Abstract

The effect of aerodynamic flow on the performance of an airborne optical system is becoming a critical issue in the development of electro-optic systems. A novel technique for aero-optic calculations that is based on commercially available software is presented. The optically relevant data from the computational fluid dynamics results are transformed into an index-of-refraction field and introduced as an input to the optical code. The data do not necessarily have to be presented in analytical form; instead it is introduced in a most general form as a discrete set of values located at a nonuniform grid of points. The modified quadratic Shepard method has been adopted for data interpolation, enabling a simple interface with virtually any software output. Several numerical simulations that demonstrate the technique are presented.

© 2004 Optical Society of America

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References

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  1. E. J. Jumper, E. J. Fitzgerald, “Recent advances in aero-optics,” Prog. Aerosp. Sci. 37, 299–339 (2001).
    [CrossRef]
  2. G. Sutton, “Aero-optical foundations and applications,” AIAA J. 23, 1525–1537 (1985).
    [CrossRef]
  3. J. H. Gladstone, T. P. Dale, “Researches on the refraction, dispersion and sensitiveness of liquids,” Philos. Trans. R. Soc. London 153, 317–343 (1863).
    [CrossRef]
  4. R. J. Renka, “Multivariate interpolation of large sets of scattered data,” ACM (Assoc. Comput. Mach.) Trans. Math. Software 14(2), 139–148 (1988).
    [CrossRef]
  5. A. Sharma, D. V. Kumar, A. K. Ghatak, “Tracing rays through graded-index media: a new method,” Appl. Opt. 21, 984–987 (1982).
    [CrossRef] [PubMed]
  6. M. P. Rimmer, “Ray tracing in inhomogeneous media,” in Optical System Design, Analysis and Production, P. J. Rogers, R. E. Fischer, eds., Proc. SPIE399, 339–344 (1983).
    [CrossRef]
  7. A. Sharma, “Computing optical path length in gradient-index media: a fast and accurate method,” Appl. Opt. 24, 4367–4370 (1985).
    [CrossRef] [PubMed]
  8. H. H. Hopkins, “Geometrical-optical treatment of frequency response,” Proc. Phys. Soc. London Ser. B 70, 1162–1172 (1957).
    [CrossRef]
  9. O. Pade, “Models of turbulence for aero-optics applications,” in 4th Iberoamerican Meeting on Optics and 7th Latin American Meeting on Optics, Lasers, and Their Applications, V. L. Brudny, S. A. Ledesma, M. C. Marconi, eds., Proc. SPIE4419, 494–498 (2001).
    [CrossRef]
  10. fluent 6.0 User Guide, (Fluent, Lebanon, N.H., 2001).
  11. D. C. Wilcox, Turbulence Modeling for CFD, 2nd ed. (DCW Industries, Inc., La Cañada, Calif., 1998).
  12. ICEM CFD 4.1 User Guide (ICEM CFD Engineering, Berkeley, Calif., 2000).
  13. CODE V 9.0 Reference Manual (Optical Research Associates, Pasadena, Calif., 2001).
  14. J. W. Goodman, Introduction to Fourier Optics2nd ed. (McGraw-Hill, New York, 1996).

2001

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

1988

R. J. Renka, “Multivariate interpolation of large sets of scattered data,” ACM (Assoc. Comput. Mach.) Trans. Math. Software 14(2), 139–148 (1988).
[CrossRef]

1985

1982

1957

H. H. Hopkins, “Geometrical-optical treatment of frequency response,” Proc. Phys. Soc. London Ser. B 70, 1162–1172 (1957).
[CrossRef]

1863

J. H. Gladstone, T. P. Dale, “Researches on the refraction, dispersion and sensitiveness of liquids,” Philos. Trans. R. Soc. London 153, 317–343 (1863).
[CrossRef]

Dale, T. P.

J. H. Gladstone, T. P. Dale, “Researches on the refraction, dispersion and sensitiveness of liquids,” Philos. Trans. R. Soc. London 153, 317–343 (1863).
[CrossRef]

Fitzgerald, E. J.

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

Ghatak, A. K.

Gladstone, J. H.

J. H. Gladstone, T. P. Dale, “Researches on the refraction, dispersion and sensitiveness of liquids,” Philos. Trans. R. Soc. London 153, 317–343 (1863).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics2nd ed. (McGraw-Hill, New York, 1996).

