Abstract

The cross-flow orientation of an optically active turbulent field was determined by Fourier transforming the wander of a laser beam propagating in the ocean. A simple physical model for the measured effect is offered, and numerical simulations are performed. The simulations are in good agreement with measurements, validating the assumptions made in the model.

© 2013 Optical Society of America

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References

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  1. G. Benedetti-Michelangeli, F. Congeduti, and G. Fiocco, J. Atmos. Sci. 29, 906 (1972).
    [CrossRef]
  2. T. Wang, G. R. Ochs, and R. S. Lawrence, Appl. Opt. 20, 4073 (1981).
    [CrossRef]
  3. D. A. Dewolf, Radio Sci. 18, 138 (1983).
    [CrossRef]
  4. G. I. Taylor, Proc. R. Soc. London Ser. A 164, 0476 (1938).
    [CrossRef]
  5. L. C. Andrews, R. L. Phillips, R. J. Sasiela, and R. R. Parenti, Opt. Eng. 45, 076001 (2006).
    [CrossRef]
  6. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).
  7. J. W. Goodman, Introduction to Fourier Optics (Roberts & Co, 2005).
  8. W. Hou, E. Jarosz, F. Dalgleish, G. Nootz, S. Woods, A. D. Weidemann, W. Goode, A. Vuorenkoski, B. Metzger, and B. Ramos, Proc. SPIE 8372, 837206 (2012).
    [CrossRef]
  9. G. Nootz, Harbor Branch, Florida Atlantic University, 5600 US 1, Fort Pierce, Florida, USA, W. Hou and F. R. Dalgleish are preparing a manuscript to be called “The effect of optical turbulence on the propagation of light beams in the ocean.”
  10. V. V. Nikishov and V. I. Nikishov, Fluid Mech. Res. 27, 82 (2000).

2012

W. Hou, E. Jarosz, F. Dalgleish, G. Nootz, S. Woods, A. D. Weidemann, W. Goode, A. Vuorenkoski, B. Metzger, and B. Ramos, Proc. SPIE 8372, 837206 (2012).
[CrossRef]

2006

L. C. Andrews, R. L. Phillips, R. J. Sasiela, and R. R. Parenti, Opt. Eng. 45, 076001 (2006).
[CrossRef]

2000

V. V. Nikishov and V. I. Nikishov, Fluid Mech. Res. 27, 82 (2000).

1983

D. A. Dewolf, Radio Sci. 18, 138 (1983).
[CrossRef]

1981

1972

G. Benedetti-Michelangeli, F. Congeduti, and G. Fiocco, J. Atmos. Sci. 29, 906 (1972).
[CrossRef]

1938

G. I. Taylor, Proc. R. Soc. London Ser. A 164, 0476 (1938).
[CrossRef]

Andrews, L. C.

L. C. Andrews, R. L. Phillips, R. J. Sasiela, and R. R. Parenti, Opt. Eng. 45, 076001 (2006).
[CrossRef]

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).

Benedetti-Michelangeli, G.

G. Benedetti-Michelangeli, F. Congeduti, and G. Fiocco, J. Atmos. Sci. 29, 906 (1972).
[CrossRef]

Congeduti, F.

G. Benedetti-Michelangeli, F. Congeduti, and G. Fiocco, J. Atmos. Sci. 29, 906 (1972).
[CrossRef]

Dalgleish, F.

W. Hou, E. Jarosz, F. Dalgleish, G. Nootz, S. Woods, A. D. Weidemann, W. Goode, A. Vuorenkoski, B. Metzger, and B. Ramos, Proc. SPIE 8372, 837206 (2012).
[CrossRef]

Dalgleish, F. R.

G. Nootz, Harbor Branch, Florida Atlantic University, 5600 US 1, Fort Pierce, Florida, USA, W. Hou and F. R. Dalgleish are preparing a manuscript to be called “The effect of optical turbulence on the propagation of light beams in the ocean.”

