Abstract

A backward ray-tracing method is proposed for aero-optics simulation. Different from forward tracing, the backward tracing direction is from the internal sensor to the distant target. Along this direction, the tracing in turn goes through the internal gas region, the aero-optics flow field, and the freestream. The coordinate value, the density, and the refractive index are calculated at each tracing step. A stopping criterion is developed to ensure the tracing stops at the outer edge of the aero-optics flow field. As a demonstration, the analysis is carried out for a typical blunt nosed vehicle. The backward tracing method and stopping criterion greatly simplify the ray-tracing computations in the aero-optics flow field, and they can be extended to our active laser illumination aero-optics study because of the reciprocity principle.

© 2018 Optical Society of America

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References

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  1. X. L. Yin, “A new subdiscipline of contemporary optics–aero-optics,” China Engineering Science 7(12), 1–6 (2005).
  2. X. L. Yin, Principle of Aero-optics (China Aerospace Publishing House, 2003).
  3. L. Xu and Y. Cai, “Influence of altitude on aero-optic imaging deviation,” Appl. Opt. 50(18), 2949–2957 (2011).
    [PubMed]
  4. G. C. Li, Aero-optics (National Defense Industry Press, 2006).
  5. G. W. Sutton, J. E. Pond, and R. Snow, “Hypersonic interceptor performance evaluation center aero-optics performance predictions,” presented at the 2nd Annual AIAA SDIO Interceptor Technology Conference, Albuquerque, NM , America (NY)6–9(June), (1993).
  6. G. W. Sutton, J. E. Pond, and R. Snow, “Hypersonic interceptor aero-optics performance predictions,” J. Spacecr. Rockets 31(4), 592–599 (1994).
  7. R. L. Clark and R. C. Ferris, “A numerical method to predict aero-optical performance in hypersonic flight,” presented at the AIAA 19th Fluid Dynamics Plasma Dynamics and Lasers Conference, Honolulu, Hawaii, 8–10 June (1987)
  8. E. J. Jumper and R. J. Hugo, “Optical phase distortion due to turbulent-fluid density fields: Quantification using the small aperture beam technique,” presented at the AIAA 23rd Plasmadynamics & Lasers Conference, Nashville, TN , America (NY)6–8(July), (1992).
  9. S. Z. Wan, X. F. Chang, and J. Yan, “Research method of aero-optical transmission effect for IR air to air missiles,” Journal of Northwestern Polytechnical University 33(04), 621–626 (2015).
  10. G. Guo, H. Liu, and B. Zhang, “Aero-optical effects of an optical seeker with a supersonic jet for hypersonic vehicles in near space,” Appl. Opt. 55(17), 4741–4751 (2016).
    [PubMed]
  11. T. Wang, Y. Zhao, D. Xu, and Q. Yang, “Numerical study of evaluating the optical quality of supersonic flow fields,” Appl. Opt. 46(23), 5545–5551 (2007).
    [PubMed]
  12. W. Merzkirch, Flow Visualization, 2nd ed,(Academic, 1987).
  13. L. Xu and Y. L. Cai, “Imaging deviation through non-uniform flow fields around high-speed flying vehicles,” Optik – Int. J. Light Electron Opt 123, 1177–1182 (2012).
  14. T. Wang, Y. Zhao, D. Xu, and Q. Y. Yang, “CFD grids-based transmission model of the rays propagating through the hypersonic flow field,” Acta Armamentarii 29(03), 282–286 (2008).
  15. C. Yan, Study on Computational Fluid Dynamics And Its Application (Beihang University, 2006).
  16. B. Z. Zhang, J. A. Yin, and H. J. Zhang, Numerical Methods of Fluid Mechanics. (China Machine Press, 2003).
  17. W. X. Yang, C. Chao, M. Y. Ding, and C. P. Zhou, “Analysis of Pneumatic Optical Effect of Turbulent Flow Field in Supersonic / Hypersonic Vehicle,” Photosystems 36(01), 88–92 (2009).

2016 (1)

2015 (1)

S. Z. Wan, X. F. Chang, and J. Yan, “Research method of aero-optical transmission effect for IR air to air missiles,” Journal of Northwestern Polytechnical University 33(04), 621–626 (2015).

