha, J. D. Trolinger, eds. Proc. SPIE2005, 116–128 (1993).

R. J. Hugo, E. J. Jumper, G. Havener, S. A. Stepanek, “Time-resolved, aero-optical measurements of a wavefront aberrated by a compressible shear layer,” AIAA paper 95-1979 (American Institute of Aeronautics and Astronautics, New York, 1995).

Kelsall, D.

Kincheloe, N.

Klein, M. V.

M. V. Klein, Optics (Wiley, New York, 1970), Chap. 2, pp. 29–31.

Leonard, A.

A. Leonard, “Review: vortex methods for flow simulation,” J. Comput. Phys. 37, 289–335 (1980).
[CrossRef]

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley, New York, 1978), Chap. 10, pp. 323–345.

Malley, M.

Masson, B.

B. Masson, L. McMackin, J. Wissler, K. Bishop, “Study of a round jet using a Shack–Hartmann wavefront sensor,” AIAA paper 95-0644 (American Institute of Aeronautics and Astronautics, New York, 1995).

McKechnie, T. S.

D. R. Neal, T. J. O’Hern, J. R. Torczynski, M. E. Warren, R. Shul, T. S. McKechnie, “Wavefront sensors for optical diagnostics in fluid mechanics: application to heated flow, turbulence and droplet evaporation,” in Optical Diagnostics in Fluid and Thermal Flow, S. S. Cha, J. D. Trolinger, eds., Proc. SPIE2005, 194–203 (1993).

McMackin, L.

B. Masson, L. McMackin, J. Wissler, K. Bishop, “Study of a round jet using a Shack–Hartmann wavefront sensor,” AIAA paper 95-0644 (American Institute of Aeronautics and Astronautics, New York, 1995).

L. McMackin, J. Wissler, N. Clark, E. Chen, K. Bishop, R. Pierson, B. Stavely, “Hartmann sensor and dynamic to-mographical analysis of organized structure in flow fields,” AIAA paper 94-2548 (American Institute of Aeronautics and Astronautics, New York, 1994).

Neal, D. R.

D. R. Neal, T. J. O’Hern, J. R. Torczynski, M. E. Warren, R. Shul, T. S. McKechnie, “Wavefront sensors for optical diagnostics in fluid mechanics: application to heated flow, turbulence and droplet evaporation,” in Optical Diagnostics in Fluid and Thermal Flow, S. S. Cha, J. D. Trolinger, eds., Proc. SPIE2005, 194–203 (1993).

O’Hern, T. J.

D. R. Neal, T. J. O’Hern, J. R. Torczynski, M. E. Warren, R. Shul, T. S. McKechnie, “Wavefront sensors for optical diagnostics in fluid mechanics: application to heated flow, turbulence and droplet evaporation,” in Optical Diagnostics in Fluid and Thermal Flow, S. S. Cha, J. D. Trolinger, eds., Proc. SPIE2005, 194–203 (1993).

Otten, L. J.

W. C. Rose, D. A. Johnson, L. J. Otten, “Summary of ALL cycle II.5 aerodynamic shear- and boundary-layer measurements,” Vol. 80 of Progress in Astronautics and Aeronautics: Aero-Optical Phenomena, K. Gilbert, L. J. Otten, eds. (American Institute of Aeronautics and Astronautics, New York, 1982), pp. 294–305.

Piersol, A. G.

J. S. Bendat, A. G. Piersol, Random Data—Analysis and Measurement Procedures, 2nd ed. (Wiley, New York, 1986), Chap. 12, pp. 425–483.

Pierson, R.

L. McMackin, J. Wissler, N. Clark, E. Chen, K. Bishop, R. Pierson, B. Stavely, “Hartmann sensor and dynamic to-mographical analysis of organized structure in flow fields,” AIAA paper 94-2548 (American Institute of Aeronautics and Astronautics, New York, 1994).

Rose, W. C.

W. C. Rose, D. A. Johnson, L. J. Otten, “Summary of ALL cycle II.5 aerodynamic shear- and boundary-layer measurements,” Vol. 80 of Progress in Astronautics and Aeronautics: Aero-Optical Phenomena, K. Gilbert, L. J. Otten, eds. (American Institute of Aeronautics and Astronautics, New York, 1982), pp. 294–305.

Roshko, A.

J. B. Wissler, A. Roshko, “Transmission of thin light beams through turbulent mixing layers,” AIAA paper 92-0658 (American Institute of Aeronautics and Astronautics, New York, 1992).

Shul, R.

