Abstract

There are several methods for measuring ground-level atmospheric turbulence parameters, such as the refractive index profile and its fluctuations, correlations of the fluctuations in space and time, and the atmospheric refractive-index structure constant. These methods are based mainly on the measurement of fluctuations in intensity and location of an image formed by light propagating in the turbulent atmosphere or the fluctuations in impinging points of narrow light beams traversing the ground-level atmosphere. Exploiting the moiré technique, we suggest a high-precision approach for determining fluctuaions in the angle of arrival. When a low-frequency grating (carrier grating) is installed at a suitable distance from a telescope, its image, practically, forms on the focal plane of the telescope objective. Superimposing a physical grating (probe grating) of the same pitch as the image grating on the image forms the moiré pattern. The atmospheric turbulence distorts the image grating. Processing the fluctuations of successive moiré fringes can yield the mentioned parameters across a rather large cross section of the atmosphere with high accuracy, because of the moiré technique's magnifying character and access to a large volume of data, and does so in a comparatively simple and reliable manner.

© 2006 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. A. S. Gurvich, I. S. Starobints, and K. A. O'Donnell, Izv. Akad. Nauk, Fiz. Atmos. Okeana 10, 413 (1974).
  5. K. Patorski, Handbook of the Moiré Fringe Technique (Elsevier, 1993).
  6. R. J. Sasiela and J. D. Shelton, J. Opt. Soc. Am. A 10, 646 (1993).
    [CrossRef]
  7. V. I. Tatarskii, Wave Propagation in a Turbulent Atmosphere (McGraw-Hill, 1961).
  8. S. Rasouli and M. T. Tavassoly, "Measurement of the refractive-index structure constant, and its profile in the ground-level atmosphere by moiré technique," in Proc. SPIE, 6364 (to be published).

2001 (1)

2000 (1)

1993 (1)

1990 (1)

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

1974 (1)

A. S. Gurvich, I. S. Starobints, and K. A. O'Donnell, Izv. Akad. Nauk, Fiz. Atmos. Okeana 10, 413 (1974).

Belen'kii, M. S.

Borgnino, J.

Conan, R.

Gillespie, P.

Gurvich, A. S.

A. S. Gurvich, I. S. Starobints, and K. A. O'Donnell, Izv. Akad. Nauk, Fiz. Atmos. Okeana 10, 413 (1974).

Martin, F.

O'Donnell, K. A.

A. S. Gurvich, I. S. Starobints, and K. A. O'Donnell, Izv. Akad. Nauk, Fiz. Atmos. Okeana 10, 413 (1974).

Patorski, K.

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

Rasouli, S.

S. Rasouli and M. T. Tavassoly, "Measurement of the refractive-index structure constant, and its profile in the ground-level atmosphere by moiré technique," in Proc. SPIE, 6364 (to be published).

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.

Starobints, I. S.

A. S. Gurvich, I. S. Starobints, and K. A. O'Donnell, Izv. Akad. Nauk, Fiz. Atmos. Okeana 10, 413 (1974).

Stewart, J. M.

Tatarskii, V. I.

V. I. Tatarskii, Wave Propagation in a Turbulent Atmosphere (McGraw-Hill, 1961).

Tavassoly, M. T.

S. Rasouli and M. T. Tavassoly, "Measurement of the refractive-index structure constant, and its profile in the ground-level atmosphere by moiré technique," in Proc. SPIE, 6364 (to be published).

Tokovinin, A.

Ziad, A.

Appl. Opt. (2)

Astron. Astrophys. (1)

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

Izv. Akad. Nauk, Fiz. Atmos. Okeana (1)

A. S. Gurvich, I. S. Starobints, and K. A. O'Donnell, Izv. Akad. Nauk, Fiz. Atmos. Okeana 10, 413 (1974).

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

Other (3)

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

V. I. Tatarskii, Wave Propagation in a Turbulent Atmosphere (McGraw-Hill, 1961).

S. Rasouli and M. T. Tavassoly, "Measurement of the refractive-index structure constant, and its profile in the ground-level atmosphere by moiré technique," in Proc. SPIE, 6364 (to be published).

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of the experimental setup.

Fig. 2
Fig. 2

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

Fig. 3
Fig. 3

(a) Sample moiré dark fringe, (b) low-frequency illumination distribution on the area containing the dark fringe, (c) derived trace of the dark fringe.

Fig. 4
Fig. 4

Typical vertical components of AA fluctuations at two arbitrary points of equal altitude versus time for two sets of data obtained under different turbulence conditions.

Fig. 5
Fig. 5

Refractive index structure constant profiles near the Earth's surface versus altitude, for two different turbulence conditions.

Equations (5)

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

e ¯ [ i ] = 1 N j = 1 N e [ i , j ] ,
σ s [ i ] = { 1 N 1 j = 1 N ( s [ i , j ] ) 2 } 1 2 .
s = ( d m d ) l ,
α [ i , j ] = 1 F d d m s [ i , j ] ,
C n 2 [ i ] = σ α 2 [ i ] D 1 3 1.14 L f ( L 0 D ) ,

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