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Efficiency of off-axis astronomical adaptive systems: comparison of experimental data for different astronomical sites L.J. Sáncheza*, V.V. Voitsekhovicha, V.G. Orlova, R. Ávilab and S. Cuevasa a
Instituto de Astronomía - UNAM, Apdo. Postal 70-264, Cd. Universitaria, 04510 México D.F. México. b Instituto de Astronomía - UNAM, J. J. Tablada 1006, Morelia, 58090 Michoacán, México. ABSTRACT
The efficiency of off-axis adaptive astronomical systems is estimated for four astronomical sites: Paranal (Chili), Roque de los Muchachos (Canary Islands), San Pedro Mártir (México) and Observatoire de Haute Provence (France). The efficiency of interest is considered through the Strehl ratio of the corrected image calculated for V, J and K bands and for 8-m class telescopes. The experimental optical turbulence strength Cn ( z ) profiles necessary for calculations have been measured with 2
balloon flights and with the Generalized Scidar. It is found that this efficiency depends mainly on the Cn ( z ) profile layered 2
structure and on the turbulence strength. Keywords: atmospheric effects, instrumentation: adaptive optics, site testing, telescopes
1. INTRODUCTION The off-axis adaptive correction is of practical importance for the observational astronomy because it allows to improve the image quality in wide-field observations. However the efficiency of off-axis correction decrease with the increasing of the angular separation between the guide and observed stars, because the light from two stars passes through different paths of the turbulent atmosphere. As a result, the image quality of the observed star becomes worse and worse with the increasing of the star separation due to the progressive decorrelation between the wavefronts produced by the stars. The theoretical treatment allowing to estimate the efficiency of off-axis correction through the long-exposure Strehl ratio SR of the image of the observed star has been suggested in Voitsekhovich et al 1. It has been shown that for the case of the perfect adaptive correction this parameter can be expressed as
SR =
(
)
16 1 1 dξξ arccos ξ − ξ 1 − ξ 2 exp − DSR (ξ D ) . ∫ π 0 2
(1)
In Eq. (1) D is the telescope diameter, and DS R denotes the residual structure function given by ∞ 5 1 4rγ z 53 DSR = 5.83k 2 ∫ dzCn2 ( z ) × r 5 3 + (γ z ) 2 F1 − , ; 2 0 6 2 (r + γ z )
*
Correspondance to: L.J. Sánchez -
[email protected]
(2)
where k is the wavenumber, Cn ( z ) is the vertical profile of the refractive index structure characteristic (or optical 2
turbulence strength), γ denotes the angular separation between the guide and observed stars, and 2 F1 denotes the Gauss hypergeometric function. As one can see from Eqs. (1, 2), the efficiency of interest depends not only on the star separation, but also on the profile
Cn2 ( z ) which shows how the optical turbulence strength is changing with the altitude. The Cn2 ( z ) profile is also a function
of the observation site, and its magnitude and functional behavior may vary quite strongly from one observatory to another and also, for the same site, within particular astroclimatic conditions. So, it is of practical interest to compare the efficiency of
off-axis correction for different astronomical sites for which the corresponding Cn ( z ) data are available. 2
In this communication we will calculate the efficiency of interest for four astronomical observatories: Paranal (Chili), Roque de Los Muchachos (Canary Islands), San Pedro Mártir (SPM, México) and Observatoire de Haute Provence (OHP, France). The Cn ( z ) profiles were measured by J. Vernin team from University of Nice Astrophysics Department using Generalized 2
Scidar (SPM profiles) and balloon techniques2. In the Section 2 we give a brief description of both techniques, while Section 3 presents the calculation results and conclusions.
