Method and device for evaluating parameters characterizing atmospheric turbulence
A method for characterizing the atmospheric turbulence, includes acquiring images of a celestial object by means of a camera coupled to a small telescope; analyzing the acquired images to determine angle of arrival fluctuations of wavefronts from positions of spots formed by the celestial object in the acquired images; determining variances of the angle of arrival fluctuations; and estimating the Fried parameter from the variances of the angle of arrival fluctuations, by setting an outer scale parameter of the atmospheric turbulence to a fixed median value.
1 . A method for characterizing atmospheric turbulence comprising:
acquiring images (SIM) of a celestial object (PS, CB) by means of a camera (CM) of CCD (Charge-Coupled Device) type, said camera (CM) is coupled to a telescope (T) of Cassegrain type, and a Barlow lens (B) is inserted between the telescope (T) and the camera (CM) to extend the focal length of the telescope T; said images (SIM) acquired by the camera (CM) are received and processed by a processing card being (PRC) arranged for:
analyzing the acquired images to determine a time series of an angle of arrival fluctuations of wavefronts in x and y directions from positions of at least one spot (IPS, P 1 , P 2 ) formed by the celestial object in the acquired images;
determining variances of the angle of arrival fluctuations; and
estimating the atmospheric turbulence by determining a Fried parameter (r 0 ), from the variances of the angle of arrival fluctuations, by setting an outer scale parameter (L 0 ) of the atmospheric turbulence to a fixed median value of 20 m plus or minus 10%, wherein the at least one spot is formed by Polaris to which the telescope is rigidly pointed.
2 . The method of claim 1 , wherein the telescope (T) is rigidly secured to a fixed support in a direction toward Polaris.
3 . The method of claim 2 , wherein the Fried parameter is estimated from the following equation:
σ
2
=
0.18
λ
2
r
0
-
1
/
3
(
D
-
1
/
3
-
1.525
L
0
-
1
/
3
)
wherein σ 2 is the variance of the angle of arrival fluctuations, λ is the wavelength of the light emitted by Polaris, r 0 is the Fried parameter, D is an aperture diameter of the telescope (T), and L 0 is the outer scale parameter.
4 . The method of claim 1 , wherein the acquired images are analyzed in a limited region around analyzed points (IPS, P 1 , P 2 ) formed by Polaris.
5 . The method of claim 1 , wherein the variance of the angle of arrival fluctuations is multiplied by cos(z), z being an angle between the direction of Polaris and the zenithal direction, at an observation site where the images are acquired.
6 . The method of claim 1 , wherein the images are acquired by the camera (CM) at an image rate of 50 to 200 images/s.
7 . A device configured to implement the method of claim 1 , to analyze images (SIM) acquired by the camera (CM) of the CCD (Charge-Coupled Device) type coupled to the telescope (T) of the Cassegrain type pointed at Polaris.
8 . The device of claim 7 , comprising the camera (CM) coupled to the telescope (T), and the processing card (PRC) receiving and processing images acquired by the camera.
9 . The device of claim 8 , wherein the telescope (T) has at least one of the following features:
it has an aperture diameter set to a value between 4 and 12 cm,
the Barlow lens (B) interfaces with the camera (CM) to increase the focal length (F) of the telescope.
10 . A non-transitory computer-readable storage medium storing a program that, when executed by a computer, causes said computer to perform said method according to claim 1 , to analyze images (SIM) acquired by the camera (CM) coupled to the telescope (T) pointed at Polaris.
11 . The device of claim 7 , wherein an optical path passes through the telescope (T) and the Barlow lens (B) to an image sensor (IS) of the camera (CM).
12 . A method for characterizing atmospheric turbulence comprising:
acquiring images of a celestial object by means of a camera coupled to a telescope; said images (SIM) acquired by a camera (CM) of CCD (Charge-Coupled Device) type, said camera is couple to a telescope (T) of Cassegrain type, and a Barlow lens (B) is inserted between the telescope (T) and the camera (CM) to extend the focal length of the telescope (T); said images (SIM) acquired by the camera (CM) are received and processed by a processing card (PRC) being arranged for:
analyzing the acquired images to determine a time series of an angle of arrival fluctuations of wavefronts in x and y directions from positions of at least one spot formed by the celestial object in the acquired images;
determining variances of the angle of arrival fluctuations; and
estimating the atmospheric turbulence by determining a Fried parameter (r 0 ), from the variances of the angle of arrival fluctuations, by setting an outer scale parameter (L 0 ) of the atmospheric turbulence to a fixed median value of 20 m plus or minus 10%, wherein the at least one spot is formed by Polaris to which the telescope is rigidly pointed.
13 . The method of claim 12 , wherein the telescope (T) is fixed on a mount and oriented towards the Moon or Sun limb (SML), the mount being motorized and controlled to compensate rotation of the Earth about its rotation axis, and the method further comprises:
analyzing the acquired images to determine the angle of arrival fluctuations of light positions of two spots (P 1 , P 2 ) spaced apart from each other on the Moon or Sun limb.
14 . The method of claim 13 , wherein the Fried parameter is estimated from the following equation:
D
α
,
s
(
θ
h
-
)
=
0.3
6
4
λ
2
r
0
-
5
/
3
D
-
1
/
3
[
1
-
0.7
9
8
(
θ
h
-
D
)
-
1
/
3
]
wherein h is the equivalent altitude of the whole atmospheric turbulence, λ is the wavelength of the light emitted by the observed limb, r 0 is the Fried parameter, D is an aperture diameter of the telescope (T), θ is an angular separation between two viewing angles θ 1 and θ 2 of considered points (P 1 , P 2 ) of the observed limb (SML), α(θ 1 ) and α(θ 2 ) are angle of arrival fluctuations at the two considered points, and D α,s (θh) is a spatial structure function of angle of arrival fluctuations α for the angular separation θ.
15 . The method of claim 14 , wherein the equivalent altitude h of the whole atmospheric turbulence is deduced from the following equation:
D
α
,
s
(
θ
a
h
-
)
D
α
,
s
(
θ
b
h
-
)
≃
D
-
1
/
3
-
0.798
(
θ
a
h
-
)
-
1
/
3
D
-
1
/
3
-
0.798
(
θ
b
h
-
)
-
1
/
3
wherein θ a and θ b are angular separations of two considered pairs of points (P 1 , P 2 ) on the observed limb (SML), and D α,s (θ a h) and D α,s (θ b h) are values of the spatial structure function (D α,s ) of angle of arrival fluctuations for the two angular separations θ a and θ b .