Abstract

Experimental measurements of the wavefronts of the light from a laser-induced breakdown (LIB) spark in non-moving air are presented and compared to spark dimensional data acquired from photographic measurements of the spark. The data show that the variation in the spark emitted wavefront between ignitions can be directly related to the motion of the spark volumetric centroid. The dominant modal components of the emitted wavefront variations are presented, as well as quantitative results for the magnitude of the wavefront variations. The results are relevant to the use of LIB as a light source for the measurement of optical aberrations such as those caused by compressible (i.e., “aero-optic”) flows around an aircraft in flight, and data are shown indicating that LIB could be successfully used to measure the aberrating effect of compressible shear layers and boundary layers at typical cruise Mach numbers.

© 2012 Optical Society of America

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References

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  1. P. D. Maker, R. W. Terhune, and C. M. Savage, “Optical third harmonic generation,” in Proceedings of the 3rd International Conference on Quantum Electronics, P. Grivet and N. Bloembergen, eds. (Columbia University, 1964), pp. 1559–1576.
  2. T. X. Phuoc, C. M. White, and D. H. McNeill, “Laser spark ignition of a jet diffusion flame,” Opt. Laser Eng. 38, 217–232 (2002).
    [CrossRef]
  3. X. F. Wang, R. Fedosejevs, and G. D. Tsakiris, “Observation of Raman scattering and hard x rays in short pulse laser interaction with high density hydrogen gas,” Opt. Commun. 146, 363–370 (1998).
    [CrossRef]
  4. A. W. Miziolek, V. Palleschi, and I. Schechter, Laser Induced Breakdown Spectroscopy, Fundamentals and Applications (Cambridge, 2006).
  5. R. M. Rennie, D. A. Duffin, and E. J. Jumper, “Characterization and aero-optic correction of a forced two-dimensional, weakly-compressible subsonic free shear layer,” AIAA J 46, 2787–2795 (2008).
    [CrossRef]
  6. S. Gordeyev, E. J. Jumper, T. Ng, and A. Cain, “Aero-optical characteristics of compressible, subsonic turbulent boundary layers,” presented at the 34th AIAA Plasmadynamics and Lasers Conference , Orlando, Florida, 23–26June2003.
  7. D. Wittich, S. Gordeyev, and E. Jumper, “Revised scaling of optical distortions caused by compressible, subsonic turbulent boundary layers,” presented at the 38th AIAA Plasmadynamics and Lasers Conference, Miami, Florida, 25–28June, 2007.
  8. E. J. Fitzgerald and E. J. Jumper, “The optical distortion mechanism in a nearly incompressible free shear layer,” J. Fluid Mech. 512, 153–189 (2004).
    [CrossRef]
  9. E. J. Jumper and E. J. Fitzgerald, “Recent advances in aero-optics,” Prog. Aerosp. Sci. 37, 299–339 (2001).
    [CrossRef]
  10. M. Wang, A. Mani, and S. Gordeyev, “Physics and computation of aero-optics,” Annu. Rev. Fluid Mech. 44, 299–321 (2012).
  11. D. R. Neal, D. J. Armstrong, E. Hedlund, M. Lederer, A. Collier, C. Spring, J. Gruetzner, G. Hebner, and J. Mansell, “Wavefront sensor testing in hypersonic flows using a laser-spark guide star,” Proc. SPIE 3172, 347–359 (1997).
  12. R. M. Rennie, M. R. Whiteley, G. Cross, D. Cavalieri, and E. J. Jumper, “Measurement of beacon anisoplanatism through a two-dimensional weakly-compressible shear layer,” presented at the 39th AIAA Plasmadynamics and Lasers Conference, Seattle, Washington, 23–26June, 2008.
  13. R. M. Rennie, M. R. Whiteley, G. Cross, D. Cavalieri, and E. J. Jumper, “Aero-optic measurements using a laser-induced air breakdown beacon,” presented at the 40th AIAA Plasmadynamics and Lasers Conference, San Antonio, Texas, 22–25June, 2009.
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    [CrossRef]
  18. T. X. Phuoc, “Laser-induced spark ignition fundamental and applications,” Opt. Lasers Eng. 44, 351–397 (2006).
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    [CrossRef]
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2012