D. R. Neal, T. J. O’Hern, J. R. Torczynski, M. E. Warren, R. Shul, T. S. McKechnie, “Wavefront sensors for optical diagnostics in fluid mechanics: application to heated flow, turbulence and droplet evaporation,” in Optical Diagnostics in Fluid and Thermal Flow, S. S. Cha, J. D. Trolinger, eds., Proc. SPIE2005, 194–203 (1993).

Smith, W. J.

W. J. Smith, Modern Optical Engineering: The Design of Optical Systems (McGraw-Hill, New York, 1966), Chap. 3, pp. 49–71.

Stavely, B.

L. McMackin, J. Wissler, N. Clark, E. Chen, K. Bishop, R. Pierson, B. Stavely, “Hartmann sensor and dynamic to-mographical analysis of organized structure in flow fields,” AIAA paper 94-2548 (American Institute of Aeronautics and Astronautics, New York, 1994).

Steinmetz, W. J.

W. J. Steinmetz, “Second moments of optical degradation due to a thin turbulent layer,” Vol. 80 of Progress in Astronautics and Aeronautics: Aero-Optical Phenomena, K. Gilbert, L. J. Otten, eds. (American Institute of Aeronautics and Astronautics, New York, 1982), pp. 78–100.

Stepanek, S. A.

R. J. Hugo, E. J. Jumper, G. Havener, S. A. Stepanek, “Time-resolved, aero-optical measurements of a wavefront aberrated by a compressible shear layer,” AIAA paper 95-1979 (American Institute of Aeronautics and Astronautics, New York, 1995).

Sutton, G. W.

M. Malley, G. W. Sutton, N. Kincheloe, “Beam-jitter measurements of turbulent aero-optical path differences,” Appl. Opt. 31, 4440–4443 (1992).
[CrossRef] [PubMed]

G. W. Sutton, “Effects of turbulent fluctuations in an optically active fluid medium,” AIAA J. 7, 1737–1743 (1969).
[CrossRef]

G. W. Sutton, ANSER, Suite 800, 1215 Jefferson Davis Highway, Arlington, Va. 22202 (personal communication, April1989).

Tatarski, V. I.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (Dover, New York, 1961), Chap. 6.

Torczynski, J. R.

D. R. Neal, T. J. O’Hern, J. R. Torczynski, M. E. Warren, R. Shul, T. S. McKechnie, “Wavefront sensors for optical diagnostics in fluid mechanics: application to heated flow, turbulence and droplet evaporation,” in Optical Diagnostics in Fluid and Thermal Flow, S. S. Cha, J. D. Trolinger, eds., Proc. SPIE2005, 194–203 (1993).

Trolinger, J. D.

J. D. Trolinger, “Aero-optical characterization of aircraft optical turrets by holography, interferometry, and shadowgraph,” Vol. 80 of Progress in Astronautics and Aeronautics: Aero-Optical Phenomena, K. Gilbert, L. J. Otten, eds. (American Institute of Aeronautics and Astronautics, New York, 1982), pp. 200–217.

Tyson, R. K.

R. K. Tyson, “The status of astronomical adaptive optics systems,” O. E. Rep. 121, 11, 13 (1994).

R. K. Tyson, Principles of Adaptive Optics (Academic, San Diego, Calif., 1991), Chap. 8, pp. 257–260.

Warren, M. E.

D. R. Neal, T. J. O’Hern, J. R. Torczynski, M. E. Warren, R. Shul, T. S. McKechnie, “Wavefront sensors for optical diagnostics in fluid mechanics: application to heated flow, turbulence and droplet evaporation,” in Optical Diagnostics in Fluid and Thermal Flow, S. S. Cha, J. D. Trolinger, eds., Proc. SPIE2005, 194–203 (1993).

Wild, W. J.

R. Q. Fugate, W. J. Wild, “Untwinkling the stars, part 2,” Sky Telescope 87(6), 20–27 (1994).

R. Q. Fugate, W. J. Wild, “Untwinkling the stars, part 1,” Sky Telescope 87(5), 20–31 (1994).

Wissler, J.

L. McMackin, J. Wissler, N. Clark, E. Chen, K. Bishop, R. Pierson, B. Stavely, “Hartmann sensor and dynamic to-mographical analysis of organized structure in flow fields,” AIAA paper 94-2548 (American Institute of Aeronautics and Astronautics, New York, 1994).

B. Masson, L. McMackin, J. Wissler, K. Bishop, “Study of a round jet using a Shack–Hartmann wavefront sensor,” AIAA paper 95-0644 (American Institute of Aeronautics and Astronautics, New York, 1995).

Wissler, J. B.

