## Optical transfer function of the supersonic mixing layer |

JOSA A, Vol. 29, Issue 12, pp. 2628-2637 (2012)

http://dx.doi.org/10.1364/JOSAA.29.002628

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### Abstract

The optical path difference (OPD) of the supersonic mixing layer with convective Mach number 0.5 is measured using the nanoparticle-based planar laser scattering technique, and its short-exposure optical transfer function (OTF) is computed with the proper orthogonal decomposition (POD). The OPD is analyzed from the viewpoint of structure function, and remarkable power law behavior is found. The power exponent is computed and analyzed. Taking the advantage of POD in capturing the energy of a signal, we present a model for the temporal evolution of OPD, which combines the deterministic and random factors together. With this model, the short-exposure OTF of the mixing layer is computed and analyzed. The amplitude modulation is evident at low frequencies, and it is almost negligible at high frequencies. The imaginary part of OTF for the mixing layer with developed vortex structures is of considerable amplitude, and the phase modulation becomes important for image degradation. We compare this phenomenon with the early result in aero-optics and explain it with the non-Gaussian statistics of OPD.

© 2012 Optical Society of America

**OCIS Codes**

(030.7060) Coherence and statistical optics : Turbulence

(110.4850) Imaging systems : Optical transfer functions

**ToC Category:**

Imaging Systems

**History**

Original Manuscript: June 25, 2012

Revised Manuscript: October 8, 2012

Manuscript Accepted: October 24, 2012

Published: November 27, 2012

**Citation**

Qiong Gao, Shihe Yi, Zongfu Jiang, Lin He, and Xiaohu Wang, "Optical transfer function of the supersonic mixing layer," J. Opt. Soc. Am. A **29**, 2628-2637 (2012)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-29-12-2628

