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

[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]

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]

S. Gordeyev and E. J. Jumper, “Fluid dynamics and aero-optics of turrets,” Prog. Aerosp. Sci. 46, 388–400 (2010).

[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]

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]

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]

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]

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]

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]

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]

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]

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]

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).

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

[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]

M. Smith and A. Smits, “Visualization of the structure of supersonic turbulent boundary layers,” Exp. Fluids 18, 288–302 (1995).

[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]

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]

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]

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]

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.

C. S. Williams and O. A. Becklund, Introduction to the Optical Transfer Function (Wiley, 1989).

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).

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]

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]

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]

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. 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]

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).

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]

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]

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, and Z. Y. Cheng, “Supersonic flow imaging via nanoparticles,” Sci. China Ser. E 52, 3640–3648 (2009).

[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.

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.

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).

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

[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).

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]

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, 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).

K. G. Gilbert and L. J. Otten, Aero-Optical Phenomena(American Institute of Aeronautics and Astronautics, 1982).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts, 2007).

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. 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]

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]

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).

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]

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]

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]

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]

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]

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, 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).

S. Gordeyev and E. J. Jumper, “Fluid dynamics and aero-optics of turrets,” Prog. Aerosp. Sci. 46, 388–400 (2010).

[CrossRef]

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

[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]

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]

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]

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]

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. 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]

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]

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).

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

[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]

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]

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]

K. G. Gilbert and L. J. Otten, Aero-Optical Phenomena(American Institute of Aeronautics and Astronautics, 1982).

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.

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]

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.

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.

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]

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, 1961).

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]

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]

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]

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]

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.

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]

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.

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

[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]

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).

C. S. Williams and O. A. Becklund, Introduction to the Optical Transfer Function (Wiley, 1989).

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]

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]

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]

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).

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]

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]

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]

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]

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]

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).

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.

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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

[CrossRef]

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]

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]

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]

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