3 Generalized seeing monitor

3.1 Instrument layout

In view of monitoring additional atmospheric parameters - the wavefront outer scale ${\cal L}_0$, the wavefront coherence time $\tau_0$ and the isoplanatic angle $\theta _0$, - which are of particular importance to adaptive optics and interferometry, a specific campaign was organized in July 1998. All these parameters were measured with GSM developed at Nice University in collaboration with MSU Martin et al.1994. The GSM was first extensively used in 1997 during the La Silla campaign in Chile Martin et al.1998,Tokovinin et al.1998, then in 1998 at the Gemini site of Cerro Pachon Vernin et al.2000 and at the VLT site of Paranal Martin et al.2000.

GSM consists of four identical units for angle of arrival (AA) measurements. Each unit has a 10 cm Maksutov telescope and a detection module to measure the stellar image position using a grating in the focal plane together with fast (200 Hz) modulation. The light transmitted by the grating is detected by a photo-multiplier in pulse counting mode. All four units work synchronously and provide the angle of arrival data with 5 ms temporal resolution. The units were equipped with simple but rigid alt-azimuth supports pointing the Polar star. The field of view of 13.7' permits observations during 30 min without re-pointing. Units 1 and 2 had a common support for DIMM-like seeing measurement in differential mode (baseline 25 cm). GSM was installed on a 3 m high rectangular arch-shape concrete pier, the optical apertures were 3.4 m above ground level. Unit 3 was located on the same pier to the east, 0.8 m from the center of the differential unit, and unit 4 was located 1.5 m below (1.9 m above ground). All units measure AA fluctuations in the horizontal direction. Thus the baselines formed by units 1-2, 1-3, 2-3 are longitudinal, baselines 1-4 and 2-4 are approximately transverse, and baseline 3-4 is oblique. Such a geometrical arrangement was chosen to explore the 2D structure of the wavefront and to determine its effective speed. Baseline lengths are optimized for maximum sensitivity to the outer scale effects for the expected decametric outer scale values. In the previous GSM missions all GSM units were located in a horizontal plane, but our present "3D'' arrangement results in the same unit configuration as projected onto the wavefront.

Data acquisition was typically 2 min long, repeated every 4 min. Data were processed immediately after acquisition. Processing includes calculation of the AA variance in each unit and AA covariances which, after suitable normalization, were compared to the pre-calculated table to find the wavefront outer scale ${\cal L}_0$. The six values of ${\cal L}_0$, corresponding to the 6 baselines of GSM, are found, and their median is taken as final result. The ${\cal L}_0$ provided by GSM is an outer scale parameter in the Von Kármán turbulence model, its relation to outer scale in some other models is studied in Ziad et al.2000.

Seeing is calculated from the differential AA variance in units 1 and 2, like in DIMM. Small corrections for photon and scintillation noise are made. Correction for finite exposure time is also performed by calculating the AA variance with 5 ms and 10 ms temporal resolution and extrapolating to the 0 ms exposure time. This latter correction was typically about 10%, because seeing at Maidanak is rather slow. Additional estimation of seeing comes from the AA variance in each unit, with a non-negligible correction for finite outer scale. A good match between differential and absolute seeing estimates is a sign that the support vibration was not important, which is a necessary condition for correct GSM operation. Also, the difference between AA variances measured by the units 3 and 4 was used to estimate the importance of ground layer turbulence, because these units were installed at different heights above ground (3.4 and 1.9 m, respectively).

The isoplanatic angle was calculated from the scintillation index, as explained in Conan et al.1999,Ziad et al.2000. Our time resolution of 5 ms is not sufficient for unbiased measurement of scintillation, but we corrected for time averaging in the same manner as for the AA.

3.2 Summary of GSM results

The 10 days measurement campaign took place in July, a month representative of the best observing period at Maidanak which extends from mid-summer to early autumn. The probability of good weather for this period is very high. Indeed, our mission started on July 16, in the conditions of stable weather with clear sky and good seeing, which persisted during the first 8 nights (July 16-23). Then, on July 24, 2 hours were lost due to cloud passages. On the night of July 25 only few GSM observations were made, because of the fog and associated humidity (the previous day was rainy). This last night is considered as lost due to weather, although the scintillation and DIMM measurements were taken as planned in its second half. In summary, we had 8 clear and 2 partially clear nights out of 10. Table 3 summarizes the measurements collected during this campaign.