Dewolf, D. A.

D. A. Dewolf, Radio Sci. 18, 138 (1983).
[CrossRef]

Fiocco, G.

G. Benedetti-Michelangeli, F. Congeduti, and G. Fiocco, J. Atmos. Sci. 29, 906 (1972).
[CrossRef]

Goode, W.

W. Hou, E. Jarosz, F. Dalgleish, G. Nootz, S. Woods, A. D. Weidemann, W. Goode, A. Vuorenkoski, B. Metzger, and B. Ramos, Proc. SPIE 8372, 837206 (2012).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (Roberts & Co, 2005).

Hou, W.

W. Hou, E. Jarosz, F. Dalgleish, G. Nootz, S. Woods, A. D. Weidemann, W. Goode, A. Vuorenkoski, B. Metzger, and B. Ramos, Proc. SPIE 8372, 837206 (2012).
[CrossRef]

G. Nootz, Harbor Branch, Florida Atlantic University, 5600 US 1, Fort Pierce, Florida, USA, W. Hou and F. R. Dalgleish are preparing a manuscript to be called “The effect of optical turbulence on the propagation of light beams in the ocean.”

Jarosz, E.

W. Hou, E. Jarosz, F. Dalgleish, G. Nootz, S. Woods, A. D. Weidemann, W. Goode, A. Vuorenkoski, B. Metzger, and B. Ramos, Proc. SPIE 8372, 837206 (2012).
[CrossRef]

Lawrence, R. S.

Metzger, B.

W. Hou, E. Jarosz, F. Dalgleish, G. Nootz, S. Woods, A. D. Weidemann, W. Goode, A. Vuorenkoski, B. Metzger, and B. Ramos, Proc. SPIE 8372, 837206 (2012).
[CrossRef]

Nikishov, V. I.

V. V. Nikishov and V. I. Nikishov, Fluid Mech. Res. 27, 82 (2000).

Nikishov, V. V.

V. V. Nikishov and V. I. Nikishov, Fluid Mech. Res. 27, 82 (2000).

Nootz, G.

W. Hou, E. Jarosz, F. Dalgleish, G. Nootz, S. Woods, A. D. Weidemann, W. Goode, A. Vuorenkoski, B. Metzger, and B. Ramos, Proc. SPIE 8372, 837206 (2012).
[CrossRef]

G. Nootz, Harbor Branch, Florida Atlantic University, 5600 US 1, Fort Pierce, Florida, USA, W. Hou and F. R. Dalgleish are preparing a manuscript to be called “The effect of optical turbulence on the propagation of light beams in the ocean.”

Ochs, G. R.

Parenti, R. R.

L. C. Andrews, R. L. Phillips, R. J. Sasiela, and R. R. Parenti, Opt. Eng. 45, 076001 (2006).
[CrossRef]

Phillips, R. L.

L. C. Andrews, R. L. Phillips, R. J. Sasiela, and R. R. Parenti, Opt. Eng. 45, 076001 (2006).
[CrossRef]

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).

Ramos, B.

W. Hou, E. Jarosz, F. Dalgleish, G. Nootz, S. Woods, A. D. Weidemann, W. Goode, A. Vuorenkoski, B. Metzger, and B. Ramos, Proc. SPIE 8372, 837206 (2012).
[CrossRef]

Sasiela, R. J.

L. C. Andrews, R. L. Phillips, R. J. Sasiela, and R. R. Parenti, Opt. Eng. 45, 076001 (2006).
[CrossRef]

Taylor, G. I.

G. I. Taylor, Proc. R. Soc. London Ser. A 164, 0476 (1938).
[CrossRef]

Vuorenkoski, A.

W. Hou, E. Jarosz, F. Dalgleish, G. Nootz, S. Woods, A. D. Weidemann, W. Goode, A. Vuorenkoski, B. Metzger, and B. Ramos, Proc. SPIE 8372, 837206 (2012).
[CrossRef]

Wang, T.

