Abstract

The interfacial fluid thickness (IFT) concept was used to develop a harmonic-mean refractive index gradient magnitude threshold to retrieve the high refractive index gradient regions of an aerodynamically heated window. The retrieved high-gradient regions were used to reconstruct the refractive index field of the window. The numerical three-dimensional optical distortion evaluation was conducted for both the reconstructed and the original refractive index fields of the window using the ray-tracing program based on a recursive algorithm. Wave aberration results show that the methodology based on the IFT concept reduces the refractive index information required to capture the essential optical distortion of the window. The method can also be used for numerically evaluating the optical distortion of the window.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. 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]
  2. H. J. Catrakis, R. C. Aguirre, J. C. Nathman, and P. J. Garcia, “Large-scale refractive turbulent interfaces and aero-optical interactions in high Reynolds number compressible separated shear layers,” J. Turbul. 7, 1–21 (2006).
    [CrossRef]
  3. R. C. Aguirre, “Turbulent fluid interfaces with applications to mixing and aero-optics,” Ph.D. dissertation (Henry Samueli School of Engineering, University of California, Irvine, 2005).
  4. L. Wu, J. C. Fang, and Z. H. Yang, “Study on aero-optical distortion simulation of high refraction index gradient regions in hypersonic turbulent flow,” Acta Opt. Sin. 29, 2952–2957(2009).
    [CrossRef]
  5. D. Yang, M. E. Thomas, and S. G. Kaplan, “Measurement of the infrared refractive index of sapphire as a function of temperature,” Proc. SPIE 4375, 53–63 (2001).
    [CrossRef]
  6. J. F. Nye, Physical Properties of Crystals (Oxford Univ. Press, 1985).
  7. 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]
  8. Y. P. Zhang and Z. G. Fan, “Study on the optical path difference of aero-optical window,” Optik 118, 557–560(2007).
    [CrossRef]
  9. D. H. Feng, S. Pan, Z. Y. Tian, and H. Li, “Research on ray tracing method in 3D discrete space with discretionary refraction index,” Acta Opt. Sin. 30, 696–701 (2010).
    [CrossRef]
  10. 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]
  11. D. C. Harris, Materials for Infrared Windows and Domes (SPIE, 1999).
    [CrossRef]
  12. W. H. Yu and W. Y. Liu, Crystal Physics (University of Science and Technology of China Press, 1998).
  13. E. Frumker and O. Pade, “Generic method for aero-optic evaluations,” Appl. Opt. 43, 3224–3228 (2004).
    [CrossRef] [PubMed]
  14. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

2010

D. H. Feng, S. Pan, Z. Y. Tian, and H. Li, “Research on ray tracing method in 3D discrete space with discretionary refraction index,” Acta Opt. Sin. 30, 696–701 (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]

2009

L. Wu, J. C. Fang, and Z. H. Yang, “Study on aero-optical distortion simulation of high refraction index gradient regions in hypersonic turbulent flow,” Acta Opt. Sin. 29, 2952–2957(2009).
[CrossRef]

2007

2006

H. J. Catrakis, R. C. Aguirre, J. C. Nathman, and P. J. Garcia, “Large-scale refractive turbulent interfaces and aero-optical interactions in high Reynolds number compressible separated shear layers,” J. Turbul. 7, 1–21 (2006).
[CrossRef]

2004

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]

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

2001

D. Yang, M. E. Thomas, and S. G. Kaplan, “Measurement of the infrared refractive index of sapphire as a function of temperature,” Proc. SPIE 4375, 53–63 (2001).
[CrossRef]

Aguirre, R. C.

H. J. Catrakis, R. C. Aguirre, J. C. Nathman, and P. J. Garcia, “Large-scale refractive turbulent interfaces and aero-optical interactions in high Reynolds number compressible separated shear layers,” J. Turbul. 7, 1–21 (2006).
[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]

R. C. Aguirre, “Turbulent fluid interfaces with applications to mixing and aero-optics,” Ph.D. dissertation (Henry Samueli School of Engineering, University of California, Irvine, 2005).