M. Wang, A. Mani, and S. Gordeyev, “Physics and computation of aero-optics,” Annu. Rev. Fluid Mech. 44, 299–321 (2012).

2010

M. G. Lofdahl, “Evaluation of image-shift measurement algorithms for solar Shack–Hartmann wavefront sensors,” Astron. Astrophys. 524, A90 (2010).
[CrossRef]

2008

R. M. Rennie, D. A. Duffin, and E. J. Jumper, “Characterization and aero-optic correction of a forced two-dimensional, weakly-compressible subsonic free shear layer,” AIAA J 46, 2787–2795 (2008).
[CrossRef]

2006

T. X. Phuoc, “Laser-induced spark ignition fundamental and applications,” Opt. Lasers Eng. 44, 351–397 (2006).

2004

2002

T. X. Phuoc, C. M. White, and D. H. McNeill, “Laser spark ignition of a jet diffusion flame,” Opt. Laser Eng. 38, 217–232 (2002).
[CrossRef]

2001

E. J. Jumper and E. J. Fitzgerald, “Recent advances in aero-optics,” Prog. Aerosp. Sci. 37, 299–339 (2001).
[CrossRef]

1998

X. F. Wang, R. Fedosejevs, and G. D. Tsakiris, “Observation of Raman scattering and hard x rays in short pulse laser interaction with high density hydrogen gas,” Opt. Commun. 146, 363–370 (1998).
[CrossRef]

M. R. Whiteley, B. M. Welsh, and M. C. Roggemann, “Optimal modal wave-front compensation for anisoplanatism in adaptive optics,” J. Opt. Soc. Am. A 15, 2097–2106(1998).
[CrossRef]

1997

D. R. Neal, D. J. Armstrong, E. Hedlund, M. Lederer, A. Collier, C. Spring, J. Gruetzner, G. Hebner, and J. Mansell, “Wavefront sensor testing in hypersonic flows using a laser-spark guide star,” Proc. SPIE 3172, 347–359 (1997).

1976

Armstrong, D. J.

D. R. Neal, D. J. Armstrong, E. Hedlund, M. Lederer, A. Collier, C. Spring, J. Gruetzner, G. Hebner, and J. Mansell, “Wavefront sensor testing in hypersonic flows using a laser-spark guide star,” Proc. SPIE 3172, 347–359 (1997).

Bindhu, C. V.

Cain, A.

S. Gordeyev, E. J. Jumper, T. Ng, and A. Cain, “Aero-optical characteristics of compressible, subsonic turbulent boundary layers,” presented at the 34th AIAA Plasmadynamics and Lasers Conference , Orlando, Florida, 23–26June2003.

Cavalieri, D.

R. M. Rennie, M. R. Whiteley, G. Cross, D. Cavalieri, and E. J. Jumper, “Measurement of beacon anisoplanatism through a two-dimensional weakly-compressible shear layer,” presented at the 39th AIAA Plasmadynamics and Lasers Conference, Seattle, Washington, 23–26June, 2008.

R. M. Rennie, M. R. Whiteley, G. Cross, D. Cavalieri, and E. J. Jumper, “Aero-optic measurements using a laser-induced air breakdown beacon,” presented at the 40th AIAA Plasmadynamics and Lasers Conference, San Antonio, Texas, 22–25June, 2009.

Collier, A.

D. R. Neal, D. J. Armstrong, E. Hedlund, M. Lederer, A. Collier, C. Spring, J. Gruetzner, G. Hebner, and J. Mansell, “Wavefront sensor testing in hypersonic flows using a laser-spark guide star,” Proc. SPIE 3172, 347–359 (1997).

