Abstract

The frequency spectrum of laser light scattered from moving rough objects is examined by temporally Fourier transforming the mutual coherence function describing the scattering. The motion of the object is introduced through the temporal dependence of the spatial variables of the mutual coherence function. A simple Doppler shift model is shown to provide a first approximaion to the result derived via coherence theory, for fully illuminated objects. An expression for the frequency broadening caused by the limited observation interval of a given rough-surface area is derived, and the correspondence with previous results is noted.

© 1977 Optical Society of America

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  1. R. E. Hiatt, T. B. A. Senior, and V. H. Weston, "A Study of surface roughness and its effect on the backscattering cross section of spheres," IRE Proc. 48, 2008–2016 (1960).
  2. H. S. Cabuyan and R. C. Murphy, "Scattering of electromagnetic waves by rough perfectly conducting circular cylinders," IEEE Trans. Antennas Propag. AP21, 893–895 (1973).
  3. J. V. Evans and Tor Hagfors, Radar Astronomy (McGraw- Hill, New York, 1968).
  4. J. van Bladel, "Electromagnetic fields in the presence of rotating bodies," IEEE Proc. 64, 301–318 (1976).
  5. N. George, "Speckle from rough, moving objects," J. Opt. Soc. Am. 66, 1182–1194 (1976).
  6. J. C. Erdmann and R. I. Gellart, "Speckle field of curved, rotating surfaces of Gaussian roughness illuminated by a laser light spot," J. Opt. Soc. Am. 66, 1194–1204 (1976).
  7. P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, Oxford 1963).
  8. J. C. Leader, "An analysis of the spatial coherence of laser light scattered by a surface with two scales of roughness," J. Opt. Soc. Am. 66, 536–546 (1976).
  9. J. C. Leader, "Bidirectional scattering of electromagnetic waves from rough surfaces," J. Appl. Phys. 42, 4808–4816 (1971).
  10. A. E. Siegman, "The antenna properties of optical heterodyne receivers," IEEE Proc. 54, 1350–1356 (1966).
  11. H. T. Yura, "Optical heterodyne signal power obtained from finite sized sources of radiation," Appl. Opt. 13, 150–157 (1974).
  12. W. B. Davenport and W. L. Root, Random Signals and Noise (McGraw-Hill, New York, 1958), pp. 107–108.
  13. D. R. Brillinger, "Fourier analysis of stationary processes," IEEE Proc. 62, 1628–1643 (1974).
  14. A more precise statement of the restrictions imposed on the antenna dimensions is provided by the two-dimensional "map" of maximum angular frequency variations W(fx max, fy max, Δ R, τ) ∼ d2 σj(2xp max/λ, 2λp max/λ; v¯)/dxpdyp.
  15. M. C. Teich, "Infrared heterodyne detection," IEEE Proc. 56, 37–46 (1968).
  16. G. Gould, S. F. Jacobs, J. T. LaTourette, M. Newstein, and P. Rabinowtiz, "Coherent detection of light scattered from a diffusely reflecting surface," Appl. Opt. 3, 648–649 (1964).
  17. A focused laser beam diameter of 50 µm was employed in the experiments described in Ref. 15. The experimental geometry resulted in a di value [Eq. (28)] of 0.5 mm. Thus in this case, the frequency broadening was primarily caused by the limited observation interval.
  18. J. C. Leader, "Hemispherical scattering of electromagnetic waves from rough surfaces," J. Opt. Soc. Am. 62, 1356 (1972). Also, McDonnell Aircraft Paper No. MCAIR-72-037.

1976 (4)

1974 (2)

H. T. Yura, "Optical heterodyne signal power obtained from finite sized sources of radiation," Appl. Opt. 13, 150–157 (1974).

D. R. Brillinger, "Fourier analysis of stationary processes," IEEE Proc. 62, 1628–1643 (1974).

1973 (1)

H. S. Cabuyan and R. C. Murphy, "Scattering of electromagnetic waves by rough perfectly conducting circular cylinders," IEEE Trans. Antennas Propag. AP21, 893–895 (1973).

1972 (1)

J. C. Leader, "Hemispherical scattering of electromagnetic waves from rough surfaces," J. Opt. Soc. Am. 62, 1356 (1972). Also, McDonnell Aircraft Paper No. MCAIR-72-037.

1971 (1)

J. C. Leader, "Bidirectional scattering of electromagnetic waves from rough surfaces," J. Appl. Phys. 42, 4808–4816 (1971).

1968 (1)

M. C. Teich, "Infrared heterodyne detection," IEEE Proc. 56, 37–46 (1968).

1966 (1)

A. E. Siegman, "The antenna properties of optical heterodyne receivers," IEEE Proc. 54, 1350–1356 (1966).

1964 (1)

1960 (1)

R. E. Hiatt, T. B. A. Senior, and V. H. Weston, "A Study of surface roughness and its effect on the backscattering cross section of spheres," IRE Proc. 48, 2008–2016 (1960).

Beckmann, P.

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, Oxford 1963).

Brillinger, D. R.