Weidemann, A. D.

W. Hou, E. Jarosz, F. Dalgleish, G. Nootz, S. Woods, A. D. Weidemann, W. Goode, A. Vuorenkoski, B. Metzger, and B. Ramos, Proc. SPIE 8372, 837206 (2012).
[CrossRef]

Woods, S.

W. Hou, E. Jarosz, F. Dalgleish, G. Nootz, S. Woods, A. D. Weidemann, W. Goode, A. Vuorenkoski, B. Metzger, and B. Ramos, Proc. SPIE 8372, 837206 (2012).
[CrossRef]

Appl. Opt.

Fluid Mech. Res.

V. V. Nikishov and V. I. Nikishov, Fluid Mech. Res. 27, 82 (2000).

J. Atmos. Sci.

G. Benedetti-Michelangeli, F. Congeduti, and G. Fiocco, J. Atmos. Sci. 29, 906 (1972).
[CrossRef]

Opt. Eng.

L. C. Andrews, R. L. Phillips, R. J. Sasiela, and R. R. Parenti, Opt. Eng. 45, 076001 (2006).
[CrossRef]

Proc. R. Soc. London Ser. A

G. I. Taylor, Proc. R. Soc. London Ser. A 164, 0476 (1938).
[CrossRef]

Proc. SPIE

W. Hou, E. Jarosz, F. Dalgleish, G. Nootz, S. Woods, A. D. Weidemann, W. Goode, A. Vuorenkoski, B. Metzger, and B. Ramos, Proc. SPIE 8372, 837206 (2012).
[CrossRef]

Radio Sci.

D. A. Dewolf, Radio Sci. 18, 138 (1983).
[CrossRef]

Other

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).

J. W. Goodman, Introduction to Fourier Optics (Roberts & Co, 2005).

G. Nootz, Harbor Branch, Florida Atlantic University, 5600 US 1, Fort Pierce, Florida, USA, W. Hou and F. R. Dalgleish are preparing a manuscript to be called “The effect of optical turbulence on the propagation of light beams in the ocean.”

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Figures (4)

Fig. 1.
Fig. 1.

Left side: beam deflection perpendicular to the flow caused by a single turbulent cell with index of refraction nc<ns if the cell is offset slightly to the right of the beam (flow direction into page). On the right, the beam deflection parallel to the flow direction is shown for a cell entering the beam from the right and flowing to the left. Graphs on top show the beam deflection in time as well as the amplitude of the Fourier transform for the situation depicted on the right and on the left, respectively.

Fig. 2.
Fig. 2.

(a) Experimental setup. (b) Individual laser beams as recorded by the camera from the back of the ground glass plate.

Fig. 3.
Fig. 3.

Simulated beam deflection data on the left and field measurements on the right. Red lines (upper trace) on the top represent beam deflection perpendicular to the flow direction and black lines (lower trace) are beam deflection parallel to the flow direction of a single beam. Middle figures show the averaged fast Fourier transform (FFT) amplitudes of 13 beams parallel and perpendicular to the flow direction in black (lower trace) and red (upper trace), respectively. Bottom graphs show the amplitude of the FFT calculated for angles from 0° to 360° with respect to the flow direction.

Fig. 4.
Fig. 4.

Histograms of beam centroid position as recorded during BOTEX. The red bars show data at 0° and 90° with respect to the flow orientation. Also shown is a Gaussian fit to the distributions (blue lines) and the variance in terms of full width at half-maximum (FWHM). The small difference in the variance is not correlated to the flow orientation as can be found by comparing the numbers at different measurement depth (data not shown).

Equations (2)

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|F(g(ta))|=|F(g(t))eiωa|=|F(g(t))|.
F(g)=g(t)eiωtdt=iωg(t)eiωtdt=iωF(g).

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