2. EXPERIMENTAL TECHNIQUES USED FOR Cn2 ( z ) MEASUREMENTS 2.1 Introduction The image degradation produced by atmospheric turbulence can be characterized by the so-called Fried's parameter3 r0 . The parameter r0 is an integral characteristic of the optical turbulence strength along the propagation path and it takes into account the overall effect of all the turbulent layers on the image degradation. In order to give the reader a feeling for the magnitude of the above quantities, a typical value of r0 = 10 cm would produce a point spread function of about one arcsecond at visible wavelengths. Temperature inhomogeneities which are generated in turbulent layers are responsible for local variations in the refractive index which perturb the propagation of incident lightwaves. The parameter which gives a measure of the local optical turbulence strength is the profile of the refractive index structure characteristic Cn ( z ) . The relationship between 2
Cn2 ( z ) and r0 was given by Fried3 via the expression: ∞ r0 (λ ) = 16.7λ −2 ∫ Cn2 ( z ) dz , 0
(3)
where λ is the wavelength. The Fried parameter r0 is sufficient for the description of many phenomena related with the wave propagation through the turbulent atmosphere. However, as one can see from Eqs. (1, 2), it is not a case for our problem because in order to estimate the efficiency of off-axis correction one needs to have a local information about the optical turbulence strength along the
propagation path: Cn ( z ) profile. We present below a brief description of two experimental techniques which allow to 2
measure this profile. 2.2 Generalized Scidar (G-SCIDAR) Cn ( z ) data 2
Avila et al.2,4,5 presented the first experimental implementation and results of the G-SCIDAR, the concept which was introduced by Fuchs6,7. For completeness, we give here a brief overview of the G-SCIDAR data acquisition.
The experimental Cn ( z ) profile used here (Fig. 1) is the median of 800 profiles obtained during three nights at the 2.1 m 2
telescope of San Pedro Mártir observatory, Baja California, México, in April 1997. A detailed description of this observing campaign is presented in Avila et al.5 The measurements were accomplished with the Generalized Scidar (G-SCIDAR) which was suggested by Fuchs 6,7 as a generalized version of the Scidar technique originally proposed by Rocca et al. 8 The data reduction consists of computing the spatial autocorrelation function of short exposure-time images of the scintillation pattern which is produced by a double star detected on a virtual plane a few kilometers beneath the pupil. A maximum entropy algorithm is used to retrieve the Cn ( z ) profile from the measured autocorrelation function. 2
The altitude resolution of G-SCIDAR profiles is proportional to the angular separation of the observed double star. The profile used here is obtained from the observation of double stars with different separations, resulting in an average altitude resolution of approximately 500 m.
Fig. 1 San Pedro Mártir experimental
Cn2 ( z ) profile from G-SCIDAR data. The corresponding Fried parameter is 16 cm (for wavelength
centered at 0.55 µm ).
2.3 Instrumented Balloon Cn ( z ) data 2
The acquisition of balloon data involves the launching of meteorological balloons equipped with sensors which measure the microstructure of the thermal field during their free flight ascent. They sample the atmosphere from the ground level up to about 25 km. The temperature structure function is defined as:
DT (r ) =
(T ( x ) − T ( x + r ))
and assessed by means of a couple of sensors separated by a distance r.
2
(4)
One can deduce the temperature structure constant profile CT ( z ) by : 2
DT (r , z ) = CT2 ( z ) r 2 3.
(5)
CT2 ( z ) and Cn2 ( z ) can be linked by virtue of the known mean pressure and temperature P and T , which are also measured on board: 2
P (z ) C ( z ) = C ( z ) 80 × 10−6 . 2 T ( z ) 2 n
2 T
(6)
The statistical computation of the structure function is performed electronically on board, in real time during the flight and the structure function is simultaneously calculated for two distinct separations. In so doing, two independent estimations of
Cn2 ( z ) are obtained. The electronic computation on board is able to transmit time, pressure, temperature and humidity Rh.
At a 1.5 s duty cycle, the whole set of information is sent to a ground receiver. The ascent speed being of the order of 4 m/s the effective vertical resolution is 6 m. We thus have at each 6 m height interval, D T(0.3 m,h), DT(0.95 m,h), P , T , Rh. From all of these measurements one can obtain a set of extremely valuable astrophysical and geophysical parameters, among
these the Cn ( z ) profile. In Fig. 2a-c we present the three Cn ( z ) profiles used for our efficiency calculation on each one of 2
2
the observatory sites choose for this calculations.. It has been shown that both techniques provide very similar results (Avila et al.2,4), but G-SCIDAR measurements are significantly cheaper and easier to obtain.
