Abstract

Heterodyne detection has been used to measure the enhanced backscattering from a standard target consisting of a plane mirror positioned behind a moving ground-glass disk (assumed to act as a phase screen). A tilt of the plane mirror in combination with spectral filtering of the detector output allows isolation of the double-scattered component of the light signal. When the illuminating laser and the local oscillator beams are correctly mode matched, the intensity of this signal displays the factor-of-2 increase that denotes full coherent enhancement. This full enhancement is preserved for a wide range of mirror to phase-screen spacing, in contrast with earlier observations in which direct-detection techniques were used.

© 1997 Optical Society of America

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References

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  1. Y. Kuga and A. Ishimaru, J. Opt. Soc. Am. A 1, 831 (1984).
  2. P. Oetking, J. Geophys. Res. 71, 2505 (1966).
    [CrossRef]
  3. E. R. Mendez and K. A. O'Donnell, Opt. Commun. 61, 91 (1987).
  4. E. Jakeman, J. Opt. Soc. Am. A 5, 1638 (1988).
  5. E. Jakeman, P. R. Tapster, and A. R. Weeks, J. Phys. D 21, 32 (1988).
    [CrossRef]
  6. M. Harris, Contemp. Phys. 36, 215 (1995).
  7. D. L. Jordan, G. D. Lewis, and E. Jakeman, Appl. Opt. 35, 3583 (1996).
    [PubMed]
  8. M. Harris, G. N. Pearson, C. A. Hill, and J. M. Vaughan, Appl. Opt. 33, 7226 (1994).
    [PubMed]
  9. G. N. Pearson, M. Harris, E. Jakeman, and D. Letalick, J. Mod. Opt. 41, 2067 (1994).

1996 (1)

1995 (1)

M. Harris, Contemp. Phys. 36, 215 (1995).

1994 (2)

G. N. Pearson, M. Harris, E. Jakeman, and D. Letalick, J. Mod. Opt. 41, 2067 (1994).

M. Harris, G. N. Pearson, C. A. Hill, and J. M. Vaughan, Appl. Opt. 33, 7226 (1994).
[PubMed]

1988 (2)

E. Jakeman, P. R. Tapster, and A. R. Weeks, J. Phys. D 21, 32 (1988).
[CrossRef]

E. Jakeman, J. Opt. Soc. Am. A 5, 1638 (1988).

1987 (1)

E. R. Mendez and K. A. O'Donnell, Opt. Commun. 61, 91 (1987).

1984 (1)

1966 (1)

P. Oetking, J. Geophys. Res. 71, 2505 (1966).
[CrossRef]

Harris, M.

M. Harris, Contemp. Phys. 36, 215 (1995).

G. N. Pearson, M. Harris, E. Jakeman, and D. Letalick, J. Mod. Opt. 41, 2067 (1994).

M. Harris, G. N. Pearson, C. A. Hill, and J. M. Vaughan, Appl. Opt. 33, 7226 (1994).
[PubMed]

Hill, C. A.

Ishimaru, A.

Jakeman, E.

D. L. Jordan, G. D. Lewis, and E. Jakeman, Appl. Opt. 35, 3583 (1996).
[PubMed]

G. N. Pearson, M. Harris, E. Jakeman, and D. Letalick, J. Mod. Opt. 41, 2067 (1994).

E. Jakeman, P. R. Tapster, and A. R. Weeks, J. Phys. D 21, 32 (1988).
[CrossRef]

E. Jakeman, J. Opt. Soc. Am. A 5, 1638 (1988).

Jordan, D. L.

Kuga, Y.

Letalick, D.

G. N. Pearson, M. Harris, E. Jakeman, and D. Letalick, J. Mod. Opt. 41, 2067 (1994).

Lewis, G. D.

Mendez, E. R.

E. R. Mendez and K. A. O'Donnell, Opt. Commun. 61, 91 (1987).

O'Donnell, K. A.

E. R. Mendez and K. A. O'Donnell, Opt. Commun. 61, 91 (1987).

Oetking, P.

P. Oetking, J. Geophys. Res. 71, 2505 (1966).
[CrossRef]

Pearson, G. N.

G. N. Pearson, M. Harris, E. Jakeman, and D. Letalick, J. Mod. Opt. 41, 2067 (1994).

M. Harris, G. N. Pearson, C. A. Hill, and J. M. Vaughan, Appl. Opt. 33, 7226 (1994).
[PubMed]

Tapster, P. R.

E. Jakeman, P. R. Tapster, and A. R. Weeks, J. Phys. D 21, 32 (1988).
[CrossRef]

Vaughan, J. M.

Weeks, A. R.

E. Jakeman, P. R. Tapster, and A. R. Weeks, J. Phys. D 21, 32 (1988).
[CrossRef]

Appl. Opt. (2)

Contemp. Phys. (1)

M. Harris, Contemp. Phys. 36, 215 (1995).

J. Geophys. Res. (1)

P. Oetking, J. Geophys. Res. 71, 2505 (1966).
[CrossRef]

J. Mod. Opt. (1)

G. N. Pearson, M. Harris, E. Jakeman, and D. Letalick, J. Mod. Opt. 41, 2067 (1994).

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

J. Phys. D (1)

E. Jakeman, P. R. Tapster, and A. R. Weeks, J. Phys. D 21, 32 (1988).
[CrossRef]

Opt. Commun. (1)

E. R. Mendez and K. A. O'Donnell, Opt. Commun. 61, 91 (1987).

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Figures (3)

Fig. 1
Fig. 1

Experimental arrangement: OI is an optical isolator, and BS is a beam splitter. Lens L1 brings the incident beam to a weak focus at the phase screen. FP is the focal plane of lens L2. The detector is placed beyond this in the plane in which mirror M2 is imaged. The geometry is arranged so that the illuminating beam and the backpropagated local oscillator (BPLO) intersect at the target independent of the orientation of M2. The target consists of a rotating ground-glass phase screen and a stationary mirror, M1, tilted about a horizontal axis (see inset for side view), ensuring a Doppler shift for double-scattered light but not for single-scattered light (dashed path).

Fig. 2
Fig. 2

Power spectrum of the heterodyne-detected light from the arrangement in Fig.  1, with mirror M1 placed close behind the phase screen. The relative height of the components (because of single-, double-, and triple-scattered light) varies with mirror to phase-screen spacing, but their frequencies and spectral widths are independent of this separation. The dotted curve shows the transmission function of the bandpass filter used to isolate the double-scattered component.

Fig. 3
Fig. 3

Measured signal power versus angular separation of the illuminating beam from the BPLO beam. The full factor-of-2 enhancement is observed for a wide range of mirror to phase-screen spacing (d).

Equations (3)

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

E(θi,θs)drdrexpiϕ(r)+ϕ(r)+k4d(r-r)2-k·(rsinθi-rsinθs)-r2Ws2-r2Wi2.
|E(θi,θs|2exp(-2P2/m02)1+l2l2exp(-2k2l2Q2),
1l2=1m02d2+1Wi2+1Ws2,1l2=1m02d2+4Wi2+Ws2.

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