 

 

Table 3: GSM data summary: number of hours T covered each night and the number of data points N. Median seeing $\beta$, median isoplanatic angle $\theta _0$ at zenith and 0.5 $\mu$m and median ${\cal L}_0$ for each night and for the whole data set

Date	T	N	$\beta_{\rm med}$	$\theta_{0 \rm med}$	${\cal L}_{0 \rm med}$
July 1998	h		arcsec.	arcsec.	m
16	4.4	69	0.96	2.02	32.6
17	7.0	100	0.58	2.49	27.2
18	4.7	99	0.74	2.24	22.6
19	6.2	96	0.52	3.49	26.2
20	7.4	104	0.53	3.43	23.2
21	7.3	101	0.63	2.48	27.3
22	6.9	99	0.87	2.41	34.6
23	7.4	103	0.74	2.52	22.8
24	7.6	79	0.79	1.79	22.7
25	0.5	7	1.21	1.14	25.0
Total	58.9	850	0.68	2.48	25.9

Figure 8: The histograms of the outer scale (top) and isoplanatic angle (bottom) estimations with GSM at Mt. Maidanak

Figure 9: Direction and velocity of the wavefront for the whole GSM mission data set, plotted as a polar diagram. The western wind of low to moderate velocity was predominant, with south-east winds being less frequent

3.3 Outer scale and isoplanatic angle

The measured ${\cal L}_0$ values, average 31.5 m and median 25.9 m, are typical of other GSM missions. The median isoplanatic angle $\theta _0$ is 2.48 $^{\prime\prime}$, mean is 2.57 $^{\prime\prime}$. The histograms of the outer scale and isoplanatic angle during the 9 nights of the mission are given in Fig. 8. All atmospheric parameters are reduced to observations at zenith at the wavelength of 500 nm.

3.4 Wavefront velocities and time constant

The temporal characteristics (velocity and direction) of the predominant turbulent layers of the atmosphere were determined from the analysis of AA temporal cross-correlation functions at all GSM baselines Conan et al.1999. The eddies carried by the winds in the layers produce several peaks in the cross-correlations. With the hypothesis of the frozen-flow, the positions of the peaks depend on the baseline and on the projection of the wind on the baseline as shown by Avila et al. AVI97. Practically, the positions of the highest peak are measured on the six cross-correlations. To reconstruct the wind vector, two non-parallel baselines are necessary. With the six baselines, 11 couples of equations lead to the 11 measurements of the wind vector. The final value is the median of these. This procedure turned out to be rather robust, and practically it gives the velocity of dominant turbulent layers. When several layers are present (which was almost always the case), our wavefront velocity vectors often fluctuate between the values typical for each layer, because of turbulence intermittency. So, the plots of wind speed and direction against time usually reveal the multi-layer structure quite well.

The overall distribution of the direction and velocity of wavefront is given in Fig. 9. A predominant western direction is apparent. It corresponds to the planetary circulation in the free atmosphere. Very low wavefront speed is obtained: it was less than 4 m/s most of the time, and never exceeded 10 m/s. Although still subject to theoretical interpretation, these measurements can be used to estimate the temporal coherence of the atmosphere: taking V = 4 m/s as representative, we obtain the atmospheric time constant $\tau = 0.31 r_0/V = 12$ ms, that is 2 to 4 times longer than at other main observatories Sarazin1995,Vernin et al.2000. Direct interferometric measurements over 19 nights at Maidanak also yielded a time constant of 12 ms Tokovinin1980.

Figure 10: Seeing measured by DIMM (solid line) and by GSM (dashed line) on the night of July 21-22 with the best seeing (left) and on July 23-24 with average seeing (right), when for the first 2 hours GSM units 1 and 2 were installed on the DIMM pier. DIMM data are smoothed by a running mean

3.5 Cross-calibration of DIMM and GSM

One of the important results obtained during the July 1998 campaign was cross-calibration of Maidanak DIMM with the GSM. As can be seen from Fig. 10, a good mutual agreement of GSM and DIMM seeing estimates exists most of the time. DIMM measurements show a larger scatter, explained by the small number of frames available for computing the variance of the image motion.

The 25%, 50% and 75% levels of the cumulative seeing distribution as measured during all 9 nights with GSM are 0.56 $^{\prime\prime}$, 0.68 $^{\prime\prime}$  and 0.84 $^{\prime\prime}$. The corresponding values for DIMM are 0.52 $^{\prime\prime}$, 0.64 $^{\prime\prime}$ and 0.82 $^{\prime\prime}$. DIMM observed stars near zenith while GSM observed Polaris, and hence both instruments sampled different volumes of the atmosphere. Correction of the GSM seeing to zenith was however not too large, $(\sec 51^\circ )^{0.6} = 1.32$.