Cross, G.

R. M. Rennie, M. R. Whiteley, G. Cross, D. Cavalieri, and E. J. Jumper, “Measurement of beacon anisoplanatism through a two-dimensional weakly-compressible shear layer,” presented at the 39th AIAA Plasmadynamics and Lasers Conference, Seattle, Washington, 23–26June, 2008.

R. M. Rennie, M. R. Whiteley, G. Cross, D. Cavalieri, and E. J. Jumper, “Aero-optic measurements using a laser-induced air breakdown beacon,” presented at the 40th AIAA Plasmadynamics and Lasers Conference, San Antonio, Texas, 22–25June, 2009.

Duffin, D. A.

R. M. Rennie, D. A. Duffin, and E. J. Jumper, “Characterization and aero-optic correction of a forced two-dimensional, weakly-compressible subsonic free shear layer,” AIAA J 46, 2787–2795 (2008).
[CrossRef]

Fedosejevs, R.

X. F. Wang, R. Fedosejevs, and G. D. Tsakiris, “Observation of Raman scattering and hard x rays in short pulse laser interaction with high density hydrogen gas,” Opt. Commun. 146, 363–370 (1998).
[CrossRef]

Fitzgerald, E. J.

E. J. Fitzgerald and E. J. Jumper, “The optical distortion mechanism in a nearly incompressible free shear layer,” J. Fluid Mech. 512, 153–189 (2004).
[CrossRef]

E. J. Jumper and E. J. Fitzgerald, “Recent advances in aero-optics,” Prog. Aerosp. Sci. 37, 299–339 (2001).
[CrossRef]

Gaeris, A. C.

Gordeyev, S.

M. Wang, A. Mani, and S. Gordeyev, “Physics and computation of aero-optics,” Annu. Rev. Fluid Mech. 44, 299–321 (2012).

D. Wittich, S. Gordeyev, and E. Jumper, “Revised scaling of optical distortions caused by compressible, subsonic turbulent boundary layers,” presented at the 38th AIAA Plasmadynamics and Lasers Conference, Miami, Florida, 25–28June, 2007.

S. Gordeyev, E. J. Jumper, T. Ng, and A. Cain, “Aero-optical characteristics of compressible, subsonic turbulent boundary layers,” presented at the 34th AIAA Plasmadynamics and Lasers Conference , Orlando, Florida, 23–26June2003.

Gruetzner, J.

D. R. Neal, D. J. Armstrong, E. Hedlund, M. Lederer, A. Collier, C. Spring, J. Gruetzner, G. Hebner, and J. Mansell, “Wavefront sensor testing in hypersonic flows using a laser-spark guide star,” Proc. SPIE 3172, 347–359 (1997).

Harilal, S. S.

Hebner, G.

D. R. Neal, D. J. Armstrong, E. Hedlund, M. Lederer, A. Collier, C. Spring, J. Gruetzner, G. Hebner, and J. Mansell, “Wavefront sensor testing in hypersonic flows using a laser-spark guide star,” Proc. SPIE 3172, 347–359 (1997).

Hedlund, E.

D. R. Neal, D. J. Armstrong, E. Hedlund, M. Lederer, A. Collier, C. Spring, J. Gruetzner, G. Hebner, and J. Mansell, “Wavefront sensor testing in hypersonic flows using a laser-spark guide star,” Proc. SPIE 3172, 347–359 (1997).

Jumper, E.

D. Wittich, S. Gordeyev, and E. Jumper, “Revised scaling of optical distortions caused by compressible, subsonic turbulent boundary layers,” presented at the 38th AIAA Plasmadynamics and Lasers Conference, Miami, Florida, 25–28June, 2007.

Jumper, E. J.

