Abstract

A new technique for visualizing the effects of turbulence in clear air and concurrent wide-area motion-blur image restoration is described. Time sequences of images of a scene are captured with an optical telescope covering a comparatively wide field of view. With short-exposure times, atmospheric distortion is frozen to provide a sequence of randomly warped images. Point-by-point registration results in x and y shift maps describing the warp for each image. These maps provide not only a striking visualization of the turbulence but also a means for dewarping each image prior to averaging to form a wide-area motion-blur-corrected result. It is believed that the technique will be of benefit in astronomy, atmospheric physics, and surveillance.

© 1999 Optical Society of America

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References

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  1. D. Fraser, G. Thorpe, A. Lambert, “Visualization of turbulence and motion-blur removal in wide-area imaging through the atmosphere,” in Signal Recovery and Synthesis, Vol. 11 of 1998 Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 16–19.
  2. G. Thorpe, D. Fraser, “Wide-area imaging through the atmosphere,” in Optics in Atmospheric Propagation, Adaptive Systems, and Lidar, A. D. Devir, A. Kohnle, C. Werner, eds., Proc. SPIE2956, 188–197 (1996).
  3. G. Thorpe, D. Fraser, “Restoration over fields of view wider than the isoplanatic patch,” in Symposium of International Astronomical Union on Very High Angular Resolution Imaging, J. G. Robertson, W. J. Tango, eds. (Kluwer Academic, Dordrecht, The Netherlands, 1994), pp. 221–223.
  4. A. Labeyrie, “Attainment of diffraction-limited resolution in large telescopes by Fourier analyzing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).
  5. R. H. T. Bates, “Astronomical speckle imaging,” Phys. Rep. 90, 203–297 (1982).
    [CrossRef]
  6. J. R. Fienup, “Phase retrieval using boundary conditions,” J. Opt. Soc. Am. A 3, 1421–1426 (1986).
    [CrossRef]
  7. R. G. Lane, “Phase retrieval using conjugate gradient minimisation,” J. Mod. Opt. 38, 1797–1813 (1991).
    [CrossRef]
  8. T. S. McKechnie, “Light propagation through the atmosphere and the properties of images formed by large ground-based telescopes,” J. Opt. Soc. Am. A 8, 346–365 (1991).
    [CrossRef]
  9. J. L. Barron, D. J. Fleet, S. S. Beauchemin, “Performance of optical flow techniques,” Int. J. Comput. Vis. 12, 43–77 (1994).
    [CrossRef]
  10. W. Pratt, “Correlation techniques of image registration,” IEEE Trans. Aerosp. Electron. Syst. IT-20, 119–120 (1974).
  11. C. D. Kuglin, D. C. Hines, “The phase correlation image alignment method,” in Proceedings of the IEEE 1975 International Conference on Cybernetics and Society (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1975), pp. 163–165.
  12. F. Ackermann, “Digital image correlation: performance and potential application in photogrammetry,” Photogram. Rec. 64, 429–439 (1984).
  13. G. Thorpe, D. Fraser, “Problems in area-based image registration from stereo,” presented at the IEEE Region Ten Conference on Digital Signal Processing Applications, Brisbane, Australia, December 2–4, 1997.
  14. G. R. Ayers, J. C. Dainty, “Iterative blind deconvolution method and its applications,” Opt. Lett. 13, 547–549 (1988).
    [CrossRef]
  15. D. L. Fried, “Optical resolution through a randomly inhomogenous medium for very long and very short exposures,” J. Opt. Soc. Am. 56, 1372–1379 (1966).
    [CrossRef]

1994 (1)

J. L. Barron, D. J. Fleet, S. S. Beauchemin, “Performance of optical flow techniques,” Int. J. Comput. Vis. 12, 43–77 (1994).
[CrossRef]

1991 (2)

1988 (1)

1986 (1)

J. R. Fienup, “Phase retrieval using boundary conditions,” J. Opt. Soc. Am. A 3, 1421–1426 (1986).
[CrossRef]

1984 (1)

F. Ackermann, “Digital image correlation: performance and potential application in photogrammetry,” Photogram. Rec. 64, 429–439 (1984).

1982 (1)

R. H. T. Bates, “Astronomical speckle imaging,” Phys. Rep. 90, 203–297 (1982).
[CrossRef]

1974 (1)

W. Pratt, “Correlation techniques of image registration,” IEEE Trans. Aerosp. Electron. Syst. IT-20, 119–120 (1974).

1970 (1)

A. Labeyrie, “Attainment of diffraction-limited resolution in large telescopes by Fourier analyzing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).

1966 (1)

Ackermann, F.

F. Ackermann, “Digital image correlation: performance and potential application in photogrammetry,” Photogram. Rec. 64, 429–439 (1984).

Ayers, G. R.

Barron, J. L.

J. L. Barron, D. J. Fleet, S. S. Beauchemin, “Performance of optical flow techniques,” Int. J. Comput. Vis. 12, 43–77 (1994).
[CrossRef]

Bates, R. H. T.

R. H. T. Bates, “Astronomical speckle imaging,” Phys. Rep. 90, 203–297 (1982).
[CrossRef]

Beauchemin, S. S.

J. L. Barron, D. J. Fleet, S. S. Beauchemin, “Performance of optical flow techniques,” Int. J. Comput. Vis. 12, 43–77 (1994).
[CrossRef]

Dainty, J. C.

Fienup, J. R.

J. R. Fienup, “Phase retrieval using boundary conditions,” J. Opt. Soc. Am. A 3, 1421–1426 (1986).
[CrossRef]

Fleet, D. J.

J. L. Barron, D. J. Fleet, S. S. Beauchemin, “Performance of optical flow techniques,” Int. J. Comput. Vis. 12, 43–77 (1994).
[CrossRef]

Fraser, D.

D. Fraser, G. Thorpe, A. Lambert, “Visualization of turbulence and motion-blur removal in wide-area imaging through the atmosphere,” in Signal Recovery and Synthesis, Vol. 11 of 1998 Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 16–19.

G. Thorpe, D. Fraser, “Wide-area imaging through the atmosphere,” in Optics in Atmospheric Propagation, Adaptive Systems, and Lidar, A. D. Devir, A. Kohnle, C. Werner, eds., Proc. SPIE2956, 188–197 (1996).

G. Thorpe, D. Fraser, “Problems in area-based image registration from stereo,” presented at the IEEE Region Ten Conference on Digital Signal Processing Applications, Brisbane, Australia, December 2–4, 1997.

G. Thorpe, D. Fraser, “Restoration over fields of view wider than the isoplanatic patch,” in Symposium of International Astronomical Union on Very High Angular Resolution Imaging, J. G. Robertson, W. J. Tango, eds. (Kluwer Academic, Dordrecht, The Netherlands, 1994), pp. 221–223.

Fried, D. L.

Hines, D. C.

C. D. Kuglin, D. C. Hines, “The phase correlation image alignment method,” in Proceedings of the IEEE 1975 International Conference on Cybernetics and Society (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1975), pp. 163–165.

Kuglin, C. D.

C. D. Kuglin, D. C. Hines, “The phase correlation image alignment method,” in Proceedings of the IEEE 1975 International Conference on Cybernetics and Society (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1975), pp. 163–165.

Labeyrie, A.

A. Labeyrie, “Attainment of diffraction-limited resolution in large telescopes by Fourier analyzing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).

Lambert, A.

D. Fraser, G. Thorpe, A. Lambert, “Visualization of turbulence and motion-blur removal in wide-area imaging through the atmosphere,” in Signal Recovery and Synthesis, Vol. 11 of 1998 Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 16–19.

Lane, R. G.

R. G. Lane, “Phase retrieval using conjugate gradient minimisation,” J. Mod. Opt. 38, 1797–1813 (1991).
[CrossRef]

McKechnie, T. S.

Pratt, W.

W. Pratt, “Correlation techniques of image registration,” IEEE Trans. Aerosp. Electron. Syst. IT-20, 119–120 (1974).

Thorpe, G.

G. Thorpe, D. Fraser, “Restoration over fields of view wider than the isoplanatic patch,” in Symposium of International Astronomical Union on Very High Angular Resolution Imaging, J. G. Robertson, W. J. Tango, eds. (Kluwer Academic, Dordrecht, The Netherlands, 1994), pp. 221–223.

G. Thorpe, D. Fraser, “Wide-area imaging through the atmosphere,” in Optics in Atmospheric Propagation, Adaptive Systems, and Lidar, A. D. Devir, A. Kohnle, C. Werner, eds., Proc. SPIE2956, 188–197 (1996).

D. Fraser, G. Thorpe, A. Lambert, “Visualization of turbulence and motion-blur removal in wide-area imaging through the atmosphere,” in Signal Recovery and Synthesis, Vol. 11 of 1998 Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 16–19.

G. Thorpe, D. Fraser, “Problems in area-based image registration from stereo,” presented at the IEEE Region Ten Conference on Digital Signal Processing Applications, Brisbane, Australia, December 2–4, 1997.