2012 (1)

L. Xu and Y. L. Cai, “Imaging deviation through non-uniform flow fields around high-speed flying vehicles,” Optik – Int. J. Light Electron Opt 123, 1177–1182 (2012).

2011 (1)

2009 (1)

W. X. Yang, C. Chao, M. Y. Ding, and C. P. Zhou, “Analysis of Pneumatic Optical Effect of Turbulent Flow Field in Supersonic / Hypersonic Vehicle,” Photosystems 36(01), 88–92 (2009).

2008 (1)

T. Wang, Y. Zhao, D. Xu, and Q. Y. Yang, “CFD grids-based transmission model of the rays propagating through the hypersonic flow field,” Acta Armamentarii 29(03), 282–286 (2008).

2007 (1)

2005 (1)

X. L. Yin, “A new subdiscipline of contemporary optics–aero-optics,” China Engineering Science 7(12), 1–6 (2005).

1994 (1)

G. W. Sutton, J. E. Pond, and R. Snow, “Hypersonic interceptor aero-optics performance predictions,” J. Spacecr. Rockets 31(4), 592–599 (1994).

Cai, Y.

Cai, Y. L.

L. Xu and Y. L. Cai, “Imaging deviation through non-uniform flow fields around high-speed flying vehicles,” Optik – Int. J. Light Electron Opt 123, 1177–1182 (2012).

Chang, X. F.

S. Z. Wan, X. F. Chang, and J. Yan, “Research method of aero-optical transmission effect for IR air to air missiles,” Journal of Northwestern Polytechnical University 33(04), 621–626 (2015).

Chao, C.

W. X. Yang, C. Chao, M. Y. Ding, and C. P. Zhou, “Analysis of Pneumatic Optical Effect of Turbulent Flow Field in Supersonic / Hypersonic Vehicle,” Photosystems 36(01), 88–92 (2009).

Ding, M. Y.

W. X. Yang, C. Chao, M. Y. Ding, and C. P. Zhou, “Analysis of Pneumatic Optical Effect of Turbulent Flow Field in Supersonic / Hypersonic Vehicle,” Photosystems 36(01), 88–92 (2009).

Guo, G.

Hugo, R. J.

E. J. Jumper and R. J. Hugo, “Optical phase distortion due to turbulent-fluid density fields: Quantification using the small aperture beam technique,” presented at the AIAA 23rd Plasmadynamics & Lasers Conference, Nashville, TN , America (NY)6–8(July), (1992).

Jumper, E. J.

E. J. Jumper and R. J. Hugo, “Optical phase distortion due to turbulent-fluid density fields: Quantification using the small aperture beam technique,” presented at the AIAA 23rd Plasmadynamics & Lasers Conference, Nashville, TN , America (NY)6–8(July), (1992).

Liu, H.

Pond, J. E.

G. W. Sutton, J. E. Pond, and R. Snow, “Hypersonic interceptor aero-optics performance predictions,” J. Spacecr. Rockets 31(4), 592–599 (1994).

G. W. Sutton, J. E. Pond, and R. Snow, “Hypersonic interceptor performance evaluation center aero-optics performance predictions,” presented at the 2nd Annual AIAA SDIO Interceptor Technology Conference, Albuquerque, NM , America (NY)6–9(June), (1993).

Snow, R.

G. W. Sutton, J. E. Pond, and R. Snow, “Hypersonic interceptor aero-optics performance predictions,” J. Spacecr. Rockets 31(4), 592–599 (1994).

G. W. Sutton, J. E. Pond, and R. Snow, “Hypersonic interceptor performance evaluation center aero-optics performance predictions,” presented at the 2nd Annual AIAA SDIO Interceptor Technology Conference, Albuquerque, NM , America (NY)6–9(June), (1993).

Sutton, G. W.

G. W. Sutton, J. E. Pond, and R. Snow, “Hypersonic interceptor aero-optics performance predictions,” J. Spacecr. Rockets 31(4), 592–599 (1994).

G. W. Sutton, J. E. Pond, and R. Snow, “Hypersonic interceptor performance evaluation center aero-optics performance predictions,” presented at the 2nd Annual AIAA SDIO Interceptor Technology Conference, Albuquerque, NM , America (NY)6–9(June), (1993).

Wan, S. Z.