J. B. Wissler, A. Roshko, “Transmission of thin light beams through turbulent mixing layers,” AIAA paper 92-0658 (American Institute of Aeronautics and Astronautics, New York, 1992).

Wolters, D. J.

D. J. Wolters, “Aerodynamic effects on airborne optical systems,” MDC A2582 (McDonnell Douglas Corporation, St. Louis, 1973).

AIAA J. (2)

G. W. Sutton, “Effects of turbulent fluctuations in an optically active fluid medium,” AIAA J. 7, 1737–1743 (1969).
[CrossRef]

E. J. Jumper, R. J. Hugo, “Quantification of aero-optical phase distortion using the small-aperture beam technique,” AIAA J. 33, 2151–2157 (1995).
[CrossRef]

Appl. Opt. (2)

J. Comput. Phys. (1)

A. Leonard, “Review: vortex methods for flow simulation,” J. Comput. Phys. 37, 289–335 (1980).
[CrossRef]

J. Fluid Mech. (1)

E. Acton, “A modelling of large eddies in an axisymmetric jet,” J. Fluid Mech. 98, 1–31 (1980).
[CrossRef]

J. Opt. Soc. Am. (1)

O. E. Rep. (1)

R. K. Tyson, “The status of astronomical adaptive optics systems,” O. E. Rep. 121, 11, 13 (1994).

Sci. Am. (1)

J. W. Hardy, “Adaptive optics,” Sci. Am. 270, 60–65 (1994).
[CrossRef]

Sky Telescope (2)

R. Q. Fugate, W. J. Wild, “Untwinkling the stars, part 1,” Sky Telescope 87(5), 20–31 (1994).

R. Q. Fugate, W. J. Wild, “Untwinkling the stars, part 2,” Sky Telescope 87(6), 20–27 (1994).

Other (22)

R. J. Hugo, E. J. Jumper, “Experimental measurement of a time-varying optical path difference using the small-aperture beam technique,” in Optical Diagnostics in Fluid and Thermal Flow, S. S. Cha, J. D. Trolinger, eds. Proc. SPIE2005, 116–128 (1993).

R. J. Hugo, E. J. Jumper, G. Havener, S. A. Stepanek, “Time-resolved, aero-optical measurements of a wavefront aberrated by a compressible shear layer,” AIAA paper 95-1979 (American Institute of Aeronautics and Astronautics, New York, 1995).

W. J. Smith, Modern Optical Engineering: The Design of Optical Systems (McGraw-Hill, New York, 1966), Chap. 3, pp. 49–71.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (Dover, New York, 1961), Chap. 6.

R. K. Tyson, Principles of Adaptive Optics (Academic, San Diego, Calif., 1991), Chap. 8, pp. 257–260.

D. Malacara, Optical Shop Testing (Wiley, New York, 1978), Chap. 10, pp. 323–345.

J. D. Trolinger, “Aero-optical characterization of aircraft optical turrets by holography, interferometry, and shadowgraph,” Vol. 80 of Progress in Astronautics and Aeronautics: Aero-Optical Phenomena, K. Gilbert, L. J. Otten, eds. (American Institute of Aeronautics and Astronautics, New York, 1982), pp. 200–217.

D. R. Neal, T. J. O’Hern, J. R. Torczynski, M. E. Warren, R. Shul, T. S. McKechnie, “Wavefront sensors for optical diagnostics in fluid mechanics: application to heated flow, turbulence and droplet evaporation,” in Optical Diagnostics in Fluid and Thermal Flow, S. S. Cha, J. D. Trolinger, eds., Proc. SPIE2005, 194–203 (1993).

L. McMackin, J. Wissler, N. Clark, E. Chen, K. Bishop, R. Pierson, B. Stavely, “Hartmann sensor and dynamic to-mographical analysis of organized structure in flow fields,” AIAA paper 94-2548 (American Institute of Aeronautics and Astronautics, New York, 1994).

B. Masson, L. McMackin, J. Wissler, K. Bishop, “Study of a round jet using a Shack–Hartmann wavefront sensor,” AIAA paper 95-0644 (American Institute of Aeronautics and Astronautics, New York, 1995).

G. Havener, F. Heltsley, “Design aspects and preliminary holographic-PIV measurements for a subsonic free shear layer flow channel,” AIAA paper 94-2550 (American Institute of Aeronautics and Astronautics, New York, 1994).

M. V. Klein, Optics (Wiley, New York, 1970), Chap. 2, pp. 29–31.

G. W. Sutton, ANSER, Suite 800, 1215 Jefferson Davis Highway, Arlington, Va. 22202 (personal communication, April1989).

J. O. Hinze, Turbulence, 2nd ed. (McGraw-Hill, New York, 1975), Chap. 5, p. 420.

J. B. Wissler, A. Roshko, “Transmission of thin light beams through turbulent mixing layers,” AIAA paper 92-0658 (American Institute of Aeronautics and Astronautics, New York, 1992).

E. J. Jumper, R. J. Hugo, J. M. Cicchiello, “Turbulent-fluid-induced optical wavefront dynamics: near- and far-field implications,” AIAA paper 94-2547 (American Institute of Aeronautics and Astronautics, New York, 1994).

R. J. Hugo, “Quantifying the spatio-temporal effects of optically-active turbulent flowfields on a coherent optical wave,” Ph.D. dissertation (University of Notre Dame, Notre Dame, Ind., 1995).

J. S. Bendat, A. G. Piersol, Random Data—Analysis and Measurement Procedures, 2nd ed. (Wiley, New York, 1986), Chap. 12, pp. 425–483.

D. J. Wolters, “Aerodynamic effects on airborne optical systems,” MDC A2582 (McDonnell Douglas Corporation, St. Louis, 1973).

W. J. Steinmetz, “Second moments of optical degradation due to a thin turbulent layer,” Vol. 80 of Progress in Astronautics and Aeronautics: Aero-Optical Phenomena, K. Gilbert, L. J. Otten, eds. (American Institute of Aeronautics and Astronautics, New York, 1982), pp. 78–100.

W. C. Rose, D. A. Johnson, L. J. Otten, “Summary of ALL cycle II.5 aerodynamic shear- and boundary-layer measurements,” Vol. 80 of Progress in Astronautics and Aeronautics: Aero-Optical Phenomena, K. Gilbert, L. J. Otten, eds. (American Institute of Aeronautics and Astronautics, New York, 1982), pp. 294–305.

K. G. Gilbert, “KC-135 aero-optical turbulent boundary-layer/shear-layer experiments,” Vol. 80 of Progress in Astronautics and Aeronautics: Aero-Optical Phenomena, K. Gilbert, L. J. Otten, eds. (American Institute of Aeronautics and Astronautics, New York, 1982), pp. 306–324.

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Figures (11)

Fig. 1
Fig. 1

Viewing aperture and small-aperture relationship.

Fig. 2
Fig. 2

Flow-field probing and jitter signal histories. 2-D, two dimensional.

Fig. 3
Fig. 3

Rms OPD error for signal-averaging techniques and probe-beam spacing.

Fig. 4
Fig. 4

OPD constructed by technique IV.

Fig. 5
Fig. 5

Cross-correlation-coefficient function at X/D = 2.0: (a) numerical model, (b) experimental.

Fig. 6
Fig. 6

Maximum cross-correlation-coefficient values.

Fig. 7
Fig. 7

Rms error in SABT-constructed OPD.

Fig. 8
Fig. 8

Waterfall plot of experimental OPD’s.

Fig. 9
Fig. 9

Schematic of a heated jet facility.

Fig. 10
Fig. 10

Overlay of an experimental flow (left) and numerical flow (right).

Fig. 11
Fig. 11

Schematic of optical bench.

Equations (14)

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Λ l A .
A Λ l .
d d s ( n τ ) = n ,
OPL ( t ) = t o t θ ( t ) U c d t ,
Δ = δ U c .
R θ 1 θ 2 , t OPD ( r Δ t ) = 1 N i = 1 N θ 1 ( t OPD r Δ t + i Δ t , x 1 ) × θ 2 ( t OPD + i Δ t , x 2 ) ,
Δ = r * Δ t .
OPL ( t , x 1 ) = t OPD Δ t θ 1 ( τ , x 1 ) U c + OPL ( t OPD Δ , x 1 )
OPL ( t , x 2 ) = t OPD t θ 2 ( τ , x 2 ) U c + OPD ( t OPD , x 2 ) .
x = x 1 + U c ( t * t )
x = x 2 + U c ( t * t ) .
OPD ( t , x ) = OPL ( t , x ) OPL ( t ) ¯ ,
rms OPD error = { 1 150 × 256 i = 1 256 j = 1 150 [ SABT OPD ( x i , t j ) actual OPD ( x i , t j ) ] 2 } 1 / 2 .
ρ θ 1 θ 2 ( τ , δ ) = R θ 1 θ 2 ( τ , δ ) σ θ 1 σ θ 2 = E [ θ 1 ( t , x ) θ 2 ( t + τ , x + δ ) ] σ θ 1 σ θ 2 ,

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