Abstract

The active illumination of a target through a turbulent medium with a monostatic transmitter–receiver results in a naturally occurring conjugate wave caused by reciprocal scattering paths that experience identical phase variations. This reciprocal path-scattering phenomenon produces an enhanced backscatter in the retroverse direction (precisely along the boresight of the pointing telescope). A dual aperture causes this intensity enhancement to take the form of Young’s interference fringes. Interference fringes produced by the reciprocal path-scattering phenomenon are temporally stable even in the presence of time-varying turbulence. Choosing the width-to-separation ratio of the dual apertures appropriately and utilizing orthogonal polarizations to suppress the time-varying common-path scattered radiation allow one to achieve interferometric sensitivity in pointing accuracy through a random medium or turbulent atmosphere. Computer simulations are compared with laboratory experimental data. This new precision pointing and tracking technique has potential applications in ground-to-space laser communications, laser power beaming to satellites, and theater missile defense scenarios.

© 1996 Optical Society of America

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References

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  1. Six papers in a special section on optical tracking, Appl. Opt. 5, 481–532 (1966).
    [PubMed]
  2. Twenty papers in a special section on acquisition, pointing, and tracking,” Opt. Eng. 32, 2647–2811 (1993).
  3. J. S. Preston, “Retro-reflexion by diffusing surfaces,” Nature 213, 1007–1008 (1967).
    [Crossref]
  4. T. S. Trowbridge, “Retroreflection from rough surfaces,” J. Opt. Soc. Am. 68, 1225–1242 (1978).
    [Crossref]
  5. Y. Kuga, A. Ishimaru, “Retroreflectance from a dense distribution of spherical particles,” J. Opt. Soc. Am. A 1, 831–835 (1984).
    [Crossref]
  6. L. W. Stockham, T. J. Love, “Investigation of the opposition effect in integrating spheres,” J. Opt. Soc. Am. 60, 251–254 (1970).
    [Crossref]
  7. W. W. Montgomery, R. H. Kohl, “Opposition effect experimentation,” Opt. Lett. 5, 546–548 (1980).
    [Crossref] [PubMed]
  8. Z. H. Gu, R. S. Dummer, A. A. Maradudin, A. R. McGurn, “Experimental study of the opposition effect in the scattering of light from a randomly rough metal surface,” Appl. Opt. 28, 537–543 (1989).
    [Crossref] [PubMed]
  9. L. Tsang, A. Ishimaru, “Backscatter enhancement of random discrete scatterers,” J. Opt. Soc. Am. A 1, 836–839 (1984).
    [Crossref]
  10. E. Jakeman, “Enhanced backscattering through a deep random phase screen,” J. Opt. Soc. Am. A 5, 1638–1648 (1988).
    [Crossref]
  11. P. R. Tapster, A. R. Weeks, E. Jakeman, “Observation of backscattering enhancement through atmospheric phase screen,” J. Opt. Soc. Am. A 6, 517–522 (1989).
    [Crossref]
  12. G. Welch, R. L. Phillips, “Simulation of enhanced backscatter by a phase screen,” J. Opt. Soc. Am. A 7, 578–584 (1990).
    [Crossref]
  13. M. Nieto-Vesperinas, “Enhanced backscattering,” Opt. Photon. News 1(12), 50–52 (1990).
    [Crossref]
  14. D. A. de Wolf, “Backscatter enhancement: random continuum and particles,” J. Opt. Soc. Am. A 8, 465–471 (1991).
    [Crossref]
  15. T. Mavroidis, J. C. Dainty, “Imaging after double passage through a random screen,” Opt. Lett. 15, 857–859 (1990).
    [Crossref] [PubMed]
  16. C. J. Solomon, J. C. Dainty, R. G. Lane, “Double passage imaging through a random phase screen using a non-redundant aperture,” J. Modern Opt. 10, 1993–2008 (1991).
    [Crossref]
  17. W. T. Rhodes, G. Welch, “Determination of a coherent wave field after double passage through a diffuser,” J. Opt. Soc. Am. A 9, 341–343 (1991).
    [Crossref]
  18. C. J. Solomon, J. C. Dainty, “Use of polarisation in double passage imaging through a random screen,” Opt. Commun. 87, 207–211 (1992).
    [Crossref]
  19. J. E. Harvey, A. Kotha, “Sparse array configurations yielding uniform MTF’s in reciprocal path imaging applications,” Opt. Commun. 106, 178–182 (1994).
    [Crossref]
  20. J. E. Harvey, A. Kotha, R. L. Phillips, “Image characteristics in applications utilizing dilute subaperture arrays,” Appl. Opt. 34, 2983–2991 (1995).
    [Crossref] [PubMed]
  21. A. Dogariu, G. D. Boreman, M. Dogariu, “Enhanced backscattering from a volume-scattering medium behind a phase screen,” Appl. Opt. (to be published).
  22. R. C. Heileman, R. L. Phillips, “Experimental measurements of statistical properties of scattered light due to double passage through a random phase screen,” in Atmospheric Propagation and Remote Sensing II, A. Kohnle, W. B. Miller, eds., Proc. SPIE1968, 662–672 (1993).
  23. A. N. Bogaturov, A. S. Gurvich, V. A. Myakinin, J. C. Dainty, C. J. Solomon, N. J. Wooder, “Use of polarization in interferometry after double passage through turbulence,” Opt. Lett. 17, 757–759 (1992).
    [Crossref] [PubMed]
  24. D. L. Fried, “Optical resolution through a randomly inhomogeneous medium for very long and very short exposures,” J. Opt. Soc. Am. 56, 1372–1379 (1966).
    [Crossref]
  25. R. N. Bracewell, The Fourier Transform and its Applications (McGraw-Hill, New York, 1965), Chap. 6, pp. 74, 101, 104.
  26. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 2, p. 9.
  27. J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978), Chap. 10, pp. 159, 166, 194, 196, 417.