S. Z. Wan, X. F. Chang, and J. Yan, “Research method of aero-optical transmission effect for IR air to air missiles,” Journal of Northwestern Polytechnical University 33(04), 621–626 (2015).

Wang, T.

T. Wang, Y. Zhao, D. Xu, and Q. Y. Yang, “CFD grids-based transmission model of the rays propagating through the hypersonic flow field,” Acta Armamentarii 29(03), 282–286 (2008).

T. Wang, Y. Zhao, D. Xu, and Q. Yang, “Numerical study of evaluating the optical quality of supersonic flow fields,” Appl. Opt. 46(23), 5545–5551 (2007).
[PubMed]

Xu, D.

T. Wang, Y. Zhao, D. Xu, and Q. Y. Yang, “CFD grids-based transmission model of the rays propagating through the hypersonic flow field,” Acta Armamentarii 29(03), 282–286 (2008).

T. Wang, Y. Zhao, D. Xu, and Q. Yang, “Numerical study of evaluating the optical quality of supersonic flow fields,” Appl. Opt. 46(23), 5545–5551 (2007).
[PubMed]

Xu, L.

L. Xu and Y. L. Cai, “Imaging deviation through non-uniform flow fields around high-speed flying vehicles,” Optik – Int. J. Light Electron Opt 123, 1177–1182 (2012).

L. Xu and Y. Cai, “Influence of altitude on aero-optic imaging deviation,” Appl. Opt. 50(18), 2949–2957 (2011).
[PubMed]

Yan, J.

S. Z. Wan, X. F. Chang, and J. Yan, “Research method of aero-optical transmission effect for IR air to air missiles,” Journal of Northwestern Polytechnical University 33(04), 621–626 (2015).

Yang, Q.

Yang, Q. Y.

T. Wang, Y. Zhao, D. Xu, and Q. Y. Yang, “CFD grids-based transmission model of the rays propagating through the hypersonic flow field,” Acta Armamentarii 29(03), 282–286 (2008).

Yang, W. X.

W. X. Yang, C. Chao, M. Y. Ding, and C. P. Zhou, “Analysis of Pneumatic Optical Effect of Turbulent Flow Field in Supersonic / Hypersonic Vehicle,” Photosystems 36(01), 88–92 (2009).

Yin, X. L.

X. L. Yin, “A new subdiscipline of contemporary optics–aero-optics,” China Engineering Science 7(12), 1–6 (2005).

Zhang, B.

Zhao, Y.

T. Wang, Y. Zhao, D. Xu, and Q. Y. Yang, “CFD grids-based transmission model of the rays propagating through the hypersonic flow field,” Acta Armamentarii 29(03), 282–286 (2008).

T. Wang, Y. Zhao, D. Xu, and Q. Yang, “Numerical study of evaluating the optical quality of supersonic flow fields,” Appl. Opt. 46(23), 5545–5551 (2007).
[PubMed]

Zhou, C. P.

W. X. Yang, C. Chao, M. Y. Ding, and C. P. Zhou, “Analysis of Pneumatic Optical Effect of Turbulent Flow Field in Supersonic / Hypersonic Vehicle,” Photosystems 36(01), 88–92 (2009).

Acta Armamentarii (1)

T. Wang, Y. Zhao, D. Xu, and Q. Y. Yang, “CFD grids-based transmission model of the rays propagating through the hypersonic flow field,” Acta Armamentarii 29(03), 282–286 (2008).

Appl. Opt. (3)

China Engineering Science (1)

X. L. Yin, “A new subdiscipline of contemporary optics–aero-optics,” China Engineering Science 7(12), 1–6 (2005).

J. Spacecr. Rockets (1)

G. W. Sutton, J. E. Pond, and R. Snow, “Hypersonic interceptor aero-optics performance predictions,” J. Spacecr. Rockets 31(4), 592–599 (1994).

Journal of Northwestern Polytechnical University (1)

S. Z. Wan, X. F. Chang, and J. Yan, “Research method of aero-optical transmission effect for IR air to air missiles,” Journal of Northwestern Polytechnical University 33(04), 621–626 (2015).

Optik – Int. J. Light Electron Opt (1)

L. Xu and Y. L. Cai, “Imaging deviation through non-uniform flow fields around high-speed flying vehicles,” Optik – Int. J. Light Electron Opt 123, 1177–1182 (2012).