Catrakis, H. J.

H. J. Catrakis, R. C. Aguirre, J. C. Nathman, and P. J. Garcia, “Large-scale refractive turbulent interfaces and aero-optical interactions in high Reynolds number compressible separated shear layers,” J. Turbul. 7, 1–21 (2006).
[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]

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]

Fang, J. C.

L. Wu, J. C. Fang, and Z. H. Yang, “Study on aero-optical distortion simulation of high refraction index gradient regions in hypersonic turbulent flow,” Acta Opt. Sin. 29, 2952–2957(2009).
[CrossRef]

Feng, D. H.

D. H. Feng, S. Pan, Z. Y. Tian, and H. Li, “Research on ray tracing method in 3D discrete space with discretionary refraction index,” Acta Opt. Sin. 30, 696–701 (2010).
[CrossRef]

Frumker, E.

Garcia, P. J.

H. J. Catrakis, R. C. Aguirre, J. C. Nathman, and P. J. Garcia, “Large-scale refractive turbulent interfaces and aero-optical interactions in high Reynolds number compressible separated shear layers,” J. Turbul. 7, 1–21 (2006).
[CrossRef]

Goodman, J. W.

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

Harris, D. C.

D. C. Harris, Materials for Infrared Windows and Domes (SPIE, 1999).
[CrossRef]

Kaplan, S. G.

D. Yang, M. E. Thomas, and S. G. Kaplan, “Measurement of the infrared refractive index of sapphire as a function of temperature,” Proc. SPIE 4375, 53–63 (2001).
[CrossRef]

Li, H.

D. H. Feng, S. Pan, Z. Y. Tian, and H. Li, “Research on ray tracing method in 3D discrete space with discretionary refraction index,” Acta Opt. Sin. 30, 696–701 (2010).
[CrossRef]

Liu, W. Y.

W. H. Yu and W. Y. Liu, Crystal Physics (University of Science and Technology of China Press, 1998).

Nathman, J. C.

H. J. Catrakis, R. C. Aguirre, J. C. Nathman, and P. J. Garcia, “Large-scale refractive turbulent interfaces and aero-optical interactions in high Reynolds number compressible separated shear layers,” J. Turbul. 7, 1–21 (2006).
[CrossRef]

Nye, J. F.

J. F. Nye, Physical Properties of Crystals (Oxford Univ. Press, 1985).

Pade, O.

Pan, S.

D. H. Feng, S. Pan, Z. Y. Tian, and H. Li, “Research on ray tracing method in 3D discrete space with discretionary refraction index,” Acta Opt. Sin. 30, 696–701 (2010).
[CrossRef]

Thomas, M. E.

D. Yang, M. E. Thomas, and S. G. Kaplan, “Measurement of the infrared refractive index of sapphire as a function of temperature,” Proc. SPIE 4375, 53–63 (2001).
[CrossRef]

Tian, Z. Y.

D. H. Feng, S. Pan, Z. Y. Tian, and H. Li, “Research on ray tracing method in 3D discrete space with discretionary refraction index,” Acta Opt. Sin. 30, 696–701 (2010).
[CrossRef]

Wang, T.

Wu, L.

L. Wu, J. C. Fang, and Z. H. Yang, “Study on aero-optical distortion simulation of high refraction index gradient regions in hypersonic turbulent flow,” Acta Opt. Sin. 29, 2952–2957(2009).
[CrossRef]

Xiao, H. S.

Xu, D.

Yang, D.

D. Yang, M. E. Thomas, and S. G. Kaplan, “Measurement of the infrared refractive index of sapphire as a function of temperature,” Proc. SPIE 4375, 53–63 (2001).
[CrossRef]

Yang, Q. Y.

Yang, Z. H.