1995 (1)

1994 (1)

J. E. Harvey, A. Kotha, “Sparse array configurations yielding uniform MTF’s in reciprocal path imaging applications,” Opt. Commun. 106, 178–182 (1994).
[Crossref]

1993 (1)

Twenty papers in a special section on acquisition, pointing, and tracking,” Opt. Eng. 32, 2647–2811 (1993).

1992 (2)

1991 (3)

1990 (3)

1989 (2)

1988 (1)

1984 (2)

1980 (1)

1978 (1)

1970 (1)

1967 (1)

J. S. Preston, “Retro-reflexion by diffusing surfaces,” Nature 213, 1007–1008 (1967).
[Crossref]

1966 (2)

Six papers in a special section on optical tracking, Appl. Opt. 5, 481–532 (1966).
[PubMed]

D. L. Fried, “Optical resolution through a randomly inhomogeneous medium for very long and very short exposures,” J. Opt. Soc. Am. 56, 1372–1379 (1966).
[Crossref]

Bogaturov, A. N.

Boreman, G. D.

A. Dogariu, G. D. Boreman, M. Dogariu, “Enhanced backscattering from a volume-scattering medium behind a phase screen,” Appl. Opt. (to be published).

Bracewell, R. N.

R. N. Bracewell, The Fourier Transform and its Applications (McGraw-Hill, New York, 1965), Chap. 6, pp. 74, 101, 104.

Dainty, J. C.

A. N. Bogaturov, A. S. Gurvich, V. A. Myakinin, J. C. Dainty, C. J. Solomon, N. J. Wooder, “Use of polarization in interferometry after double passage through turbulence,” Opt. Lett. 17, 757–759 (1992).
[Crossref] [PubMed]

C. J. Solomon, J. C. Dainty, “Use of polarisation in double passage imaging through a random screen,” Opt. Commun. 87, 207–211 (1992).
[Crossref]

C. J. Solomon, J. C. Dainty, R. G. Lane, “Double passage imaging through a random phase screen using a non-redundant aperture,” J. Modern Opt. 10, 1993–2008 (1991).
[Crossref]

T. Mavroidis, J. C. Dainty, “Imaging after double passage through a random screen,” Opt. Lett. 15, 857–859 (1990).
[Crossref] [PubMed]

de Wolf, D. A.