Photosystems (1)

W. X. Yang, C. Chao, M. Y. Ding, and C. P. Zhou, “Analysis of Pneumatic Optical Effect of Turbulent Flow Field in Supersonic / Hypersonic Vehicle,” Photosystems 36(01), 88–92 (2009).

Other (8)

C. Yan, Study on Computational Fluid Dynamics And Its Application (Beihang University, 2006).

B. Z. Zhang, J. A. Yin, and H. J. Zhang, Numerical Methods of Fluid Mechanics. (China Machine Press, 2003).

R. L. Clark and R. C. Ferris, “A numerical method to predict aero-optical performance in hypersonic flight,” presented at the AIAA 19th Fluid Dynamics Plasma Dynamics and Lasers Conference, Honolulu, Hawaii, 8–10 June (1987)

E. J. Jumper and R. J. Hugo, “Optical phase distortion due to turbulent-fluid density fields: Quantification using the small aperture beam technique,” presented at the AIAA 23rd Plasmadynamics & Lasers Conference, Nashville, TN , America (NY)6–8(July), (1992).

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

X. L. Yin, Principle of Aero-optics (China Aerospace Publishing House, 2003).

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

G. W. Sutton, J. E. Pond, and R. Snow, “Hypersonic interceptor performance evaluation center aero-optics performance predictions,” presented at the 2nd Annual AIAA SDIO Interceptor Technology Conference, Albuquerque, NM , America (NY)6–9(June), (1993).

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Figures (9)

Fig. 1
Fig. 1 Illustration of air density distribution and geometry for backward ray-tracing.
Fig. 2
Fig. 2 Local CFD grid.
Fig. 3
Fig. 3 Mean flow density contours.
Fig. 4
Fig. 4 Refractive index bilinear interpolation.
Fig. 5
Fig. 5 Ray-tracing process from the (k-1)th step to the kth step.
Fig. 6
Fig. 6 Backward Ray-Tracing. Example of the special distribution of refractive index in front of the vehicle optics. Plots are for various angles LOS from the vehicle axis. (Alt = 25km, Ma = 3, AoA = 0°)
Fig. 7
Fig. 7 Backward Ray-Tracing. Example of the special distribution of refractive index in front of the vehicle optics. Plots are for various altitudes. (Ma = 3, AoA = 0°, LOS = 5°).
Fig. 8
Fig. 8 Forward Ray Tracing. Example of the special distribution of refractive index in front of the vehicle optics. Plots are for various angles LOS from the vehicle axis. (Alt = 25km, Ma = 3, AoA = 0°).
Fig. 9
Fig. 9 Comparison of forward tracing steps and backward tracing steps (Alt = 25km, Ma = 3, AoA = 0°, LOS = 5°).

Tables (1)

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Table 1 Coverage of combinations parameters for which ray deviations were computed.

Equations (12)

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n=1+ K GD ρ,
K GD =2.23× 10 4 (1+ 7.52× 10 3 λ 2 ),
u= u 1 φ 1 + u 2 φ 2 + u 3 φ 3 + u 4 φ 4
{ φ 1 = 1 4 ( 1ξ )( 1η ) φ 2 = 1 4 ( 1+ξ )( 1η ) φ 3 = 1 4 ( 1+ξ )( 1+η ), φ 4 = 1 4 ( 1ξ )( 1+η )
{ x= i=1 4 φ i ( ξ,η ) x i y= i=1 4 φ i ( ξ,η ) y i
y- y k-1 = f k-1 ' ( x k-1 )(x- x k-1 )
γ k1 ={ π+arctan f k1 ' ( x k-1 ),arctan f k1 ' ( x k1 )<0 arctant f k1 ' ( x k-1 ),arctan f k1 ' ( x k1 )0
y y k1 = 1 f k-1 ' ( x k-1 ) (x- x k-1 )
θ k1 =arccos (1, f k1 ' ( x k1 ))( a k1 , b k1 ) | 1, f k1 ' ( x k1 ) || a k1 , b k1 |
sin θ k1 sin β k1 = n k n k1
y y k1 =tan[ β k1 + γ k1 ( π 2 ) ](x x k1 )
| n p=q - n f |δ,q=0,1,,m ,

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