R. M. Rennie, D. A. Duffin, and E. J. Jumper, “Characterization and aero-optic correction of a forced two-dimensional, weakly-compressible subsonic free shear layer,” AIAA J 46, 2787–2795 (2008).
[CrossRef]

E. J. Fitzgerald and E. J. Jumper, “The optical distortion mechanism in a nearly incompressible free shear layer,” J. Fluid Mech. 512, 153–189 (2004).
[CrossRef]

E. J. Jumper and E. J. Fitzgerald, “Recent advances in aero-optics,” Prog. Aerosp. Sci. 37, 299–339 (2001).
[CrossRef]

S. Gordeyev, E. J. Jumper, T. Ng, and A. Cain, “Aero-optical characteristics of compressible, subsonic turbulent boundary layers,” presented at the 34th AIAA Plasmadynamics and Lasers Conference , Orlando, Florida, 23–26June2003.

R. M. Rennie, M. R. Whiteley, G. Cross, D. Cavalieri, and E. J. Jumper, “Aero-optic measurements using a laser-induced air breakdown beacon,” presented at the 40th AIAA Plasmadynamics and Lasers Conference, San Antonio, Texas, 22–25June, 2009.

R. M. Rennie, M. R. Whiteley, G. Cross, D. Cavalieri, and E. J. Jumper, “Measurement of beacon anisoplanatism through a two-dimensional weakly-compressible shear layer,” presented at the 39th AIAA Plasmadynamics and Lasers Conference, Seattle, Washington, 23–26June, 2008.

Klein, M. V.

M. V. Klein, Optics (Wiley, 1970).

Lederer, M.

D. R. Neal, D. J. Armstrong, E. Hedlund, M. Lederer, A. Collier, C. Spring, J. Gruetzner, G. Hebner, and J. Mansell, “Wavefront sensor testing in hypersonic flows using a laser-spark guide star,” Proc. SPIE 3172, 347–359 (1997).

Lofdahl, M. G.

M. G. Lofdahl, “Evaluation of image-shift measurement algorithms for solar Shack–Hartmann wavefront sensors,” Astron. Astrophys. 524, A90 (2010).
[CrossRef]

Maker, P. D.

P. D. Maker, R. W. Terhune, and C. M. Savage, “Optical third harmonic generation,” in Proceedings of the 3rd International Conference on Quantum Electronics, P. Grivet and N. Bloembergen, eds. (Columbia University, 1964), pp. 1559–1576.

Mani, A.

M. Wang, A. Mani, and S. Gordeyev, “Physics and computation of aero-optics,” Annu. Rev. Fluid Mech. 44, 299–321 (2012).

Mansell, J.

D. R. Neal, D. J. Armstrong, E. Hedlund, M. Lederer, A. Collier, C. Spring, J. Gruetzner, G. Hebner, and J. Mansell, “Wavefront sensor testing in hypersonic flows using a laser-spark guide star,” Proc. SPIE 3172, 347–359 (1997).

McNeill, D. H.

T. X. Phuoc, C. M. White, and D. H. McNeill, “Laser spark ignition of a jet diffusion flame,” Opt. Laser Eng. 38, 217–232 (2002).
[CrossRef]

Miziolek, A. W.

A. W. Miziolek, V. Palleschi, and I. Schechter, Laser Induced Breakdown Spectroscopy, Fundamentals and Applications (Cambridge, 2006).

Najmabadi, F.

Neal, D. R.

D. R. Neal, D. J. Armstrong, E. Hedlund, M. Lederer, A. Collier, C. Spring, J. Gruetzner, G. Hebner, and J. Mansell, “Wavefront sensor testing in hypersonic flows using a laser-spark guide star,” Proc. SPIE 3172, 347–359 (1997).

Ng, T.

S. Gordeyev, E. J. Jumper, T. Ng, and A. Cain, “Aero-optical characteristics of compressible, subsonic turbulent boundary layers,” presented at the 34th AIAA Plasmadynamics and Lasers Conference , Orlando, Florida, 23–26June2003.

Noll, R. J.