Dogariu, A.

A. Dogariu, G. D. Boreman, M. Dogariu, “Enhanced backscattering from a volume-scattering medium behind a phase screen,” Appl. Opt. (to be published).

Dogariu, M.

A. Dogariu, G. D. Boreman, M. Dogariu, “Enhanced backscattering from a volume-scattering medium behind a phase screen,” Appl. Opt. (to be published).

Dummer, R. S.

Fried, D. L.

D. L. Fried, “Optical resolution through a randomly inhomogeneous medium for very long and very short exposures,” J. Opt. Soc. Am. 56, 1372–1379 (1966).
[Crossref]

Gaskill, J. D.

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978), Chap. 10, pp. 159, 166, 194, 196, 417.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 2, p. 9.

Gu, Z. H.

Gurvich, A. S.

Harvey, J. E.

J. E. Harvey, A. Kotha, R. L. Phillips, “Image characteristics in applications utilizing dilute subaperture arrays,” Appl. Opt. 34, 2983–2991 (1995).
[Crossref] [PubMed]

J. E. Harvey, A. Kotha, “Sparse array configurations yielding uniform MTF’s in reciprocal path imaging applications,” Opt. Commun. 106, 178–182 (1994).
[Crossref]

Heileman, R. C.

R. C. Heileman, R. L. Phillips, “Experimental measurements of statistical properties of scattered light due to double passage through a random phase screen,” in Atmospheric Propagation and Remote Sensing II, A. Kohnle, W. B. Miller, eds., Proc. SPIE1968, 662–672 (1993).

Ishimaru, A.

Jakeman, E.

Kohl, R. H.

Kotha, A.

J. E. Harvey, A. Kotha, R. L. Phillips, “Image characteristics in applications utilizing dilute subaperture arrays,” Appl. Opt. 34, 2983–2991 (1995).
[Crossref] [PubMed]

J. E. Harvey, A. Kotha, “Sparse array configurations yielding uniform MTF’s in reciprocal path imaging applications,” Opt. Commun. 106, 178–182 (1994).
[Crossref]

Kuga, Y.

Lane, R. G.

C. J. Solomon, J. C. Dainty, R. G. Lane, “Double passage imaging through a random phase screen using a non-redundant aperture,” J. Modern Opt. 10, 1993–2008 (1991).
[Crossref]

Love, T. J.

Maradudin, A. A.

Mavroidis, T.

McGurn, A. R.

Montgomery, W. W.

Myakinin, V. A.

Nieto-Vesperinas, M.

M. Nieto-Vesperinas, “Enhanced backscattering,” Opt. Photon. News 1(12), 50–52 (1990).
[Crossref]

Phillips, R. L.

J. E. Harvey, A. Kotha, R. L. Phillips, “Image characteristics in applications utilizing dilute subaperture arrays,” Appl. Opt. 34, 2983–2991 (1995).
[Crossref] [PubMed]

G. Welch, R. L. Phillips, “Simulation of enhanced backscatter by a phase screen,” J. Opt. Soc. Am. A 7, 578–584 (1990).
[Crossref]

R. C. Heileman, R. L. Phillips, “Experimental measurements of statistical properties of scattered light due to double passage through a random phase screen,” in Atmospheric Propagation and Remote Sensing II, A. Kohnle, W. B. Miller, eds., Proc. SPIE1968, 662–672 (1993).

Preston, J. S.

J. S. Preston, “Retro-reflexion by diffusing surfaces,” Nature 213, 1007–1008 (1967).
[Crossref]

Rhodes, W. T.

Solomon, C. J.

C. J. Solomon, J. C. Dainty, “Use of polarisation in double passage imaging through a random screen,” Opt. Commun. 87, 207–211 (1992).
[Crossref]

A. N. Bogaturov, A. S. Gurvich, V. A. Myakinin, J. C. Dainty, C. J. Solomon, N. J. Wooder, “Use of polarization in interferometry after double passage through turbulence,” Opt. Lett. 17, 757–759 (1992).
[Crossref] [PubMed]

C. J. Solomon, J. C. Dainty, R. G. Lane, “Double passage imaging through a random phase screen using a non-redundant aperture,” J. Modern Opt. 10, 1993–2008 (1991).
[Crossref]

Stockham, L. W.

