Al-Ithawi2017 Article CharacterizationOfAtmosphericO PDF
Al-Ithawi2017 Article CharacterizationOfAtmosphericO PDF
Al-Ithawi2017 Article CharacterizationOfAtmosphericO PDF
DOI 10.1007/s12596-017-0431-0
RESEARCH ARTICLE
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J Opt
Theory pupil, and when the apparent angle of the observed object
is large (r [ 10), the beams will be perturbed by com-
Fried parameter r0 pletely different atmospheric degradations, it results a
decorrelation of the wavefronts arriving on the pupil then is
In 1965 Fried proposed a so-called parameter of Fried, which spoken of anisoplanatism.
represents the spatial wavelength width of the perturbed The parameter h0 (isoplanatic angle) depends on the
wavefront. This parameter is defined as the meter that should altitude H, characteristic of the turbulent layers and the
have a telescope out of the atmosphere so that its resolution is parameter of Fried r0 by h0 = 0.314 r0/H, where H given by
equivalent to that imposed by the turbulence. R0 is expressed " #5=3
as a function of the optical energy of the turbulence char- r þ1
0 Cn2 ðhÞdh
H¼ ð3Þ
acterized by the constant of structure C2n (h) of the index r þa 2
0 Cn ðhÞdh
fluctuations Of air refraction given by Roddier [1].
Fried in 1982 showed that the isoplanatic angle corre-
2 33=5
Zþa sponds to the phase variance and which is expressed as a
r0 ¼ 416:7k 2
Cn ðhÞdh5
2
: ð1Þ function of the turbulence profile, and also the critical
0 angle from which the atmospheric degradation will change,
it is defined by the following relation:
A parameter expresses the quality of the image at the 3=5
Z þ1
focal point of a telescope corresponds to the width at half
h0 ¼ 2:905k2 Cn2 ðhÞdh ð4Þ
maximum of the diffraction spot was calculated by Dier- 0
ickx [17] as a function of the Fried parameter. It is the
seeing S defined by: S ¼ r0k r0 is a chromatic parameter and
The coherence time
varies in k5=6 (r0k5/6) while S is almost-achromatic and
varies in k1=6 (S ak-1/6). The coherence time s0 characterizes the time of evolution
of the deformations of the wavefront. The evolution of this
The external scale l0 parameter, depends on the distribution of the wind (direc-
tion, velocity) [13]
It defines the maximum size of wavefront disturbances that
s0 ¼ 0:314 r0 /v ð5Þ
remain consistent. The external scale l0 of the wavefront
coherence linked to the external scale characterizing the where V is the wind velocity for the observation of imaging
turbulent dynamics and the function of the turbulence with high angular resolution, the exposure time must be
optical energy characterized by the constant destructure less than the time of evolution of the turbulence.
$?? 2
0 Cn(h)dh
It is computed by the equation:
r þ1 L0Cn2 ðhÞdh The effects of turbulence
1=3 0
l0 ¼ ð2Þ
r þa 2
0 Cn ðhÞdh Scintillation
The domain of isoplanatic angle The most obvious manifestation of turbulence is the scin-
tillation of stars, which is observed by the human eye as the
The isoplanic field is defined as the field defined by the brightness of stars, also the change of the color of a single
isoplanatic angle h0 (the critical angle from which the star corresponds to fluctuations in amplitude of the wave
atmospheric degradation will change in the order of one to reaching the ground. In case of small telescopes, the
a few s from arc), where the angle of isoplanatic corre- scintillation is a random modulation of the overall inten-
sponds to the angle between two light beams coming from sity, but for large telescopes it contributed to the total
the same object. Since the beams do not pass the exact degradation of an image. Relatively the scintillation
same volume of turbulence, decorrelation of the phase as a depends on the profile of the refractive index C2n and to
function of the angular distance h, an important parameter quantify it we use the expression of the spectral density of
is the spatial separation of the beams at the altitude written the amplitude fluctuation. It is given by the model of
in the form: r = h h that is to say, if the angle is small Kolmogorov equation below:
Z þ1
(r \ 10), the turbulence layer is located near the pupil and
the beams pass through regions of identical turbulence for WA;0 ðf Þ ¼ 0:3870k 2
Cn2 ðhÞdhf 11=2 sin2 pkhf 2 ð6Þ
0
which the deformations of the wave fronts arriving at the
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Agitation
Instrumentation
Telescope
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The camera
Experimental part
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surface). It should be noted that the measurements are not 3. D.L. Fried, PASP 56, 1372 (1966)
sufficient enough and the fluxes are not very great, also the 4. S.M. Crawford, L. Catala, A. Ziad, M. Carbillet, Thesis, Faculty
of Science, University of Nice–Franch (2011)
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and the transverse r0 are not precise. For a site with little G. Prieto, R. Allen, D. Carona, in Proc. SPIE Vol. 7735, Ground-
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773574, 2010)
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possible. All this is more true as this study does not take Bustos, S. Els, R. Riddle, J. Seguel, T. Travouillon, J. Vasquez,
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light of the city of Nice. Roland, SPIE Conf. Montreal (2014) 9145
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Acknowledgements This work has been supported by the University A&A 491, 917 (2008)
of Nice Sophia Antipolis in the laboratory (Lagrange) and Calern 12. C.U. Keller, R. Navarro, B.R. Brandl, Field Guide to Astro-
observatory Nice, France. Special thanks to the authors Aziz Ziad for nomical Instrumentation (2015)
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