L. Wu, J. C. Fang, and Z. H. Yang, “Study on aero-optical distortion simulation of high refraction index gradient regions in hypersonic turbulent flow,” Acta Opt. Sin. 29, 2952–2957(2009).
[CrossRef]

Yu, W. H.

W. H. Yu and W. Y. Liu, Crystal Physics (University of Science and Technology of China Press, 1998).

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.

Acta Opt. Sin.

L. Wu, J. C. Fang, and Z. H. Yang, “Study on aero-optical distortion simulation of high refraction index gradient regions in hypersonic turbulent flow,” Acta Opt. Sin. 29, 2952–2957(2009).
[CrossRef]

D. H. Feng, S. Pan, Z. Y. Tian, and H. Li, “Research on ray tracing method in 3D discrete space with discretionary refraction index,” Acta Opt. Sin. 30, 696–701 (2010).
[CrossRef]

AIAA J.

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]

Appl. Opt.

J. Turbul.

H. J. Catrakis, R. C. Aguirre, J. C. Nathman, and P. J. Garcia, “Large-scale refractive turbulent interfaces and aero-optical interactions in high Reynolds number compressible separated shear layers,” J. Turbul. 7, 1–21 (2006).
[CrossRef]

Optik

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

D. Yang, M. E. Thomas, and S. G. Kaplan, “Measurement of the infrared refractive index of sapphire as a function of temperature,” Proc. SPIE 4375, 53–63 (2001).
[CrossRef]

Other

J. F. Nye, Physical Properties of Crystals (Oxford Univ. Press, 1985).

R. C. Aguirre, “Turbulent fluid interfaces with applications to mixing and aero-optics,” Ph.D. dissertation (Henry Samueli School of Engineering, University of California, Irvine, 2005).

D. C. Harris, Materials for Infrared Windows and Domes (SPIE, 1999).
[CrossRef]

W. H. Yu and W. Y. Liu, Crystal Physics (University of Science and Technology of China Press, 1998).

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Refractive index grid model of the window.

Fig. 2
Fig. 2

Discrete optical path in a refractive index grid of the window. P is the point of propagation in the optical path P P 1 . The cubic is the closest refractive index grid encircling P. G 1 , G 2 , G 3 , G 4 , G 5 , G 6 , G 7 , and G 8 are the nodes of the refractive index grid. The z axis is parallel to the z direction of the window.

Fig. 3
Fig. 3

Definitions of the azimuth and elevation incident angles. The curved arrows indicate positive angles.

Fig. 4
Fig. 4

Ray tracing on the deformed surface of the window. A , B , C , and D are the nodes of the deformed surface grid encircling intersection point E of the incident ray and the deformed surface. A, B, C, and D are also the counterparts of the nondeformed surface grid encircling intersection point E.

Fig. 5
Fig. 5

Simplified heat flux distribution on the outside surface of the window obtained from the wind tunnel experiment.

Fig. 6
Fig. 6

Color-scale maps of the (a) temperature, (b) sum deformation, and (c) equivalent von Mises strain fields of the window at 15 s .

Fig. 7
Fig. 7

Color-scale maps of the slices of the refractive index gradient magnitude field of the window at 15 s at the planes of (a)  x = 40 mm and (b)  y = 40 mm .

Fig. 8
Fig. 8

Color-scale maps of the (a) reconstructed and (b) original refractive index fields of the window at 15 s .

Fig. 9
Fig. 9

Wave aberration results of the window obtained from (a) the original refractive index field and (b) the reconstructed refractive index field for the 0 ° / 75 ° (azimuth/elevation) incident angle.