3. CALCULATION RESULTS WITH DIFFERENT Cn2 ( z ) PROFILES We have chosen for our calculations the Cn ( z ) data obtained at four observatories: Paranal (Chili), Roque de Los 2
Muchachos (Canary Islands), San Pedro Mártir (México) and Observatoire de Haute Provence (France). The calculations of Strehl efficiency have been performed for 8-meters-class telescopes because the telescopes of this class are either already operating, under construction or they are planned to be build. The efficiency of off-axis correction is presented for three bands (V, J, K) centered at 0.55, 1.25 and 2.2 µm which are of interest for observers. Fig. 3 plot the Strehl ratio calculated for different sites versus the angular separation between two stars. Graphs are plotted for three wavelengths which are of interest in astronomical applications: 0.55, 1.25 and 2.2 µm . Since the calculations have been made for the case of perfect adaptive correction, the graphs present the upper limit of the efficiency of off-axis adaptive correction that can be reached with a real adaptive system. One can see from Fig. 3 that the quality of off-axis adaptive correction is quite different for the four considered sites. This effect appears due to a significant difference in profile's behavior with the altitude. As it follows from Eq. (2), the quality of off-axis correction is mainly affected by the quantity
∫
L
0
dzz 5 3Cn2 ( z ) . So, speaking in general terms, the profiles with an
optical turbulence strength concentrated mainly near-to-the ground give better results. Comparing the results presented in Fig. 3, one can conclude that the quality of off-axis correction can differ quite strongly (up to several times) from one observatory to another. This difference mainly appeared due to the different behavior of the associated Cn ( z ) profiles with the altitude. 2
Our present investigations has shown that, among the compared sites, one can expect the best quality of off-axis adaptive correction at San Pedro Mártir observatory. However, it is only a previous conclusion because this set of presently available
Cn2 ( z ) data is not big enough. We are planning to carry out in the future more complete Cn2 ( z ) data analysis and
measurements.
Fig 2. Experimental
Cn2 ( z )
profiles from balloon data used in calculations. The calculated Fried parameter in cm (at λ = 0.55 µm) for
each profile is: a 17.0 b 5.0, c 10.3 .
Fig 3. Strehl ratio versus the angular separation between the stars for 8 m telescope. a V band, b J band and c K band. Lines coding is: San Pedro Mártir, México (continous line), Paranal, Chili(dotted line), Roque de los Muchachos, Canary Islands (dashed line), OHP, France (i) (dotted-dashed line) and OHP, France (ii) (3 dots-dashed line).
ACKNOWLEDGEMENTS We are indebted to J. Vernin and M. Azouit from University of Nice (France) Astrophysics Department for kindly providing balloon and Generalized Scidar data used in this investigation. This work was supported by ECOS-ANUIES-CONACYT grant M97U01. L.J. Sánchez received support by Consejo Nacional de Ciencia y Tecnología (México) project 400354-5I29854E.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9.
V.V. Voitsekhovich, V.G. Orlov, S. Cuevas and R. Avila, “Efficiency of off-axis astronomical adaptive systems: comparison of theoretical and experimental data”, Astron. & Astroph. Suppl. Ser., 133, 247, 1998. R. Avila, J. Vernin, M. Chun and L. J. Sánchez, “Turbulence and wind profiling with Generalized Scidar at Cerro Pachón” in these proceedings. D.L. Fried, “Optical resolution through a Randomly Inhomogeneous Medium for very long and very short exposures”, J. Opt. Soc. Am. 56, 1372, 1966 R. Avila, J. Vernin and E. Masciadri, 1997, “Whole atmosphere profiling with Generalized Scidar”, Appl. Opt. 36, 7898, 1997 R. Avila, J. Vernin and S. Cuevas “Turbulence profiles with Generalized Scidar at San Pedro Mártir Observatory”, Publ. Astron. Soc. Pac., 110, 1106, 1998 A. Fuchs, “Contribution à l’étude de l’apparition de la turbulence optique dans les couches minces. Concept du Scidar généralisé”, Ph.D. dissertation. Université de Nice-Sophia Antipolis, 1995 A. Fuchs, M. Tallon and J. Vernin, “Focusing on a turbulent layer: Principle of the Generalized SCIDAR”, Publ. Astron. Soc. Pac., 110, 86, 1998 A. Rocca, F. Roddier and J. Vernin, “Detection of atmospheric turbulent layers by spatiotemporal and spatioangular correlation measurements of stellar light scintillation”, J. Opt. Soc. Am. A 64, 1000, 1974 V.G. Orlov, V.V. Voitsekhovich, L.J. Sánchez , S. Cuevas and R. Ávila, “Analysis of the off -axis point spread function of astronomical adaptive systems for the site of San Pedro Mártir”, in these proceedings.