Tapster, P. R.

Trowbridge, T. S.

Tsang, L.

Weeks, A. R.

Welch, G.

Wooder, N. J.

Appl. Opt. (3)

J. Modern Opt. (1)

C. J. Solomon, J. C. Dainty, R. G. Lane, “Double passage imaging through a random phase screen using a non-redundant aperture,” J. Modern Opt. 10, 1993–2008 (1991).
[Crossref]

J. Opt. Soc. Am. (1)

D. L. Fried, “Optical resolution through a randomly inhomogeneous medium for very long and very short exposures,” J. Opt. Soc. Am. 56, 1372–1379 (1966).
[Crossref]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (7)

Nature (1)

J. S. Preston, “Retro-reflexion by diffusing surfaces,” Nature 213, 1007–1008 (1967).
[Crossref]

Opt. Commun. (1)

J. E. Harvey, A. Kotha, “Sparse array configurations yielding uniform MTF’s in reciprocal path imaging applications,” Opt. Commun. 106, 178–182 (1994).
[Crossref]

Opt. Commun. (1)

C. J. Solomon, J. C. Dainty, “Use of polarisation in double passage imaging through a random screen,” Opt. Commun. 87, 207–211 (1992).
[Crossref]

Opt. Eng. (1)

Twenty papers in a special section on acquisition, pointing, and tracking,” Opt. Eng. 32, 2647–2811 (1993).

Opt. Lett. (3)

Opt. Photon. News (1)

M. Nieto-Vesperinas, “Enhanced backscattering,” Opt. Photon. News 1(12), 50–52 (1990).
[Crossref]

Other (5)

A. Dogariu, G. D. Boreman, M. Dogariu, “Enhanced backscattering from a volume-scattering medium behind a phase screen,” Appl. Opt. (to be published).

R. C. Heileman, R. L. Phillips, “Experimental measurements of statistical properties of scattered light due to double passage through a random phase screen,” in Atmospheric Propagation and Remote Sensing II, A. Kohnle, W. B. Miller, eds., Proc. SPIE1968, 662–672 (1993).

R. N. Bracewell, The Fourier Transform and its Applications (McGraw-Hill, New York, 1965), Chap. 6, pp. 74, 101, 104.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 2, p. 9.

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978), Chap. 10, pp. 159, 166, 194, 196, 417.

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Figures (14)

Fig. 1
Fig. 1

Conjugate-wave formation by RPS through a random phase screen or turbulent medium.

Fig. 2
Fig. 2

Monostatic laser imaging configuration used to demonstrate the EBS phenomenon.

Fig. 3
Fig. 3

Computer simulation of the EBS phenomenon (110 realizations).

Fig. 4
Fig. 4

Measured irradiance profile through the enhancement (1.0-s exposure time).

Fig. 5
Fig. 5

Schematic illustration, showing that two separate targets result in two broad scattering functions and a single backscatter enhancement.

Fig. 6
Fig. 6

Experimentally measured profile, indicating two separate scattering functions and a single backscatter enhancement.

Fig. 7
Fig. 7

Experimentally measured intensity profile through the enhancement as the target is displaced from the boresight. Note that the enhancement remains fixed on the telescope boresight and the scattering function shifts with the geometrical image of the target.

Fig. 8
Fig. 8

Superposition of experimentally measured scattering functions, indicating the envelope of enhancement heights.

Fig. 9
Fig. 9

Optical layout for precision tracking, utilizing EBS with a dual aperture.

Fig. 10
Fig. 10

CCD image and irradiance profile of (a) monostatic measurements, demonstrating static fringes over a 10-s exposure time; (b) bistatic measurements, demonstrating time-varying (blurred) fringes.