Hopkins, H. H.

H. H. Hopkins, “Geometrical-optical treatment of frequency response,” Proc. Phys. Soc. London Ser. B 70, 1162–1172 (1957).
[CrossRef]

Jumper, E. J.

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

Kumar, D. V.

Pade, O.

O. Pade, “Models of turbulence for aero-optics applications,” in 4th Iberoamerican Meeting on Optics and 7th Latin American Meeting on Optics, Lasers, and Their Applications, V. L. Brudny, S. A. Ledesma, M. C. Marconi, eds., Proc. SPIE4419, 494–498 (2001).
[CrossRef]

Renka, R. J.

R. J. Renka, “Multivariate interpolation of large sets of scattered data,” ACM (Assoc. Comput. Mach.) Trans. Math. Software 14(2), 139–148 (1988).
[CrossRef]

Rimmer, M. P.

M. P. Rimmer, “Ray tracing in inhomogeneous media,” in Optical System Design, Analysis and Production, P. J. Rogers, R. E. Fischer, eds., Proc. SPIE399, 339–344 (1983).
[CrossRef]

Sharma, A.

Sutton, G.

G. Sutton, “Aero-optical foundations and applications,” AIAA J. 23, 1525–1537 (1985).
[CrossRef]

Wilcox, D. C.

D. C. Wilcox, Turbulence Modeling for CFD, 2nd ed. (DCW Industries, Inc., La Cañada, Calif., 1998).

ACM (Assoc. Comput. Mach.) Trans. Math. Software

R. J. Renka, “Multivariate interpolation of large sets of scattered data,” ACM (Assoc. Comput. Mach.) Trans. Math. Software 14(2), 139–148 (1988).
[CrossRef]

AIAA J.

G. Sutton, “Aero-optical foundations and applications,” AIAA J. 23, 1525–1537 (1985).
[CrossRef]

Appl. Opt.

Philos. Trans. R. Soc. London

J. H. Gladstone, T. P. Dale, “Researches on the refraction, dispersion and sensitiveness of liquids,” Philos. Trans. R. Soc. London 153, 317–343 (1863).
[CrossRef]

Proc. Phys. Soc. London Ser. B

H. H. Hopkins, “Geometrical-optical treatment of frequency response,” Proc. Phys. Soc. London Ser. B 70, 1162–1172 (1957).
[CrossRef]

Prog. Aerosp. Sci.

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

Other

O. Pade, “Models of turbulence for aero-optics applications,” in 4th Iberoamerican Meeting on Optics and 7th Latin American Meeting on Optics, Lasers, and Their Applications, V. L. Brudny, S. A. Ledesma, M. C. Marconi, eds., Proc. SPIE4419, 494–498 (2001).
[CrossRef]

fluent 6.0 User Guide, (Fluent, Lebanon, N.H., 2001).

D. C. Wilcox, Turbulence Modeling for CFD, 2nd ed. (DCW Industries, Inc., La Cañada, Calif., 1998).

ICEM CFD 4.1 User Guide (ICEM CFD Engineering, Berkeley, Calif., 2000).

CODE V 9.0 Reference Manual (Optical Research Associates, Pasadena, Calif., 2001).

J. W. Goodman, Introduction to Fourier Optics2nd ed. (McGraw-Hill, New York, 1996).

M. P. Rimmer, “Ray tracing in inhomogeneous media,” in Optical System Design, Analysis and Production, P. J. Rogers, R. E. Fischer, eds., Proc. SPIE399, 339–344 (1983).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

MTF for analytically calculated versus numerically interpolated index of refraction and the gradient.

Fig. 2
Fig. 2

Code V ray-tracing picture for the boresight error.

Fig. 3
Fig. 3

MTF for the user-defined surface on a nonuniform grid.

Fig. 4
Fig. 4

MTF of the spherical dome at Mach 2 speed under standard atmospheric conditions.

Equations (8)

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

n=1+Gρ/ρref.
ddsnrdrds=gradnr.
nx, y=n0-αx2+y2.
Φx, y=κ0nx, yΔ=κ0n0Δ-κ0αΔx2+y2,
f=1/2αΔ.
gradnx, y=-2αxiˆ-2αyjˆ.
nx, y=c+α*y,
Yimage=F tanαΔ,

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