Palleschi, V.

A. W. Miziolek, V. Palleschi, and I. Schechter, Laser Induced Breakdown Spectroscopy, Fundamentals and Applications (Cambridge, 2006).

Phuoc, T. X.

T. X. Phuoc, “Laser-induced spark ignition fundamental and applications,” Opt. Lasers Eng. 44, 351–397 (2006).

T. X. Phuoc, C. M. White, and D. H. McNeill, “Laser spark ignition of a jet diffusion flame,” Opt. Laser Eng. 38, 217–232 (2002).
[CrossRef]

Ready, J. F.

J. F. Ready, Effects of High-Power Laser Radiation (Academic, 1971).

Rennie, R. M.

R. M. Rennie, D. A. Duffin, and E. J. Jumper, “Characterization and aero-optic correction of a forced two-dimensional, weakly-compressible subsonic free shear layer,” AIAA J 46, 2787–2795 (2008).
[CrossRef]

R. M. Rennie, M. R. Whiteley, G. Cross, D. Cavalieri, and E. J. Jumper, “Measurement of beacon anisoplanatism through a two-dimensional weakly-compressible shear layer,” presented at the 39th AIAA Plasmadynamics and Lasers Conference, Seattle, Washington, 23–26June, 2008.

R. M. Rennie, M. R. Whiteley, G. Cross, D. Cavalieri, and E. J. Jumper, “Aero-optic measurements using a laser-induced air breakdown beacon,” presented at the 40th AIAA Plasmadynamics and Lasers Conference, San Antonio, Texas, 22–25June, 2009.

Roggemann, M. C.

Savage, C. M.

P. D. Maker, R. W. Terhune, and C. M. Savage, “Optical third harmonic generation,” in Proceedings of the 3rd International Conference on Quantum Electronics, P. Grivet and N. Bloembergen, eds. (Columbia University, 1964), pp. 1559–1576.

Schechter, I.

A. W. Miziolek, V. Palleschi, and I. Schechter, Laser Induced Breakdown Spectroscopy, Fundamentals and Applications (Cambridge, 2006).

Spring, C.

D. R. Neal, D. J. Armstrong, E. Hedlund, M. Lederer, A. Collier, C. Spring, J. Gruetzner, G. Hebner, and J. Mansell, “Wavefront sensor testing in hypersonic flows using a laser-spark guide star,” Proc. SPIE 3172, 347–359 (1997).

Terhune, R. W.

P. D. Maker, R. W. Terhune, and C. M. Savage, “Optical third harmonic generation,” in Proceedings of the 3rd International Conference on Quantum Electronics, P. Grivet and N. Bloembergen, eds. (Columbia University, 1964), pp. 1559–1576.

Tillack, M. S.

Tsakiris, G. D.

X. F. Wang, R. Fedosejevs, and G. D. Tsakiris, “Observation of Raman scattering and hard x rays in short pulse laser interaction with high density hydrogen gas,” Opt. Commun. 146, 363–370 (1998).
[CrossRef]

Wang, M.

M. Wang, A. Mani, and S. Gordeyev, “Physics and computation of aero-optics,” Annu. Rev. Fluid Mech. 44, 299–321 (2012).

Wang, X. F.

X. F. Wang, R. Fedosejevs, and G. D. Tsakiris, “Observation of Raman scattering and hard x rays in short pulse laser interaction with high density hydrogen gas,” Opt. Commun. 146, 363–370 (1998).
[CrossRef]

Welsh, B. M.

White, C. M.

T. X. Phuoc, C. M. White, and D. H. McNeill, “Laser spark ignition of a jet diffusion flame,” Opt. Laser Eng. 38, 217–232 (2002).
[CrossRef]

Whiteley, M. R.