Fig. 11
Fig. 11

Theoretical EBS function (caused by a dual aperture) superposed on an experimental measurement in the presence of turbulence (1-s exposure time). The asymmetry in the sidelobes caused by the pointing error is evident.

Fig. 12
Fig. 12

Pointing error calibration curve, indicating interferometric accuracy.

Fig. 13
Fig. 13

Comparison of experimental data with theoretical predictions.

Fig. 14
Fig. 14

Diffraction-limited angular PSF of the pointing telescope.

Equations (19)

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U A B ( ) ( y 1 ) = exp ( i 2 k f 1 ) i λ f 1 F { rect ( y 0 a / 2 b ) } η = y 1 f 1 ,
U A B ( ) ( y 1 ) = exp ( i 2 k f 1 ) i λ f 1 b sinc ( y 1 λ f 1 / b ) exp ( i 2 π a 2 y 1 λ f 1 ) .
U A B ( ) + ( y 1 ) = U A B ( ) ( y 1 ) δ ( y 1 Δ ) = exp ( i 2 k f 1 ) i λ f 1 b sinc ( y 1 λ f 1 / b ) × exp ( i 2 π a 2 y 1 λ f 1 ) δ ( y 1 Δ ) .
U A B ( ) ( y 2 ) = exp ( i 2 k f 1 ) i λ f 1 F { U A B ( ) + ( y 1 ) } η= y 2 / λ f 1 .
U A B ( ) ( y 2 ) = exp ( i 4 k f 1 ) rect ( y 2 + a / 2 b ) * exp ( i 2 π Δ y 2 λ f 1 ) ,
U A B ( ) + ( y 2 ) = U A B ( ) ( y 2 ) rect ( y 2 + a / 2 b )
U A B ( ) + ( y 2 ) = exp ( i 4 k f 1 ) × [ rect ( y 2 + a / 2 b ) * exp ( i 2 π Δ y 2 λ f 1 ) ] × rect ( y 2 + a / 2 b ) ,
U A B ( ) + ( y 2 ) = exp ( i 4 k f 1 ) × { [ rect ( y 2 b ) * exp ( i 2 π Δ y 2 λ f 1 ) ] rect ( y 2 b ) } * δ ( y 2 + a 2 ) .
U B A ( ) + ( y 2 ) = exp ( i 4 k f 1 ) × { [ rect ( y 2 b ) * exp ( i 2 π Δ y 2 λ f 1 ) ] rect ( y 2 b ) } * δ ( y 2 a 2 ) .
U + ( y 2 ) = U A B ( ) + ( y 2 ) + U B A ( ) + ( y 2 ) .
U + ( y 2 ) = exp ( i 4 k f 1 ) × { [ rect ( y 2 b ) * exp ( i 2 π Δ y 2 λ f 1 ) ] rect ( y 2 b ) } * [ δ ( y 2 a 2 ) + δ ( y 2 + a 2 ) ] .
U ( y 3 ) = exp ( i 2 k f 2 ) i λ f 2 F { U + ( y 2 ) } η= y 3 / λ f 2 .
U ( y 3 ) = K i [ b sinc ( y 3 λ f 2 / b ) δ ( y 3 + Δ f 2 f 1 ) * b sinc ( y 3 λ f 2 / b ) ] 2 cos ( π y 3 λ f 2 / a ) ,
U ( y 3 ) = K 2 b 2 i sinc ( Δ λ f 1 / b ) sinc ( y 3 + Δ f 2 / f 1 λ f 2 / b ) × cos ( π y 3 λ f 2 / a ) ,
I 3 ( y 3 ) = | U ( y 3 ) | 2 = 4 b 4 sinc 2 ( Δ λ f 1 / b ) × [ sinc 2 ( y 3 + Δ f 2 / f 1 λ f 2 / b ) cos 2 ( π y 3 λ f 2 / a ) ] .
R = I 3 I 1 I 3 + I 1 ,
R rms = [ ( R ex R th ) 2 N ] 1 / 2 ,
rms error = 0 .09774 arcmin .
α rms σ diff = 0 . 09774 arcmin 2 . 44 λ / D = 0 . 012 .

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