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### References

- K. G. Gilbert and L. J. Otten, Aero-Optical Phenomena(American Institute of Aeronautics and Astronautics, 1982).
- E. J. Jumper and E. J. Fitzgerald, “Resent advances in aero-optics,” Prog. Aerosp. Sci. 37, 299–339 (2001). [CrossRef]
- M. Wang, A. Mani, and S. Gordeyev, “Physics and computation of aero-optics,” Ann. Rev. Fluid Mech. 44, 299–321 (2012). [CrossRef]
- S. Gordeyev and E. J. Jumper, “Fluid dynamics and aero-optics of turrets,” Prog. Aerosp. Sci. 46, 388–400 (2010). [CrossRef]
- R. E. Childs, “Prediction and control of turbulent aero-optical distortion using large eddy simulation,” in Proceedings of Annual Interceptor Technology Conference (American Institute of Aeronautics and Astronautics, 1993), pp. 1993–2670.
- R. J. Hugo and E. J. Jumper, “Experimental measurement of a time-varying optical path difference by the small-aperture beam technique,” Appl. Opt. 35, 4436–4447 (1996). [CrossRef]
- R. J. Hugo and E. J. Jumper, “Applicability of the aero-optic linking equation to a highly coherent, transitional shear layer,” Appl. Opt. 39, 4392–4401 (2000). [CrossRef]
- M. Malley, G. W. Sutton, and N. Kincheloe, “Beam-jitter measurements of turbulent aero-optical path differences,” Appl. Opt. 31, 4440–4443 (1992). [CrossRef]
- E. J. Jumper and R. J. Hugo, “Quantification of aero-optical distortion using the small-aperture beam technique,” AIAA J. 33, 2151–2157 (1995). [CrossRef]
- R. J. Hugo, E. J. Jumper, G. Havener, and C. Stepanek, “Time-resolved wave front measurements through a compressible free shear layer,” AIAA J. 35, 671–677 (1997). [CrossRef]
- 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).
- H. J. Catrakis and R. C. Aguirre, “New interfacial fluid thickness approach in aero-optics with applications to compressible turbulence,” AIAA J. 42, 1973–1981 (2004). [CrossRef]
- F. R. Zubair and H. J. Catrakis, “Aero-optical interaction along laser beam propagation paths in compressible turbulence,” AIAA J. 45, 1663–1674 (2007). [CrossRef]
- F. R. Zubair and H. J. Catrakis, “On separated shear layers and the fractal geometry of turbulent scalar interfaces at large Reynolds numbers,” J. Fluid Mech. 624, 389–411(2009). [CrossRef]
- C. R. Truman and M. J. Lee, “Effects of organized turbulent structures on the phase distortion in a coherent beam propagating through a turbulent shear flow,” Phys. Fluids A. 2, 851–857 (1990). [CrossRef]
- 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]
- 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]
- M. R. Visbal and D. P. Rizzeta, “Effect of flow excitation on aero-optical aberration,” in 46th AIAA Aerospace Sciences Meeting (American Institute of Aeronautics and Astronautics, 2008), paper 2008-1074.
- M. R. Visbal, “Numerical simulation of aero-optical aberration through weakly-compressible shear layers,” in Proceedings of 39th AIAA Fluid Dynamics Conference (American Institute of Aeronautics and Astronautics, 2009), paper 2009-4298.
- D. P. Rizzetta, M. R. Visbal, and P. E. Morgan, “A high-order compact finite-difference scheme for large-eddy simulation of active flow control,” Prog. Aerosp. Sci. 44, 397–426 (2008). [CrossRef]
- Y. X. Zhao, S. H. Yi, L. F. Tian, and Z. Y. Cheng, “Supersonic flow imaging via nanoparticles,” Sci. China Ser. E 52, 3640–3648 (2009). [CrossRef]
- S. H. Yi, L. F. Tian, Y. X. Zhao, L. He, and Z. Y. Cheng, “Aero-optical aberration measuring method based on NPLS and its application,” Chin. Sci. Bull. 55, 3545–3549 (2010). [CrossRef]
- Y. X. Zhao, S. H. Yi, L. F. Tian, L. He, and Z. Y. Cheng, “Density field measurement and approximate reconstruction of supersonic mixing layer,” Chin. Sci. Bull. 55, 2004–2009 (2010). [CrossRef]
- L. F. Tian, S. H. Yi, 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]
- H. Lin, S. H. Yi, Y. X. Zhao, L. F. Tian, and Z. Chen, “Visualization of coherent structures in a supersonic flat-plate boundary layer,” Chin. Sci. Bull. 56, 489–494 (2011).
- H. Lin, S. H. Yi, Y. X. Zhao, L. F. Tian, and Z. Chen, “Experimental study of a supersonic turbulent boundary layer using PIV, ” Sci. China Ser. G 54, 1702–1709 (2011). [CrossRef]
- Q. Gao, Z. F. Jiang, S. H. Yi, and Y. X. Zhao, “Optical path difference of the supersonic mixing layer,” Appl. Opt. 49, 3786–3792 (2010). [CrossRef]
- Q. Gao, S. H. Yi, Z. F. Jiang, Y. X. Zhao, and W. K. Xie, “Analysing the structure of the optical path length of supersonic mixing layer with wavelet methods,” Chin. Phys. B 21, 064701(2012). [CrossRef]
- M. Smith, A. Smits, and R. Miles, “Compressible boundary-layer density cross section by UV Rayleigh scattering,” Opt. Lett. 14, 916–918 (1989). [CrossRef]
- M. Smith and A. Smits, “Visualization of the structure of supersonic turbulent boundary layers,” Exp. Fluids 18, 288–302 (1995). [CrossRef]
- V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, 1961).
- Q. Gao, Z. F. Jiang, S. H. Yi, L. He, and X. H. Wang, “Universal form of the power spectrum of the aero-optical aberration caused by the supersonic turbulent boundary layer,” Opt. Express (submitted).
- G. Berkooz, P. Holmes, and J. L. Lumley, “The proper orthogonal decomposition in the analysis of turbulent flows,” Annu. Rev. Fluid Mech. 25, 539–575 (1993). [CrossRef]
- P. Holmes, J. L. Lumley, and G. Berkooz, Turbulence, Coherent Structures, Dynamical Systems and Symmetry (Cambridge University, 1996).
- C. R. Truman, R. I. Zadoks, B. Staveley, and H. Barsum, “Prediction and measurement of aero-optic effects through the dynamics of a passive scalar in turbulent shear flow,” in AIAA 18th Aerospace Ground Testing Conference (American Institute of Aeronautics and Astronautics, 1994), paper 1994-2549.
- J. M. Cicchiello and E. J. Jumper, “Low-order representation of fluid-optic interactions associated with a shear layer,” in 39th AIAA Aerospace Sciences Meeting and Exhibit (American Institute of Aeronautics and Astronautics, 2001), paper 2001-0952.
- C. S. Williams and O. A. Becklund, Introduction to the Optical Transfer Function (Wiley, 1989).
- J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
- W. J. Steinmetz, “Second moments of optical degradation due to a thin boundary layer,” in Aero-Optical Phenomena, K. G. Gilber and L. J. Otten, eds. (American Institute of Aeronautics and Astronautics, 1982), pp. 78–100.
- J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts, 2007).

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