M. R. Whiteley, B. M. Welsh, and M. C. Roggemann, “Optimal modal wave-front compensation for anisoplanatism in adaptive optics,” J. Opt. Soc. Am. A 15, 2097–2106(1998).
[CrossRef]

R. M. Rennie, M. R. Whiteley, G. Cross, D. Cavalieri, and E. J. Jumper, “Aero-optic measurements using a laser-induced air breakdown beacon,” presented at the 40th AIAA Plasmadynamics and Lasers Conference, San Antonio, Texas, 22–25June, 2009.

R. M. Rennie, M. R. Whiteley, G. Cross, D. Cavalieri, and E. J. Jumper, “Measurement of beacon anisoplanatism through a two-dimensional weakly-compressible shear layer,” presented at the 39th AIAA Plasmadynamics and Lasers Conference, Seattle, Washington, 23–26June, 2008.

Wittich, D.

D. Wittich, S. Gordeyev, and E. Jumper, “Revised scaling of optical distortions caused by compressible, subsonic turbulent boundary layers,” presented at the 38th AIAA Plasmadynamics and Lasers Conference, Miami, Florida, 25–28June, 2007.

AIAA J

R. M. Rennie, D. A. Duffin, and E. J. Jumper, “Characterization and aero-optic correction of a forced two-dimensional, weakly-compressible subsonic free shear layer,” AIAA J 46, 2787–2795 (2008).
[CrossRef]

Annu. Rev. Fluid Mech.

M. Wang, A. Mani, and S. Gordeyev, “Physics and computation of aero-optics,” Annu. Rev. Fluid Mech. 44, 299–321 (2012).

Appl. Opt.

Appl. Spectrosc.

Astron. Astrophys.

M. G. Lofdahl, “Evaluation of image-shift measurement algorithms for solar Shack–Hartmann wavefront sensors,” Astron. Astrophys. 524, A90 (2010).
[CrossRef]

J. Fluid Mech.

E. J. Fitzgerald and E. J. Jumper, “The optical distortion mechanism in a nearly incompressible free shear layer,” J. Fluid Mech. 512, 153–189 (2004).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

X. F. Wang, R. Fedosejevs, and G. D. Tsakiris, “Observation of Raman scattering and hard x rays in short pulse laser interaction with high density hydrogen gas,” Opt. Commun. 146, 363–370 (1998).
[CrossRef]

Opt. Laser Eng.

T. X. Phuoc, C. M. White, and D. H. McNeill, “Laser spark ignition of a jet diffusion flame,” Opt. Laser Eng. 38, 217–232 (2002).
[CrossRef]

Opt. Lasers Eng.

T. X. Phuoc, “Laser-induced spark ignition fundamental and applications,” Opt. Lasers Eng. 44, 351–397 (2006).

Proc. SPIE

D. R. Neal, D. J. Armstrong, E. Hedlund, M. Lederer, A. Collier, C. Spring, J. Gruetzner, G. Hebner, and J. Mansell, “Wavefront sensor testing in hypersonic flows using a laser-spark guide star,” Proc. SPIE 3172, 347–359 (1997).

Prog. Aerosp. Sci.

E. J. Jumper and E. J. Fitzgerald, “Recent advances in aero-optics,” Prog. Aerosp. Sci. 37, 299–339 (2001).
[CrossRef]

Other

S. Gordeyev, E. J. Jumper, T. Ng, and A. Cain, “Aero-optical characteristics of compressible, subsonic turbulent boundary layers,” presented at the 34th AIAA Plasmadynamics and Lasers Conference , Orlando, Florida, 23–26June2003.

D. Wittich, S. Gordeyev, and E. Jumper, “Revised scaling of optical distortions caused by compressible, subsonic turbulent boundary layers,” presented at the 38th AIAA Plasmadynamics and Lasers Conference, Miami, Florida, 25–28June, 2007.

P. D. Maker, R. W. Terhune, and C. M. Savage, “Optical third harmonic generation,” in Proceedings of the 3rd International Conference on Quantum Electronics, P. Grivet and N. Bloembergen, eds. (Columbia University, 1964), pp. 1559–1576.

