Abstract

When a slightly divergent laser beam passes through a turbulent ground level atmosphere and strikes a linear grating, fluctuating self-images are formed at Talbot distances. By superimposing a similar grating on one of the self-images, even for the case of parallel gratings’ lines, fluctuating moiré fringes are formed owing to the beam divergence. Recording the successive moiré patterns by a CCD camera and feeding them to a computer, after filtering the higher spatial frequencies, produces highly magnified fluctuations of the laser beam. Using moiré fringe fluctuations we have calculated the fluctuations of the angle of arrival and the atmospheric refractive index structure constant. The implementation of the technique is straightforward, a telescope is not required, fluctuations can be magnified more than ten times, and the precision of the technique is similar to that reported in our previous work.

© 2008 Optical Society of America

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References

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  1. M. Sarazin and F. Roddier, Astron. Astrophys. 227, 294 (1990).
  2. A. Ziad, R. Conan, A. Tokovinin, F. Martin, and J. Borgnino, Appl. Opt. 39, 5415 (2000).
    [CrossRef]
  3. M. S. Belen'kii, J. M. Stewart, and P. Gillespie, Appl. Opt. 40, 1321 (2001).
    [CrossRef]
  4. S. Rasouli and M. T. Tavassoly, Opt. Lett. 31, 3276 (2006).
    [CrossRef] [PubMed]
  5. S. Rasouli and M. T. Tavassoly, Proc. SPIE 6364, 63640G (2006).
    [CrossRef]
  6. S. Rasouli, K. Madanipour, and M. T. Tavassoly, Proc. SPIE 6364, 63640K (2006).
    [CrossRef]
  7. J. Stricker, and B. Zakharin, Exp. Fluids 23, 76 (1997).
    [CrossRef]
  8. I. Glatt and O. Kafri, Chem. Eng. Sci. 39, 1637 (1984).
    [CrossRef]
  9. K. Patorski, Handbook of the Moiré Fringe Technique (Elsevier, 1993).
  10. R. J. Sasiela and J. D. Shelton, J. Opt. Soc. Am. A 10, 646 (1993).
    [CrossRef]

2006 (3)

S. Rasouli and M. T. Tavassoly, Opt. Lett. 31, 3276 (2006).
[CrossRef] [PubMed]

S. Rasouli and M. T. Tavassoly, Proc. SPIE 6364, 63640G (2006).
[CrossRef]

S. Rasouli, K. Madanipour, and M. T. Tavassoly, Proc. SPIE 6364, 63640K (2006).
[CrossRef]

2001 (1)

2000 (1)

1997 (1)

J. Stricker, and B. Zakharin, Exp. Fluids 23, 76 (1997).
[CrossRef]

1993 (1)

1990 (1)

M. Sarazin and F. Roddier, Astron. Astrophys. 227, 294 (1990).

1984 (1)

I. Glatt and O. Kafri, Chem. Eng. Sci. 39, 1637 (1984).
[CrossRef]

Belen'kii, M. S.

Borgnino, J.

Conan, R.

Gillespie, P.

Glatt, I.

I. Glatt and O. Kafri, Chem. Eng. Sci. 39, 1637 (1984).
[CrossRef]

Kafri, O.

I. Glatt and O. Kafri, Chem. Eng. Sci. 39, 1637 (1984).
[CrossRef]

Madanipour, K.

S. Rasouli, K. Madanipour, and M. T. Tavassoly, Proc. SPIE 6364, 63640K (2006).
[CrossRef]

Martin, F.

Patorski, K.

K. Patorski, Handbook of the Moiré Fringe Technique (Elsevier, 1993).

Rasouli, S.

S. Rasouli, K. Madanipour, and M. T. Tavassoly, Proc. SPIE 6364, 63640K (2006).
[CrossRef]

S. Rasouli and M. T. Tavassoly, Proc. SPIE 6364, 63640G (2006).
[CrossRef]

S. Rasouli and M. T. Tavassoly, Opt. Lett. 31, 3276 (2006).
[CrossRef] [PubMed]

Roddier, F.

M. Sarazin and F. Roddier, Astron. Astrophys. 227, 294 (1990).

Sarazin, M.

M. Sarazin and F. Roddier, Astron. Astrophys. 227, 294 (1990).

Sasiela, R. J.

Shelton, J. D.

Stewart, J. M.

Stricker, J.

J. Stricker, and B. Zakharin, Exp. Fluids 23, 76 (1997).
[CrossRef]

Tavassoly, M. T.

S. Rasouli, K. Madanipour, and M. T. Tavassoly, Proc. SPIE 6364, 63640K (2006).
[CrossRef]

S. Rasouli and M. T. Tavassoly, Proc. SPIE 6364, 63640G (2006).
[CrossRef]

S. Rasouli and M. T. Tavassoly, Opt. Lett. 31, 3276 (2006).
[CrossRef] [PubMed]

Tokovinin, A.

Zakharin, B.

J. Stricker, and B. Zakharin, Exp. Fluids 23, 76 (1997).
[CrossRef]

Ziad, A.

Appl. Opt. (2)

Astron. Astrophys. (1)

M. Sarazin and F. Roddier, Astron. Astrophys. 227, 294 (1990).

Chem. Eng. Sci. (1)

I. Glatt and O. Kafri, Chem. Eng. Sci. 39, 1637 (1984).
[CrossRef]

Exp. Fluids (1)

J. Stricker, and B. Zakharin, Exp. Fluids 23, 76 (1997).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Lett. (1)

Proc. SPIE (2)

S. Rasouli and M. T. Tavassoly, Proc. SPIE 6364, 63640G (2006).
[CrossRef]

S. Rasouli, K. Madanipour, and M. T. Tavassoly, Proc. SPIE 6364, 63640K (2006).
[CrossRef]

Other (1)

K. Patorski, Handbook of the Moiré Fringe Technique (Elsevier, 1993).

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Figures (3)

Fig. 1
Fig. 1

Schematic of the experimental setup. D . F . , G 1 , G 2 , L 1 , and S . F . represent the neutral density filter, first grating, second grating, Fourier transforming lens, and the spatial filter, respectively.

Fig. 2
Fig. 2

(a) Typical moiré pattern and (b) the corresponding low-frequency illumination distribution.

Fig. 3
Fig. 3

(a) and (c) Typical horizontal components of AA fluctuations at a point on the first grating versus time for two sets of data obtained at two different turbulence conditions. (b) and (d) Mean values of the AA fluctuations of the wavefront on the first grating surface corresponding to (a) and (c), respectively.

Equations (9)

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

2 k d 2 λ = L Z k L + Z k ,
L d = L + Z k d + δ d
Z k = L d δ d .
d m = d 2 δ d .
s = d m d l .
α = l Z k .
α = s L .
α = s d m d Z k
C n 2 = σ α 2 D 1 3 1.14 L f ( L 0 D ) ,

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