Tables (2)

Tables Icon

Table 1 Main Physical Properties of the Standard Zinc Sulfide Crystal Near 300 K

Tables Icon

Table 2 Refractive Index Variations of the Point with Maximum Temperature Variation and the Point with Maximum Equivalent Von Mises Strain Variation at 15 s a

Equations (20)

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

n ( λ , T ) = n ( λ , T 0 ) + Δ n T = n ( λ , T 0 ) + n ( λ , T ) T Δ T ,
B 11 x 1 2 + B 22 x 2 2 + B 33 x 3 2 = 1 ,
B 11 = B 22 = B 33 = n 0 2 .
Δ B = [ B 11 B 11 B 22 B 22 B 33 B 33 B 23 B 23 B 31 B 31 B 12 B 12 ] = [ P 11 P 12 P 12 0 0 0 P 12 P 11 P 12 0 0 0 P 12 P 12 P 11 0 0 0 0 0 0 P 44 0 0 0 0 0 0 P 44 0 0 0 0 0 0 P 44 ] [ ε 11 ε 22 ε 33 γ 23 γ 31 γ 12 ] ,
Δ n 11 = n 11 n 11 = ( B 11 ) 1 / 2 B 11 1 / 2 0.5 n 0 3 ( P 11 ε 11 + P 12 ε 22 + P 12 ε 33 ) , Δ n 22 = n 22 n 22 = ( B 22 ) 1 / 2 B 22 1 / 2 0.5 n 0 3 ( P 12 ε 11 + P 11 ε 22 + P 12 ε 33 ) , Δ n 33 = n 33 n 33 = ( B 33 ) 1 / 2 B 33 1 / 2 0.5 n 0 3 ( P 12 ε 11 + P 12 ε 22 + P 11 ε 33 ) , Δ n 23 = n 23 n 23 = ( B 23 ) 1 / 2 B 23 1 / 2 0.5 n 0 3 P 44 γ 23 , Δ n 31 = n 31 n 31 = ( B 31 ) 1 / 2 B 31 1 / 2 0.5 n 0 3 P 44 γ 31 , Δ n 12 = n 12 n 12 = ( B 12 ) 1 / 2 B 12 1 / 2 0.5 n 0 3 P 44 γ 12 ,
h i ( x , y , z ) = 1 / | n i ( x , y , z ) | ,
h T = i = 1 N h i / N ,
G T = 1 / h T = N / ( i = 1 N h i ) = N / [ i = 1 N ( 1 / | n i ( x , y , z ) | ) ] .
n P = [ i = 1 8 ( n i j = 1 j i 8 d j ) ] / [ i = 1 8 ( j = 1 j i 8 d j ) ] , d j = [ ( x P x j ) 2 + ( y P y j ) 2 + ( z P z j ) 2 ] 1 / 2 ,
OPL i = T 0 T 0 + Δ T ( n i l i T + l i n i T ) d T + ε 0 ε 0 + Δ ε ( n i l i ε + l i n i ε ) d ε ,
OPL = i OPL i .
W k ( x , y ) = 2 π λ ( OPL k OPL 0 ) ,
OPL 0 = 1 N r k OPL k
W ( x , y ) = k W k ( x , y ) = k 2 π λ ( OPL k OPL 0 ) .
r = Cov ( R 1 , R ) [ D ( R 1 ) D ( R ) ] 1 / 2 = i = 1 81 j = 1 81 k = 1 9 ( R 1 i j k R 1 a ) ( R i j k R a ) { [ i = 1 81 j = 1 81 k = 1 9 ( R 1 i j k R 1 a ) 2 ] [ i = 1 81 j = 1 81 k = 1 9 ( R i j k R a ) 2 ] } 1 / 2 ,
n ( x , y ) = c + α x ,
ϕ ( x , y ) = 2 π λ n ( x , y ) d = 2 π λ c d + 2 π λ α x d ,
A ( x , y ) = circ [ 2 ( x 2 + y 2 ) 1 / 2 / D ] exp [ j ϕ ( x , y ) ] ,
PSF ( x , y ) = | A ( x , y ) exp [ j 2 π λ f ( x x + y y ) ] d x d y | 2 = | λ f D 2 [ ( x d α f ) 2 + y 2 ] 1 / 2 J 1 { π D λ f [ ( x d α f ) 2 + y 2 ] 1 / 2 } | 2 ,
x Peak = d α f .

Metrics