D. R. Brillinger, "Fourier analysis of stationary processes," IEEE Proc. 62, 1628–1643 (1974).

Cabuyan, H. S.

H. S. Cabuyan and R. C. Murphy, "Scattering of electromagnetic waves by rough perfectly conducting circular cylinders," IEEE Trans. Antennas Propag. AP21, 893–895 (1973).

Davenport, W. B.

W. B. Davenport and W. L. Root, Random Signals and Noise (McGraw-Hill, New York, 1958), pp. 107–108.

Erdmann, J. C.

Evans, J. V.

J. V. Evans and Tor Hagfors, Radar Astronomy (McGraw- Hill, New York, 1968).

Gellart, R. I.

George, N.

Gould, G.

Hagfors, Tor

J. V. Evans and Tor Hagfors, Radar Astronomy (McGraw- Hill, New York, 1968).

Hiatt, R. E.

R. E. Hiatt, T. B. A. Senior, and V. H. Weston, "A Study of surface roughness and its effect on the backscattering cross section of spheres," IRE Proc. 48, 2008–2016 (1960).

Jacobs, S. F.

LaTourette, J. T.

Leader, J. C.

J. C. Leader, "An analysis of the spatial coherence of laser light scattered by a surface with two scales of roughness," J. Opt. Soc. Am. 66, 536–546 (1976).

J. C. Leader, "Hemispherical scattering of electromagnetic waves from rough surfaces," J. Opt. Soc. Am. 62, 1356 (1972). Also, McDonnell Aircraft Paper No. MCAIR-72-037.

J. C. Leader, "Bidirectional scattering of electromagnetic waves from rough surfaces," J. Appl. Phys. 42, 4808–4816 (1971).

Murphy, R. C.

H. S. Cabuyan and R. C. Murphy, "Scattering of electromagnetic waves by rough perfectly conducting circular cylinders," IEEE Trans. Antennas Propag. AP21, 893–895 (1973).

Newstein, M.

Rabinowtiz, P.

Root, W. L.

W. B. Davenport and W. L. Root, Random Signals and Noise (McGraw-Hill, New York, 1958), pp. 107–108.

Senior, T. B. A.

R. E. Hiatt, T. B. A. Senior, and V. H. Weston, "A Study of surface roughness and its effect on the backscattering cross section of spheres," IRE Proc. 48, 2008–2016 (1960).

Siegman, A. E.

A. E. Siegman, "The antenna properties of optical heterodyne receivers," IEEE Proc. 54, 1350–1356 (1966).

Spizzichino, A.

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, Oxford 1963).

Teich, M. C.

M. C. Teich, "Infrared heterodyne detection," IEEE Proc. 56, 37–46 (1968).

van Bladel, J.

J. van Bladel, "Electromagnetic fields in the presence of rotating bodies," IEEE Proc. 64, 301–318 (1976).

Weston, V. H.

R. E. Hiatt, T. B. A. Senior, and V. H. Weston, "A Study of surface roughness and its effect on the backscattering cross section of spheres," IRE Proc. 48, 2008–2016 (1960).

Yura, H. T.

Appl. Opt. (2)

IEEE Proc. (4)

D. R. Brillinger, "Fourier analysis of stationary processes," IEEE Proc. 62, 1628–1643 (1974).

A. E. Siegman, "The antenna properties of optical heterodyne receivers," IEEE Proc. 54, 1350–1356 (1966).

J. van Bladel, "Electromagnetic fields in the presence of rotating bodies," IEEE Proc. 64, 301–318 (1976).

M. C. Teich, "Infrared heterodyne detection," IEEE Proc. 56, 37–46 (1968).

IEEE Trans. Antennas Propag. (1)

H. S. Cabuyan and R. C. Murphy, "Scattering of electromagnetic waves by rough perfectly conducting circular cylinders," IEEE Trans. Antennas Propag. AP21, 893–895 (1973).

IRE Proc. (1)

R. E. Hiatt, T. B. A. Senior, and V. H. Weston, "A Study of surface roughness and its effect on the backscattering cross section of spheres," IRE Proc. 48, 2008–2016 (1960).

J. Appl. Phys. (1)

J. C. Leader, "Bidirectional scattering of electromagnetic waves from rough surfaces," J. Appl. Phys. 42, 4808–4816 (1971).

J. Opt. Soc. Am. (4)

Other (5)

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, Oxford 1963).

J. V. Evans and Tor Hagfors, Radar Astronomy (McGraw- Hill, New York, 1968).

W. B. Davenport and W. L. Root, Random Signals and Noise (McGraw-Hill, New York, 1958), pp. 107–108.

A more precise statement of the restrictions imposed on the antenna dimensions is provided by the two-dimensional "map" of maximum angular frequency variations W(fx max, fy max, Δ R, τ) ∼ d2 σj(2xp max/λ, 2λp max/λ; v¯)/dxpdyp.

A focused laser beam diameter of 50 µm was employed in the experiments described in Ref. 15. The experimental geometry resulted in a di value [Eq. (28)] of 0.5 mm. Thus in this case, the frequency broadening was primarily caused by the limited observation interval.

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