LOTUCE: A new monitor for turbulence characterization inside telescope s dome

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1 Florence, Italy. May ISBN: DOI:.89/AOELT.5 LOTUCE: A new monitor for turbulence characterization inside telescope s dome Aziz Ziad a, Wassila Dali Ali, Julien Borgnino, Marc Sarazin, and Bernard Buzzoni Laboratoire J.L. Lagrange-UMR 79, Université de Nice-Sophia Antipolis/CNRS/OCA, Parc Valrose F-68 Nice Cedex, France, European Southern Observatory, Karl-Schwarzschild-Strasse, D-8578 Garching bei München, Germany Abstract. For the characterization of the turbulence inside a dome, an instrument LOTUCE, has been developed jointly by Lagrange Laboratory and ESO. The objective is to learn from results of LOTUCE inside a large telescope dome such as a UT of VLTI in order to optimize the E-ELT enclosure design. The LOTUCE instrument was tested in optical laboratory in different conditions of turbulence at the Observatoire de la Côte d Azur. Then, first measurements were performed with LOTUCE in the.5m telescope dome at La Silla Observatory. LOTUCE consists of four parallel laser beams leading to six different baselines and therefore, to six Angle of Arrival (AA) covariances in addition to the variance. The best fit of these measurements with the theoretical covariances leads to the atmospheric turbulence model. Then, other turbulence parameters are estimated from AA spatio-temporal analysis. INTRODUCTION Local turbulence due to the immediate environment of the telescope must be taken into account in the dome design, particularly for large telescopes such as the E-ELT project. A better knowledge of this local turbulence and its modeling becomes crucial if one wants to optimize the performances of the telescope. In contrast with the rest of the atmosphere, the surface layer turbulence is affected by ground and environment characteristics (convective flow, roughness, etc.). This turbulence in the surface layer interacts with the telescope enclosure and generates turbulence inside the dome. Some models were proposed to link the image quality to the heat dissipation in the surface layer[]. Here, we present an optical experiment LOTUCE (LOcal TUrbulenCe Experiment) to characterize the surface layer and the turbulence inside the telescope enclosure [, ]. It consists of the wavefront analysis by means of parallel laser beams on a multi-baseline configuration. The fluctuations of the Angle of Arrival (AA) are measured with a CCD camera from spots displacements and their longitudinal and transverse covariances at different baselines are compared to the theoretical ones. The choice of the configuration of the parallel beams is important to obtain an optimal sampling of these AA covariances. We use weighted least-square method to fit the measured AA covariances with theoretical forms deduced from the usual models of turbulence (Kolmogorov, von Kàrmàn, Greenwood-Tarazano, Exponential) []. Then, the whole parameters characterizing this turbulence are provided from a complete spatio-temporal analysis of AA fluctuations. The first LOTUCE tests revealed the presence of vibrations due to external sources even if the instrument is isolated. The vibration spectrum has been characterized and then the prevailing frequencies are removed by numerical filtering. The sensitivity has been also checked and the instrument is able to measure weak turbulence. a ziad@unice.fr

2 AO for ELT III The principle of the use of laser beams in the study of optical turbulence was introduced by various authors particularly for horizontal propagation for the measurement of inertial range limits corresponding to the inner and outer scales. Indeed, the scintillation of laser beams with different apertures or wavelengths has been used for the estimation of the inner scale [5 7]. On the other hand, AA fluctuations have been also used for characterization of local turbulence by [8,9] particularly for the outer scale measurement. Theoretical background. Spatial statistics of Angle-of-Arrival fluctuations Characterization and modeling of dome turbulence is based on AA measurements. The statistical analysis of these AA fluctuations lead to the model describing this kind of turbulence and the associated parameters. Indeed, estimated AA covariances obtained at well distributed different baselines compared to theoretical ones lead to the model of turbulent media. We consider the normalized AA longitudinal and transverse covariances as used in the GSM instrument [,] Γ α = C α(b, D, L ) σ α(d, L ) () where σ α(d, L ) is the variance of AA fluctuations. This expression is Fried s parameter r and wavelength λ independent. The AA covariance expression for two telescopes of diameter D separated by a baseline B is given by [,]: C α (B, D, L ) = πλ f W ϕ ( f, L )[J (π f B) cos(γ)j (π f B)][ J (π f D) ]d f () π f D where J n represents the n th order Bessel functions of the first kind and γ is the baseline angle with the x-direction. Useful formulae for this AA covariance is given in []. The AA variance σ α(d, L ) is obtained from Eq. at the origin B =. In the case of von Kàrmàn model and L >> D, an approximation of this AA variance is given in []: σ α(d, L ).79λ r 5/ [D /.55L / ] () The Fried parameter r is the size of a spatial coherence area of the perturbed wavefront and it depends physically on the structure constant of refractive index fluctuations CN (h) integrated along the propagation path as: r = ( ) π. λ CN(h)dh /5. () The AA structure function σ d is also an interesting quantity for turbulence characterization particularly for seeing estimation by means of DIMM instrument [5]. This quantity is differential allowing to avoid vibration effects and less sensitive to outer scale. Since σ d = [σ d (D, L ) C α (B, D, L )], the expression of the AA structure function is completely deduced from Eq.. For the transverse and longitudinal cases, the expression of σ d is given by [,6] when B > D:

3 Aziz Ziad et al.: LOTUCE: monitor of dome turbulence σ d = K l/tλ r 5/ D / (5) where K l/t is a constant depending on the ratio B/D as: K l =.(.57( B D ) /.( B D ) 7/ ) (6) K t =.(.855( B D ) / +.( B D ) 7/ ) (7) Thus, using the DIMM method one can have estimation of Fried s parameter r or seeing in both longitudinal and transverse directions. These estimations should lead to the same results if exposure time is short enough. On the other, variance and covariance are appropriate for estimation of outer scale L if r is provided by DIMM method.. Temporal spectrum of AA fluctuations Different authors have demonstrated the interest of AA spectral analysis for the characterization of the atmospheric turbulence. Indeed, the PSD of AA fluctuations presents different regimes of temporal frequency ν [7,] : a ν / for low frequency domain, a ν / for intermediate frequencies and for high frequency a ν / or a ν 8/ depending on spatial filtering. The cutoff frequencies separating these different regimes are proportional to v/l and D/L where v is the wind speed and D the telescope diameter. Thus, the estimation of the high cut-off frequency lead to the wind speed v and then combined with the low cut-off frequency estimation provide the outer scale L value. On the other hand, estimation of the wind speed could be used to estimate the coherence time which is given by Roddier formulae τ =.r /v [8,9].. Modeling the dome turbulence The LOTUCE monitor uses several separated laser beams propagating simultaneously in a turbulent media and leading to several different baselines. The corresponding longitudinal (γ = o ) and transverse (γ = 9 o ) covariances are then compared to the theoretical ones to test the validity of the four commonly used models which are the Kolmogorov, von Kàrmàn, Greenwood- Tarazano and Exponential model. This method has been successfully used in the GSM instrument. The existing atmospheric turbulence models are characterized by their phase power spectra []: For the von Kàrmàn (vk) model, one has: [ Wϕ vk ( f, L ) =.9r 5/ f + ] /6 (8) L and in the case of the Greenwood-Tarazano (GT) model, W GT ϕ ( f, L ) =.9r 5/ or in the case of the Exponential (Ex) model : [ f + f L ] /6 (9) Wϕ Ex ( f, L ) =.9r 5/ f / ( exp( f L )). ()

4 AO for ELT III All these models tend to the Kolomogorov one when the outer scale is considered infinite. In the case where these models do not adjust the measurements, we can construct other models by changing the powers and constants of the existing ones []. The instrument provides for each acquisition two sets of AA covariances in longitudinal and transverse directions. Then, we use weighted least-square method on data obtained to test usual models of turbulence. This is built on the hypothesis that the optimum description of a set of data is one which minimizes the weighted sum of squares of deviations of the experimental normalized covariances Γ i α from the theoretical fitting function Γ α (B i, L ). It can be written as χ = n [Γα i Γ α (B i, L )]. () i= σ i where n is the number of baselines and σ i is the variance of Γ i α that acts as a weighting factor for each spatial covariance. Minimization of χ is obtained by varying the non-fixed parameter L of the model with the help of pre-calculated grids from Eq. and Eq.. LOTUCE Instrument The LOTUCE instrument consists of a laser multibeam which is initially provided by one laser diode [,]. Optical fibers and fiber couplers are used to split in several parallel beams ( or 5). A filter of density (ND) is also used to reduce flux intensity and to avoid, therefore, the detector saturation. Then a collimator with achromatic lenses is used to obtain parallel beams of cm diameter (Figure ). This beam diameter has been chosen in respect of inner scale value (between few mm to cm) which represents the smallest detail in the perturbed wavefront. The different beams propagate inside a local turbulence which we want to characterize. The separation between the different beams is very important to obtain an optimal sampling of the AA covariance curves. A specific study has been dedicated to this issue based on numerical simulation (see next paragraph). Then, using mirrors and beam splitters, the parallel beams are oriented on a small telescope (D=-cm and f/) (Figure ) which will make them converge in the CCD located in its focal plane. A Barlow lens X is associated to the telescope to elongate its focal distance to increase the sensitivity to AA fluctuations. The different beams are separated by adjusting mirrors and beam splitters orientations. Thus, each laser parallel beam leads to a light spot on the CCD allowing the reconstruction of the longitudinal and transverse covariance curves of AA fluctuations to be compared to the theoretical models. As explained above, the choice of beam size is of order of inner scale of turbulence but beam should be larger enough to reduce the spot spread on the CCD. The size of each beam is, therefore, fixed to cm, this corresponds to the pupil diameter of our optical system. With a focal distance f m, the detector sampling is.5 /pix for a CCD Prosilica GC65 (659x9pix and pixel = 7.microns). It is possible to use Barlow s lens X to elongate the focal distance to increase the instrument sensitivity which could reach. /pix with a Barlow X. There is a strong sensitivity of the AA covariance to the outer scale for metric and submetric values of the baseline []. The choice of baseline values is a trade-off between instrumental constraints and the need to sample regularly longitudinal and transverse AA covariances. The upper limit of the baseline was chosen in regards to the outer scale which should be smaller than in the atmosphere. The LOTUCE instrument configuration is changeable in real time to be adjusted to the turbulence conditions.

5 Aziz Ziad et al.: LOTUCE: monitor of dome turbulence Fig.. The schematic optical device of the LOTUCE instrument. Fig.. LOTUCE, monitor of dome turbulence installed in a laboratory at the Observatoire de la Côte d Azur. Top and bottom panels show respectively the source and the reception benches. In the middle panel are presented reception bench components (reflecting mirror, beam splitter, telescope and CCD). Noise sources The error sources affecting the proposed instrument are similar to DIMM s ones. Typical errors in this kind of experiment are essentially due to the centroid determination, the statistical error and finally the exposure time. This last is not very important since we use a laser beam as a source with stabilization to ensure the flux constancy for a large time. The source is fixed and then the instrument is not affected by vibrations contrary to the seeing monitors where a tracking system is used. We could plan to use wind-screen to protect the instrument from the wind effect. As described in [6] the centroid determination error comes from the CCD readout noise (RON) and the signal Poisson noise (the images are considered corrected with the flat field). The RON error is now well modeled (Eq. 9 of [6]) and estimations are possible which are expected to be reduced since the source flux is not limited. The photon noise σ p has less impact on the measurement than the RON error since the CCD is directly illuminated. The variance σ p could be estimated using models (Eq. of [6]) but some factors are determined

6 AO for ELT III by means of numerical simulation and laboratory tests. The statistical error will be minimized by making a long series of images acquisition and in the other hand, we will use very short exposure time ( ms) for each frame to avoid the exposure time debiasing. As shown in Figure, the beams have the same length but we have different residual paths in the detector block. For small baselines the energy due to these residual propagation should be weak and would not affect the results. On the other hand, if the AA variances for the different spots are not equal, one have to conclude that is due to these residual propagations. This could be estimated by placing the source bench close to the detector bench and then we have access only to the residual propagation variances that we have to subtract from the measurements. 5 First results In the framework of the E-ELT project, a prototype of the LOTUCE instrument has been developed (Figure ) and tested in optical laboratory in different conditions of turbulence [,]. This instrument was also installed in the dome of the.5m telescope at La Silla Observatory and first results are presented in a dedicated paper by []. In this section, we present only measurements obtained in laboratory conditions. The tests in the laboratory revealed the presence of vibrations due to external sources even if the instrument is isolated. The vibration spectrum has been characterized and then the prevailing frequencies are removed by soft filtering. The sensitivity has been checked and the instrument is able to measure weak turbulence of order of as at λ = 65nm. After vibrations removing, data are ready for statistical analysis and turbulence characterization. The first analysis to be performed is the isotropy validation which is necessary for use of Kolmogorov theory. Fig. shows AA variances measured with LOTUCE in laboratory in x and y directions for each spot. In right panel, we have the whole data variances for which the correlation coefficient is more than.7. Even if this correlation coefficient is very correct, the isotropy is probably biased by convection since the LOTUCE benches are at m above the ground. 5 σ y (as ) spot spot spot spot 5 (as ) σ y σ x (as ) σ x (as ) Fig.. AA variances measured with LOTUCE in laboratory in x and y directions for each spot and for whole data (right panel). The correlation coefficient is larger than.7. Once the isotropy hypothesis confirmed, we used spots fluctuations (AA) to deduce first estimations of Fried parameter r on the different baselines from DIMM method (Eqs 5 and 7) in both transverse and longitudinal directions. Fig. shows comparisons of r measured in x and y directions in laboratory conditions at λ = 65nm. These results are obtained from AA structure

7 Aziz Ziad et al.: LOTUCE: monitor of dome turbulence functions for different baselines B = 5, 5,,, 5 and cm. These measurements of r in x and y directions are coherent because of a short exposure time ms and a small wind speed ry (m) rx (m) Fig.. Comparison of r measured in x and y directions in laboratory at λ = 65nm for baselines of 5, 5,,, 5 and cm (from left to right and top to bottom). The four parallel laser beams lead to six different baselines in addition to the variance measurement and then these seven measurements are used to fit with the theoretical models. Fig. 5 shows an example of these AA covariances measured with LOTUCE in laboratory. These covariances are indicated by the median value over 56 measurements, while the error bars correspond to the standard deviation. Different models have been used to fit these data and to extract the outer scale value which is of m in the case of von Kàrmàn model. As expected, these first results obtained with LOTUCE in laboratory lead to small values of outer scale m (left panel of Fig. 6). Right panel of Fig. 6 shows an example of AA spectral density measured with LOTUCE in laboratory. The cut-off frequencies lead to a wind speed of.m/s and an outer scale of.7m. This latter confirmed the values of L obtained from AA covariances (Fig.5)..6 Covariances longitudinales (s.a ) L =m, r =cm exp (N=56) vk Ex GT Base (m) Fig. 5. Example AA covariance measured with LOTUCE in laboratory. These covariances are represented by the median value and the error bars indicate the standard deviation over 56 samples.

8 AO for ELT III 7 f / 6 5 f / N W α (sa ) f 8/ 5 L (m) Fig. 6. Example of outer scale histogram and AA spectral density measured with LOTUCE in laboratory. ν(hz) Acknowledgments This work is supported by ESO and the University of Nice-Sophia Antipolis in the framework of the E-ELT project. References. Racine, R., Salmon D., Cowley D., Sovka J., PASP, (99). Dali Ali W., PhD thesis of Unisity of Nice Sophia Antipolis, (). Ziad A. Dali-Ali W., Borgnino J., Sarazin M., SPIE Proceedings 8, () 9. Voitsekhovich, V. V., J. Opt. Soc. Am. A, (995) 6 5. Livingston, P., Appl. Opt., (97) Hill, R. and Ochs, G. Appl. Opt. 7, (978) 7. Ochs, G. and Hill, R., Appl. Opt. 5, (985) Consortini, A., R. L. and Stefanutti, L., Appl. Opt., (97) 5 9. Consortini, A., I. C. and Paoli, G., Optics Communications, () 9. Avila, R., Ziad A., et al., J. Opt. Soc. Am. A, (997) 7. Ziad, A., Borgnino J., et al., Appl. Opt. 9, () 55. Borgnino, J., Martin F., Ziad A., Optics Communications 9, (99) 67. Conan, R., Borgnino J., Ziad A. and Martin, F., J. Opt. Soc. Am. A 7, () 87. Ziad, A., Borgnino J., Martin, F., and Agabi, A., A&A 8, (99) 5. Sarazin M. and Roddier F., A&A 7, (99) 9 6. Tokovinin A., PASP, () Conan J.M., J. Opt. Soc. Am. A, (995) Roddier F., Gilli J.M., and Lund G., J. Opt. (Paris) (98) 6 9. Ziad A., Borgnino J., et al., J. Opt.: Pure & Applied Optics, (). Berdja A., Osborn J., Sarazin M., Dali Ali W., Ziad A., AOELT III Conf. Proceed., ()