Astron. Astrophys. (1)

A. Labeyrie, “Attainment of diffraction-limited resolution in large telescopes by Fourier analyzing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).

IEEE Trans. Aerosp. Electron. Syst. (1)

W. Pratt, “Correlation techniques of image registration,” IEEE Trans. Aerosp. Electron. Syst. IT-20, 119–120 (1974).

Int. J. Comput. Vis. (1)

J. L. Barron, D. J. Fleet, S. S. Beauchemin, “Performance of optical flow techniques,” Int. J. Comput. Vis. 12, 43–77 (1994).
[CrossRef]

J. Mod. Opt. (1)

R. G. Lane, “Phase retrieval using conjugate gradient minimisation,” J. Mod. Opt. 38, 1797–1813 (1991).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Opt. Lett. (1)

Photogram. Rec. (1)

F. Ackermann, “Digital image correlation: performance and potential application in photogrammetry,” Photogram. Rec. 64, 429–439 (1984).

Phys. Rep. (1)

R. H. T. Bates, “Astronomical speckle imaging,” Phys. Rep. 90, 203–297 (1982).
[CrossRef]

Other (5)

D. Fraser, G. Thorpe, A. Lambert, “Visualization of turbulence and motion-blur removal in wide-area imaging through the atmosphere,” in Signal Recovery and Synthesis, Vol. 11 of 1998 Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 16–19.

G. Thorpe, D. Fraser, “Wide-area imaging through the atmosphere,” in Optics in Atmospheric Propagation, Adaptive Systems, and Lidar, A. D. Devir, A. Kohnle, C. Werner, eds., Proc. SPIE2956, 188–197 (1996).

G. Thorpe, D. Fraser, “Restoration over fields of view wider than the isoplanatic patch,” in Symposium of International Astronomical Union on Very High Angular Resolution Imaging, J. G. Robertson, W. J. Tango, eds. (Kluwer Academic, Dordrecht, The Netherlands, 1994), pp. 221–223.

C. D. Kuglin, D. C. Hines, “The phase correlation image alignment method,” in Proceedings of the IEEE 1975 International Conference on Cybernetics and Society (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1975), pp. 163–165.

G. Thorpe, D. Fraser, “Problems in area-based image registration from stereo,” presented at the IEEE Region Ten Conference on Digital Signal Processing Applications, Brisbane, Australia, December 2–4, 1997.

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Figures (9)

Fig. 1
Fig. 1

(a) Wide-area illumination of turbulent layer(s), (b) position-dependent tip–tilt. (In these diagrams objects are shown at close range, so details, such as parallelism of wave fronts and ray angles, are only approximations for distant objects. Similarly, the illumination beams are approximations and do not show dispersion.)

Fig. 2
Fig. 2

(a), (b) Two successive frames of derived x shift maps from the Theophilus sequence. (White indicates a shift to the left; black indicates a shift to the right; mid-gray means no shift.)

Fig. 3
Fig. 3

(a), (b) Shift vectors, superimposed on the Theophilus background, from two successive frames (not the same two frames as in Fig. 2).

Fig. 4
Fig. 4

(a) Lunar crater Theophilus after two-pass restoration; (b) resulting, derived motion-blur PSF.

Fig. 5
Fig. 5

Average pairwise cross correlations of 50 shift maps from the Theophilus sequence (a) from x shifts and (b) from y shifts.

Fig. 6
Fig. 6

(a), (b) Shift vectors, superimposed on aircraft tail background, from two successive frames.

Fig. 7
Fig. 7

(a) Single-frame distorted aircraft image, (b) motion-restored and residual deblurred image.

Fig. 8
Fig. 8

(a), (b) Shift vectors, superimposed on hut background, from two successive frames.

Fig. 9
Fig. 9

(a) Single-frame distorted hut image, (b) motion-restored and residual deblurred image.

Equations (7)

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

h(x, y)=F-1 F[ f0(x, y)]F[ f1(x, y)],
r(x, y)=w1(x, y)w2(x, y),
R=W1*W2,
P=exp[ j arg(R)]
g(x, y)n=h(x, y)n[f(x, y)]+η(x, y)n,
g(x, y)n=s(x, y)n{h(x, y)an[ f(x, y)]}+η(x, y)n,
g(x, y)n=1N n=1Ng(x, y)n=1N n=1N(s(x, y)n{h(x, y)an[f(x, y)]}+η(x, y)n)=hg1N n=1Nh(x, y)an[f(x, y)]+1N n=1Nη(x, y)n,

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