OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 49, Iss. 19 — Jul. 1, 2010
  • pp: 3786–3792

Optical path difference of the supersonic mixing layer

Qiong Gao, Zongfu Jiang, Shihe Yi, and Yuxin Zhao  »View Author Affiliations

Applied Optics, Vol. 49, Issue 19, pp. 3786-3792 (2010)

View Full Text Article

Enhanced HTML    Acrobat PDF (636 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The distorted wavefront due to the density fluctuation of the supersonic mixing layer is measured by the nano-based planar laser scattering technique, with the spatiotemporal resolutions as 10 1 mm and 1 μs (time interval between two exposures), respectively. The optical path difference (OPD) is analyzed from the viewpoints of correlation and structure functions. Depending on the structure of the flow field, the type of the correlation function is Gaussian or exponential. The power index of the structure function is about 1.1, and the consistency over many cases is quite good. The far-field propagation of the Gaussian beam is simulated by Fourier transform, and the Strehl ratio is calculated with the rms of the OPD. The beam center and beam spread about the center in the far field are calculated, and are dominated by the statistics of the tilt of the distorted wavefront. The results indicate that aero-optical aberrations can severely limit the performance of airborne laser systems.

© 2010 Optical Society of America

OCIS Codes
(030.6600) Coherence and statistical optics : Statistical optics
(030.7060) Coherence and statistical optics : Turbulence

ToC Category:
Coherence and Statistical Optics

Original Manuscript: April 19, 2010
Manuscript Accepted: June 1, 2010
Published: June 29, 2010

Qiong Gao, Zongfu Jiang, Shihe Yi, and Yuxin Zhao, "Optical path difference of the supersonic mixing layer," Appl. Opt. 49, 3786-3792 (2010)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. K. G. Gilbert and L. J. Otten, eds., Aero-Optical Phenomena (American Institute of Aeronautics and Astronautics, 1980).
  2. E. J. Jumper and E. J. Fitzgerald, “Recent advances in aero-optics,” Prog. Aerosp. Sci. 37, 299–339 (2001). [CrossRef]
  3. J. D. Trolinger, “Aero-optical characterization of aircraft optical turrets by holography, interferometry and shadowgraph,” in Aero-Optical Phenomena, K.G.Gilbert and L.J.Otten, eds. (American Institute of Aeronautics and Astronautics, 1982), pp. 200–217.
  4. M. Malley, G. W. Sutton, and N. Kincheloe, “Beam-jitter measurements of turbulent aero-optical path differences,” Appl. Opt. 31, 4440–4443 (1992). [CrossRef] [PubMed]
  5. R. J. Hugo and E. J. Jumper, “Experimental measurement of a time-varying optical path difference using the small-aperture beam technique,” Appl. Opt. 35, 4436–4447 (1996). [CrossRef] [PubMed]
  6. S. Abado, S. Gordeyev, and E. J. Jumper, “Designing and testing a high bandwidth 2-D wave front sensor for aero-optics,” Proc. SPIE 7466, 746602 (2009). [CrossRef]
  7. P. E. Dimotakis, H. J. Catrakis, and D. C. Fourguette, “Flow structure and optical beam propagation in high-Reynolds-number gas-phase shear layers and jets,” J. Fluid Mech. 433, 105–134 (2001).
  8. F. R. Zubair and H. J. Catrakis, “Aero-optical interactions along laser beam propagation paths in compressible turbulence,” AIAA J. 45, 1663–1674 (2007). [CrossRef]
  9. S. H. Yi, Y. X. Zhao, L. He, Y. Z. Cheng, and L. F. Tian, “NPLS technique and its application in visualization of the supersonic turbulence,” Chin. Conf. Theoret. Appl. Mech. Beijing (2007).
  10. Y. X. Zhao, “Experimental study of the spatiotemporal structure of supersonic mixing layer,” Ph.D. dissertation (College of Aerospace and Material Engineering, National University of Defense Technology, 2008).
  11. L. F. Tian, S. H. Xi, Y. X. Zhao, L. He, and Y. Z. Cheng, “Study of density field measurement based on NPLS technique in supersonic flow,” Sci. China Ser. G 52, 1357–1363(2009). [CrossRef]
  12. Y. X. Zhao, S. H. Xi, L. F. Tian, L. He, and Y. Z. Cheng, “Multiresolution analysis of density fluctuation in supersonic mixing layer,” Sci. China Tech. Sci. 53, 584–591 (2010). [CrossRef]
  13. E. J. Fitzgerald and E. J. Jumper, “The optical distortion mechanism in a nearly incompressible free shear layer,” J. Fluid Mech. 512, 153–189 (2001).
  14. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, 1961).
  15. V. N. Mahajan, “Strehl ratio for aberrations in terms of their aberration variance,” J. Opt. Soc. Am. 73, 860–861 (1983). [CrossRef]
  16. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  17. A. Mani, M. Wang, and P. Moin, “Statistical description of the free-space propagation of highly aberrated optical beams,” J. Opt. Soc. Am. A 23, 3027–3035 (2006). [CrossRef]
  18. A. Mani, P. Moin, and M. Wang, “Computational study of optical distortions by separated shear layers and turbulent wakes,” J. Fluid Mech. 625, 273–298 (2009). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3
Fig. 4 Fig. 5

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited