Abstract

Aero-optic imaging deviation is a kind of aero-optic effect. It characterizes the image position displacement on an imaging plane. This paper studies the influence of altitude on aero-optic imaging deviation. The Reynolds-averaged Navier–Stokes solver provided in FLUENT was used for flow computations. The Runge–Kutta method based ray tracing was adopted for optics calculations. The orthogonal array was brought in for the experiment arrangement. Four representative suites of imaging deviations and imaging deviation slopes were obtained in the altitude range of 1060km. The results show that as altitude increases, the imaging deviation decreases, and the imaging deviation slope approaches zero from a negative value.

© 2011 Optical Society of America

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References

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  1. M. M. Malley, G. W. Sutton, and N. Kincheloe, “Beam-jitter measurements of turbulent aero-optic path differences,” Appl. Opt. 31, 4440–4443 (1992).
    [CrossRef] [PubMed]
  2. G. W. Sutton, J. E. Pond, R. Snow, and Y. F. Hwang, “Hypersonic interceptor aero-optics performance predictions,” J. Spacecr. Rockets 31, 592–599 (1994).
    [CrossRef]
  3. G. W. Sutton, “Effect of inhomogeneous turbulence on imaging through turbulent layers,” Appl. Opt. 33, 3972–3976 (1994).
    [CrossRef] [PubMed]
  4. G. C. Li, Aero-Optics (National Defense Industry Press, 2006).
  5. E. J. Jumper and R. J. Hugo, “Optical phase distortion due to turbulent-fluid density fields: quantification using the small-aperture beam technique,” in Proceedings of the 23rd Plasmadynamics & Lasers Conference, AIAA-92-3020 (American Institute of Aeronautics and Astronautics, Washington, D.C., 1992).
  6. 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] [PubMed]
  7. E. J. Jumper and E. J. Fitzgerald, “Recent advances in aero-optics,” Prog. Aerosp. Sci. 37, 299–339 (2001).
    [CrossRef]
  8. R. L. Clark, M. Banish, and J. Hammer, “Fundamentals of aero-optic phenomena,” in Proceedings of the 18th AIAA Aerospace Ground Testing Conference, AIAA-94-2545 (American Institute of Aeronautics and Astronautics, Washington, D.C., 1994).
  9. E. Frumker and O. Padé, “Generic method for aero-optic evaluations,” Appl. Opt. 43, 3224–3228 (2004).
    [CrossRef] [PubMed]
  10. T. Wang, Y. Zhao, D. Xu, and Q. Y. Yang, “Numerical study of evaluating the optical quality of supersonic flow fields,” Appl. Opt. 46, 5545–5551 (2007).
    [CrossRef] [PubMed]
  11. Y. Zhao, T. Wang, D. Xu, and Q. Y. Yang, “CFD grids-based transmission model of the rays propagating through the hypersonic flow field,” Acta Armamentarii 29, 282–286(2008).
  12. O. Padé, “Models of turbulence for aero-optics applications,” Proc. SPIE 4419, 494–498 (2001).
    [CrossRef]
  13. J. E. Pond and G. W. Sutton, “Aero-optic performance of an aircraft forward-facing optical turret,” J. Aircraft 43, 600–607 (2006).
    [CrossRef]
  14. V. A. Banakh, D. A. Marakasov, and A. A. Sukharev, “Reconstruction of the radial dependence of the structural characteristic of the refractive index in a supersonic gas flow from laser beam intensity fluctuations,” Opt. Spectrosc. 108, 117–122(2010).
    [CrossRef]
  15. D. W. Miller, “AIT interceptor performance predictions,” in Proceedings of the 2nd Annual AIAA/SDIO Interceptor Technology Conference, AIAA-93-2683 (American Institute of Aeronautics and Astronautics, Washington, D.C., 1993).
  16. R. L. Clark and R. C. Farris, “A numerical method to predict aero-optical performance in hypersonic flight,” in Proceedings of the 19th Fluid Dynamics, Plasma and Lasers Conference, AIAA-87-1396 (American Institute of Aeronautics and Astronautics, Washington, D.C., 1987).
  17. J. E. Pond, C. T. Welch, and G. W. Sutton, “Side mounted IR window aero-optic and aerothermal analysis,” Proc. SPIE 3705, 266–275 (1999).
    [CrossRef]
  18. J. J. Gierloff, S. J. Robertson, and D. H. Bouska, “Computer analysis of aero-optic effects,” in Proceedings of the AIAA/SDIO Annual Interceptor Technology Conference, AIAA-92-2794 (American Institute of Aeronautics and Astronautics, Washington, D.C., 1992).
  19. X. L. Yin, Principle of Aero-Optics (China Astronautics, 2003).
  20. H. S. Xiao and Z. G. Fan, “Imaging quality evaluation of aerodynamically heated optical dome using ray tracing,” Appl. Opt. 49, 5049–5058 (2010).
    [CrossRef] [PubMed]
  21. Y. P. Zhang and Z. G. Fan, “Study on the optical path difference of aero-optical window,” Optik 118, 557–560 (2007).
    [CrossRef]
  22. O. Padé, E. Frumker, and P. I. Rojt, “Optical distortions caused by propagation through turbulent shear layers,” Proc. SPIE 5237, 31–38 (2004).
    [CrossRef]
  23. O. Padé, “Optical propagation through turbulent jets,” Proc. SPIE 5572, 24–33 (2004).
    [CrossRef]
  24. FLUENT 6.1 User’s Guide (2001), http://www.ansys.com.
  25. W. Merzkirch, Flow Visualization, 2nd ed. (Academic, 1987).
  26. L. Xu and Y. L. Cai, “Infrared homing head aero-optic performance analysis,” Tech. Rep. (Xi’an Jiaotong University, 2008).
  27. L. Xu and Y. L. Cai, “Imaging deviation through non-uniform flow field around high-speed flying vehicle,” Tech. Rep. (Xi’an Jiaotong University, 2010).
  28. M. Born and E. Wolf, Principles of Optics, 6th ed.(Pergamon, 1980).
  29. Y. T. Qiao, Gradient Index Optics (Science Press, 1991).
  30. S. H. He, Z. Q. Wen, and T. Lou, Design of Experiments and Data Processing (National University of Defense Technology Press, 2002).

2010 (2)

V. A. Banakh, D. A. Marakasov, and A. A. Sukharev, “Reconstruction of the radial dependence of the structural characteristic of the refractive index in a supersonic gas flow from laser beam intensity fluctuations,” Opt. Spectrosc. 108, 117–122(2010).
[CrossRef]

H. S. Xiao and Z. G. Fan, “Imaging quality evaluation of aerodynamically heated optical dome using ray tracing,” Appl. Opt. 49, 5049–5058 (2010).
[CrossRef] [PubMed]

2008 (1)

Y. Zhao, T. Wang, D. Xu, and Q. Y. Yang, “CFD grids-based transmission model of the rays propagating through the hypersonic flow field,” Acta Armamentarii 29, 282–286(2008).

2007 (2)

2006 (1)

J. E. Pond and G. W. Sutton, “Aero-optic performance of an aircraft forward-facing optical turret,” J. Aircraft 43, 600–607 (2006).
[CrossRef]

2004 (3)

O. Padé, E. Frumker, and P. I. Rojt, “Optical distortions caused by propagation through turbulent shear layers,” Proc. SPIE 5237, 31–38 (2004).
[CrossRef]

O. Padé, “Optical propagation through turbulent jets,” Proc. SPIE 5572, 24–33 (2004).
[CrossRef]

E. Frumker and O. Padé, “Generic method for aero-optic evaluations,” Appl. Opt. 43, 3224–3228 (2004).
[CrossRef] [PubMed]

2001 (2)

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

O. Padé, “Models of turbulence for aero-optics applications,” Proc. SPIE 4419, 494–498 (2001).
[CrossRef]

1999 (1)

J. E. Pond, C. T. Welch, and G. W. Sutton, “Side mounted IR window aero-optic and aerothermal analysis,” Proc. SPIE 3705, 266–275 (1999).
[CrossRef]

1996 (1)

1994 (2)

G. W. Sutton, J. E. Pond, R. Snow, and Y. F. Hwang, “Hypersonic interceptor aero-optics performance predictions,” J. Spacecr. Rockets 31, 592–599 (1994).
[CrossRef]

G. W. Sutton, “Effect of inhomogeneous turbulence on imaging through turbulent layers,” Appl. Opt. 33, 3972–3976 (1994).
[CrossRef] [PubMed]

1992 (1)

Banakh, V. A.

V. A. Banakh, D. A. Marakasov, and A. A. Sukharev, “Reconstruction of the radial dependence of the structural characteristic of the refractive index in a supersonic gas flow from laser beam intensity fluctuations,” Opt. Spectrosc. 108, 117–122(2010).
[CrossRef]

Banish, M.

R. L. Clark, M. Banish, and J. Hammer, “Fundamentals of aero-optic phenomena,” in Proceedings of the 18th AIAA Aerospace Ground Testing Conference, AIAA-94-2545 (American Institute of Aeronautics and Astronautics, Washington, D.C., 1994).

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed.(Pergamon, 1980).

Bouska, D. H.

J. J. Gierloff, S. J. Robertson, and D. H. Bouska, “Computer analysis of aero-optic effects,” in Proceedings of the AIAA/SDIO Annual Interceptor Technology Conference, AIAA-92-2794 (American Institute of Aeronautics and Astronautics, Washington, D.C., 1992).

Cai, Y. L.

L. Xu and Y. L. Cai, “Imaging deviation through non-uniform flow field around high-speed flying vehicle,” Tech. Rep. (Xi’an Jiaotong University, 2010).

L. Xu and Y. L. Cai, “Infrared homing head aero-optic performance analysis,” Tech. Rep. (Xi’an Jiaotong University, 2008).

Clark, R. L.

R. L. Clark and R. C. Farris, “A numerical method to predict aero-optical performance in hypersonic flight,” in Proceedings of the 19th Fluid Dynamics, Plasma and Lasers Conference, AIAA-87-1396 (American Institute of Aeronautics and Astronautics, Washington, D.C., 1987).

R. L. Clark, M. Banish, and J. Hammer, “Fundamentals of aero-optic phenomena,” in Proceedings of the 18th AIAA Aerospace Ground Testing Conference, AIAA-94-2545 (American Institute of Aeronautics and Astronautics, Washington, D.C., 1994).

Fan, Z. G.

H. S. Xiao and Z. G. Fan, “Imaging quality evaluation of aerodynamically heated optical dome using ray tracing,” Appl. Opt. 49, 5049–5058 (2010).
[CrossRef] [PubMed]

Y. P. Zhang and Z. G. Fan, “Study on the optical path difference of aero-optical window,” Optik 118, 557–560 (2007).
[CrossRef]

Farris, R. C.

R. L. Clark and R. C. Farris, “A numerical method to predict aero-optical performance in hypersonic flight,” in Proceedings of the 19th Fluid Dynamics, Plasma and Lasers Conference, AIAA-87-1396 (American Institute of Aeronautics and Astronautics, Washington, D.C., 1987).

Fitzgerald, E. J.

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

Frumker, E.

E. Frumker and O. Padé, “Generic method for aero-optic evaluations,” Appl. Opt. 43, 3224–3228 (2004).
[CrossRef] [PubMed]

O. Padé, E. Frumker, and P. I. Rojt, “Optical distortions caused by propagation through turbulent shear layers,” Proc. SPIE 5237, 31–38 (2004).
[CrossRef]

Gierloff, J. J.

J. J. Gierloff, S. J. Robertson, and D. H. Bouska, “Computer analysis of aero-optic effects,” in Proceedings of the AIAA/SDIO Annual Interceptor Technology Conference, AIAA-92-2794 (American Institute of Aeronautics and Astronautics, Washington, D.C., 1992).

Hammer, J.

R. L. Clark, M. Banish, and J. Hammer, “Fundamentals of aero-optic phenomena,” in Proceedings of the 18th AIAA Aerospace Ground Testing Conference, AIAA-94-2545 (American Institute of Aeronautics and Astronautics, Washington, D.C., 1994).

He, S. H.

S. H. He, Z. Q. Wen, and T. Lou, Design of Experiments and Data Processing (National University of Defense Technology Press, 2002).

Hugo, R. J.

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] [PubMed]

E. J. Jumper and R. J. Hugo, “Optical phase distortion due to turbulent-fluid density fields: quantification using the small-aperture beam technique,” in Proceedings of the 23rd Plasmadynamics & Lasers Conference, AIAA-92-3020 (American Institute of Aeronautics and Astronautics, Washington, D.C., 1992).

Hwang, Y. F.

G. W. Sutton, J. E. Pond, R. Snow, and Y. F. Hwang, “Hypersonic interceptor aero-optics performance predictions,” J. Spacecr. Rockets 31, 592–599 (1994).
[CrossRef]

Jumper, E. J.

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

E. J. Jumper and R. J. Hugo, “Optical phase distortion due to turbulent-fluid density fields: quantification using the small-aperture beam technique,” in Proceedings of the 23rd Plasmadynamics & Lasers Conference, AIAA-92-3020 (American Institute of Aeronautics and Astronautics, Washington, D.C., 1992).

Kincheloe, N.

Li, G. C.

G. C. Li, Aero-Optics (National Defense Industry Press, 2006).

Lou, T.

S. H. He, Z. Q. Wen, and T. Lou, Design of Experiments and Data Processing (National University of Defense Technology Press, 2002).

Malley, M. M.

Marakasov, D. A.

V. A. Banakh, D. A. Marakasov, and A. A. Sukharev, “Reconstruction of the radial dependence of the structural characteristic of the refractive index in a supersonic gas flow from laser beam intensity fluctuations,” Opt. Spectrosc. 108, 117–122(2010).
[CrossRef]

Merzkirch, W.

W. Merzkirch, Flow Visualization, 2nd ed. (Academic, 1987).

Miller, D. W.

D. W. Miller, “AIT interceptor performance predictions,” in Proceedings of the 2nd Annual AIAA/SDIO Interceptor Technology Conference, AIAA-93-2683 (American Institute of Aeronautics and Astronautics, Washington, D.C., 1993).

Padé, O.

O. Padé, “Optical propagation through turbulent jets,” Proc. SPIE 5572, 24–33 (2004).
[CrossRef]

O. Padé, E. Frumker, and P. I. Rojt, “Optical distortions caused by propagation through turbulent shear layers,” Proc. SPIE 5237, 31–38 (2004).
[CrossRef]

E. Frumker and O. Padé, “Generic method for aero-optic evaluations,” Appl. Opt. 43, 3224–3228 (2004).
[CrossRef] [PubMed]

O. Padé, “Models of turbulence for aero-optics applications,” Proc. SPIE 4419, 494–498 (2001).
[CrossRef]

Pond, J. E.

J. E. Pond and G. W. Sutton, “Aero-optic performance of an aircraft forward-facing optical turret,” J. Aircraft 43, 600–607 (2006).
[CrossRef]

J. E. Pond, C. T. Welch, and G. W. Sutton, “Side mounted IR window aero-optic and aerothermal analysis,” Proc. SPIE 3705, 266–275 (1999).
[CrossRef]

G. W. Sutton, J. E. Pond, R. Snow, and Y. F. Hwang, “Hypersonic interceptor aero-optics performance predictions,” J. Spacecr. Rockets 31, 592–599 (1994).
[CrossRef]

Qiao, Y. T.

Y. T. Qiao, Gradient Index Optics (Science Press, 1991).

Robertson, S. J.

J. J. Gierloff, S. J. Robertson, and D. H. Bouska, “Computer analysis of aero-optic effects,” in Proceedings of the AIAA/SDIO Annual Interceptor Technology Conference, AIAA-92-2794 (American Institute of Aeronautics and Astronautics, Washington, D.C., 1992).

Rojt, P. I.

O. Padé, E. Frumker, and P. I. Rojt, “Optical distortions caused by propagation through turbulent shear layers,” Proc. SPIE 5237, 31–38 (2004).
[CrossRef]

Snow, R.

G. W. Sutton, J. E. Pond, R. Snow, and Y. F. Hwang, “Hypersonic interceptor aero-optics performance predictions,” J. Spacecr. Rockets 31, 592–599 (1994).
[CrossRef]

Sukharev, A. A.

V. A. Banakh, D. A. Marakasov, and A. A. Sukharev, “Reconstruction of the radial dependence of the structural characteristic of the refractive index in a supersonic gas flow from laser beam intensity fluctuations,” Opt. Spectrosc. 108, 117–122(2010).
[CrossRef]

Sutton, G. W.

J. E. Pond and G. W. Sutton, “Aero-optic performance of an aircraft forward-facing optical turret,” J. Aircraft 43, 600–607 (2006).
[CrossRef]

J. E. Pond, C. T. Welch, and G. W. Sutton, “Side mounted IR window aero-optic and aerothermal analysis,” Proc. SPIE 3705, 266–275 (1999).
[CrossRef]

G. W. Sutton, “Effect of inhomogeneous turbulence on imaging through turbulent layers,” Appl. Opt. 33, 3972–3976 (1994).
[CrossRef] [PubMed]

G. W. Sutton, J. E. Pond, R. Snow, and Y. F. Hwang, “Hypersonic interceptor aero-optics performance predictions,” J. Spacecr. Rockets 31, 592–599 (1994).
[CrossRef]

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

Wang, T.

Y. Zhao, T. Wang, D. Xu, and Q. Y. Yang, “CFD grids-based transmission model of the rays propagating through the hypersonic flow field,” Acta Armamentarii 29, 282–286(2008).

T. Wang, Y. Zhao, D. Xu, and Q. Y. Yang, “Numerical study of evaluating the optical quality of supersonic flow fields,” Appl. Opt. 46, 5545–5551 (2007).
[CrossRef] [PubMed]

Welch, C. T.

J. E. Pond, C. T. Welch, and G. W. Sutton, “Side mounted IR window aero-optic and aerothermal analysis,” Proc. SPIE 3705, 266–275 (1999).
[CrossRef]

Wen, Z. Q.

S. H. He, Z. Q. Wen, and T. Lou, Design of Experiments and Data Processing (National University of Defense Technology Press, 2002).

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 6th ed.(Pergamon, 1980).

Xiao, H. S.

Xu, D.

Y. Zhao, T. Wang, D. Xu, and Q. Y. Yang, “CFD grids-based transmission model of the rays propagating through the hypersonic flow field,” Acta Armamentarii 29, 282–286(2008).

T. Wang, Y. Zhao, D. Xu, and Q. Y. Yang, “Numerical study of evaluating the optical quality of supersonic flow fields,” Appl. Opt. 46, 5545–5551 (2007).
[CrossRef] [PubMed]

Xu, L.

L. Xu and Y. L. Cai, “Infrared homing head aero-optic performance analysis,” Tech. Rep. (Xi’an Jiaotong University, 2008).

L. Xu and Y. L. Cai, “Imaging deviation through non-uniform flow field around high-speed flying vehicle,” Tech. Rep. (Xi’an Jiaotong University, 2010).

Yang, Q. Y.

Y. Zhao, T. Wang, D. Xu, and Q. Y. Yang, “CFD grids-based transmission model of the rays propagating through the hypersonic flow field,” Acta Armamentarii 29, 282–286(2008).

T. Wang, Y. Zhao, D. Xu, and Q. Y. Yang, “Numerical study of evaluating the optical quality of supersonic flow fields,” Appl. Opt. 46, 5545–5551 (2007).
[CrossRef] [PubMed]

Yin, X. L.

X. L. Yin, Principle of Aero-Optics (China Astronautics, 2003).

Zhang, Y. P.

Y. P. Zhang and Z. G. Fan, “Study on the optical path difference of aero-optical window,” Optik 118, 557–560 (2007).
[CrossRef]

Zhao, Y.

Y. Zhao, T. Wang, D. Xu, and Q. Y. Yang, “CFD grids-based transmission model of the rays propagating through the hypersonic flow field,” Acta Armamentarii 29, 282–286(2008).

T. Wang, Y. Zhao, D. Xu, and Q. Y. Yang, “Numerical study of evaluating the optical quality of supersonic flow fields,” Appl. Opt. 46, 5545–5551 (2007).
[CrossRef] [PubMed]

Acta Armamentarii (1)

Y. Zhao, T. Wang, D. Xu, and Q. Y. Yang, “CFD grids-based transmission model of the rays propagating through the hypersonic flow field,” Acta Armamentarii 29, 282–286(2008).

Appl. Opt. (6)

J. Aircraft (1)

J. E. Pond and G. W. Sutton, “Aero-optic performance of an aircraft forward-facing optical turret,” J. Aircraft 43, 600–607 (2006).
[CrossRef]

J. Spacecr. Rockets (1)

G. W. Sutton, J. E. Pond, R. Snow, and Y. F. Hwang, “Hypersonic interceptor aero-optics performance predictions,” J. Spacecr. Rockets 31, 592–599 (1994).
[CrossRef]

Opt. Spectrosc. (1)

V. A. Banakh, D. A. Marakasov, and A. A. Sukharev, “Reconstruction of the radial dependence of the structural characteristic of the refractive index in a supersonic gas flow from laser beam intensity fluctuations,” Opt. Spectrosc. 108, 117–122(2010).
[CrossRef]

Optik (1)

Y. P. Zhang and Z. G. Fan, “Study on the optical path difference of aero-optical window,” Optik 118, 557–560 (2007).
[CrossRef]

Proc. SPIE (4)

O. Padé, E. Frumker, and P. I. Rojt, “Optical distortions caused by propagation through turbulent shear layers,” Proc. SPIE 5237, 31–38 (2004).
[CrossRef]

O. Padé, “Optical propagation through turbulent jets,” Proc. SPIE 5572, 24–33 (2004).
[CrossRef]

O. Padé, “Models of turbulence for aero-optics applications,” Proc. SPIE 4419, 494–498 (2001).
[CrossRef]

J. E. Pond, C. T. Welch, and G. W. Sutton, “Side mounted IR window aero-optic and aerothermal analysis,” Proc. SPIE 3705, 266–275 (1999).
[CrossRef]

Prog. Aerosp. Sci. (1)

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

Other (14)

R. L. Clark, M. Banish, and J. Hammer, “Fundamentals of aero-optic phenomena,” in Proceedings of the 18th AIAA Aerospace Ground Testing Conference, AIAA-94-2545 (American Institute of Aeronautics and Astronautics, Washington, D.C., 1994).

G. C. Li, Aero-Optics (National Defense Industry Press, 2006).

E. J. Jumper and R. J. Hugo, “Optical phase distortion due to turbulent-fluid density fields: quantification using the small-aperture beam technique,” in Proceedings of the 23rd Plasmadynamics & Lasers Conference, AIAA-92-3020 (American Institute of Aeronautics and Astronautics, Washington, D.C., 1992).

J. J. Gierloff, S. J. Robertson, and D. H. Bouska, “Computer analysis of aero-optic effects,” in Proceedings of the AIAA/SDIO Annual Interceptor Technology Conference, AIAA-92-2794 (American Institute of Aeronautics and Astronautics, Washington, D.C., 1992).

X. L. Yin, Principle of Aero-Optics (China Astronautics, 2003).

D. W. Miller, “AIT interceptor performance predictions,” in Proceedings of the 2nd Annual AIAA/SDIO Interceptor Technology Conference, AIAA-93-2683 (American Institute of Aeronautics and Astronautics, Washington, D.C., 1993).

R. L. Clark and R. C. Farris, “A numerical method to predict aero-optical performance in hypersonic flight,” in Proceedings of the 19th Fluid Dynamics, Plasma and Lasers Conference, AIAA-87-1396 (American Institute of Aeronautics and Astronautics, Washington, D.C., 1987).

FLUENT 6.1 User’s Guide (2001), http://www.ansys.com.

W. Merzkirch, Flow Visualization, 2nd ed. (Academic, 1987).

L. Xu and Y. L. Cai, “Infrared homing head aero-optic performance analysis,” Tech. Rep. (Xi’an Jiaotong University, 2008).

L. Xu and Y. L. Cai, “Imaging deviation through non-uniform flow field around high-speed flying vehicle,” Tech. Rep. (Xi’an Jiaotong University, 2010).

M. Born and E. Wolf, Principles of Optics, 6th ed.(Pergamon, 1980).

Y. T. Qiao, Gradient Index Optics (Science Press, 1991).

S. H. He, Z. Q. Wen, and T. Lou, Design of Experiments and Data Processing (National University of Defense Technology Press, 2002).

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Figures (12)

Fig. 1
Fig. 1

Aero-optic imaging deviation induced by the nonuniform flow field around high-speed flying vehicle.

Fig. 2
Fig. 2

Conical-head flying vehicle.

Fig. 3
Fig. 3

C-type computational grid.

Fig. 4
Fig. 4

Mean density contours of Run 1 (Mach number 3, 0 ° angle of attack). (a)–(f)  10 60 km altitude cases.

Fig. 5
Fig. 5

Mean density contours of Run 2 (Mach number 6, 5 ° angle of attack). (a)–(f)  10 60 km altitude cases.

Fig. 6
Fig. 6

Mean density contours of Run 3 (Mach number 3, 5 ° angle of attack). (a)–(f)  10 60 km altitude cases.

Fig. 7
Fig. 7

Mean density contours of Run 4 (Mach number 6, 0 ° angle of attack). (a)–(f)  10 60 km altitude cases.

Fig. 8
Fig. 8

Imaging deviation and imaging deviation slope of Run 1 versus altitude.

Fig. 9
Fig. 9

Imaging deviation and imaging deviation slope of Run 2 versus altitude.

Fig. 10
Fig. 10

Imaging deviation and imaging deviation slope of Run 3 versus altitude.

Fig. 11
Fig. 11

Imaging deviation and imaging deviation slope of Run 4 versus altitude.

Fig. 12
Fig. 12

Density distributions along propagation paths through nonuniform flow fields for 10 60 km altitude cases of Run 1.

Tables (2)

Tables Icon

Table 1 Orthogonal Array L 4 ( 2 3 )

Tables Icon

Table 2 Flight Conditions

Equations (17)

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

ρ t + x i ( ρ u i ) = 0 ,
t ( ρ u i ) + x j ( ρ u i u j ) = p x i + x j [ μ ( u i x j + u j x i 2 3 δ i j u l x l ) ] + x j ( ρ u i u j ¯ ) ,
n = 1 + K GD ρ ,
K GD ( λ ) = 2.23 × 10 4 ( 1 + 7.52 × 10 3 λ 2 ) .
d d s [ n ( r ) d r d s ] = n ( r ) ,
T = n d r d s = d r d t ,
t = d s n , d t = d s n .
d 2 r d t 2 = n n = 1 2 n 2 .
R = ( x y ) , T = ( T x T y ) = n ( d x / d s d y / d s ) , and D = n ( n / x n / y ) = 1 2 ( n 2 / x n 2 / y ) ,
d 2 R d t 2 = D ( R ) .
{ R n + 1 = R n + Δ t [ T n + 1 6 ( A + 2 B ) ] T n + 1 = T n + 1 6 ( A + 4 B + C ) ,
{ A = Δ t D ( R n ) B = Δ t D ( R n + Δ t 2 T n + 1 8 Δ t A ) C = Δ t D ( R n + Δ t T n + 1 2 Δ t B ) .
OPL = C n d s .
OPD = C ( n 1 ) d s .
d = d i + 1 d i 1 2 Δ x .
d = d i + 1 d i Δ x .
d = d i d i 1 Δ x .

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