A. W. Miziolek, V. Palleschi, and I. Schechter, Laser Induced Breakdown Spectroscopy, Fundamentals and Applications (Cambridge, 2006).

R. M. Rennie, M. R. Whiteley, G. Cross, D. Cavalieri, and E. J. Jumper, “Measurement of beacon anisoplanatism through a two-dimensional weakly-compressible shear layer,” presented at the 39th AIAA Plasmadynamics and Lasers Conference, Seattle, Washington, 23–26June, 2008.

R. M. Rennie, M. R. Whiteley, G. Cross, D. Cavalieri, and E. J. Jumper, “Aero-optic measurements using a laser-induced air breakdown beacon,” presented at the 40th AIAA Plasmadynamics and Lasers Conference, San Antonio, Texas, 22–25June, 2009.

J. F. Ready, Effects of High-Power Laser Radiation (Academic, 1971).

M. V. Klein, Optics (Wiley, 1970).

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Figures (15)

Fig. 1.
Fig. 1.

Schematic of optical system to measure flow-induced (“aero-optic”) aberrations using a LIB spark.

Fig. 2.
Fig. 2.

Layout of experiment to photograph and measure wavefronts of spark emissions. See Table 2 for values for the shown parameters.

Fig. 3.
Fig. 3.

Examples of spark images acquired using camera. Incoming laser beam is from the right side of each image.

Fig. 4.
Fig. 4.

Spark dimensions acquired from camera images, for different f-numbers (fL/DL) of the laser focusing optics.

Fig. 5.
Fig. 5.

Root mean square variation of spark dimensions from camera images.

Fig. 6.
Fig. 6.

Absolute difference of spark volumetric centroid from mean, |ΔCxi|¯, averaged over data set.

Fig. 7.
Fig. 7.

Dependence of spark centroid location Cz on input laser pulse energy, for a set of images with fL/DL=15.

Fig. 8.
Fig. 8.

Three instantaneous realizations of the wavefront from the spark (with optical tip/tilt removed), measured using the optical setup shown in Fig. 2 (fC/DC=40).

Fig. 9.
Fig. 9.

Wavefront difference for a source that is displaced a distance ε along the optical axis of the focusing lens.

Fig. 10.
Fig. 10.

Measured rms wavefront variations over the aperture DC, averaged over the sample set, and compared with Eq. (8).

Fig. 11.
Fig. 11.

Zernike defocus coefficient for measured wavefront versus total intensity on wavefront-sensor CCD array for a data set with fC/DC=25, EE0=22mJ.

Fig. 12.
Fig. 12.

Example of a spark wavefront acquired using a smaller f-number (fC/DC=16) than allowed by Eq. (5), which shows noticeable comatic as well as defocus distortion. Laser pulse energy EE0=10mJ.

Fig. 13.
Fig. 13.

Comparison of rms wavefront variations over the aperture DC computed using a ray-tracing routine with the predictions of Eq. (8).

Fig. 14.
Fig. 14.

Generation of wavefront tip/tilt due to motion δ of spark.

Fig. 15.
Fig. 15.

Measured tip/tilt rms variations and comparison to Eq. (9), θC=10°.

Tables (2)

Tables Icon

Table 1. Experimentally Measured Optical Aberrations Reported for Standard Aero-Optic Flows in the Mach-Number Range 0.7 to 0.9a

Tables Icon

Table 2. Values of Experimental Parameters

Equations (9)

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

xi=w(x,y,z)xidVdV,
Cxi=xidVdV=πxir2dzdV,
|ΔCxi|¯=ΣN|CxiCxi¯|N,
DSfCf1f2DAfA.
fCDCDSDWfADA.
Wd=εr22fC2.
Wrms=ε27.7(fCDC)2.
Wrms¯=|ΔC|¯27.7(fCDC)2.
ϕ=CZsinθCfC.

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