2. Experiment and measurements

The DIMM principle is to produce twin images of a star with the same telescope via two entrance pupils separated by a distance d in order to eliminate erratic motions of the telescope. The knowledge of the phase structure function, which is assumed to result from Kolmogorovian turbulence, enables us to assess the longitudinal and transverse (parallel and perpendicular to the aperture aligment) variance of differential image motions as given by

with k(l)=0.541 and k(t)=0.810, which holds when D/d 0.5 (see e.g. Sarazin & Roddier 1990). The variance and the Fried parameter (r₀) are related by

From the above relations two independent r₀ values are obtained. From r₀, classical astronomical seeing ) is obtained through (Dierickx 1992). To simplify the nomenclature we will hereafter refer to this as FWHM or seeing.

The DA/IAC DIMM consists of an 8-inch Celestron, an equatorial mount, a pulsed intensified CCD camera and an image grabber (MATROX) connected to a PC computer. A mask made of two diaphragms (60-mm diameter) is located at the entrance pupil of the telescope, and a prism (of about 30'' deflection) is placed over one of them to produce two images. To match the pixel size, the focal length is enlarged using an eyepiece with an optical gain . The twin images of a star are captured by the intensified camera with a exposure time ms, short enough to freeze the wave-front. The video signal is then digitized.

Seeing is referred to zenith taking into account the appropriate air-mass correction, the zenithal angle being small (). FWHM is accurate to better than 0.1'' and, under reasonably good conditions it is possible to monitor the seeing with a temporal sampling rate of less than half a minute for several hours, thanks to the automatic guiding.

Seeing data to be analysed in this paper have been obtained at two sites at the ORM, one near the location of the Telescopio Nazionale Galileo (TNG) (hereafter referred to as site A) and a second one close to the William Herschel (4.2 m) Telescope (WHT, site B). In Fig. 1 (click here) the location of sites A and B are marked on a portion of the ORM map. The locations of three telescopes, the WHT, the TNG and the Nordic Optical Telescope (NOT), used as reference points, are also indicated.

 
Figure 1:   Map of the ORM showing the location of sites A and B. The location of the Telescopio Nazionale Galileo (TNG), the Nordic Optical telescope (NOT) and the William Herschel Telescope (WHT) are also indicated for reference. The volcano rim of the Caldera de Taburiente flanks the observatory to the south

 

month Ndata min ('') mean ('') std ('') median ('')

11-94 6744 0.26 0.81 0.34 0.74

01-95 11957 0.23 0.94 0.64 0.77

02-95 10582 0.2 0.95 0.44 0.84

03-95 3793 0.32 1.13 0.87 0.77

04-95 9119 0.26 0.82 0.5 0.66

05-95 11906 0.17 0.74 0.37 0.64

06-95 11724 0.20 0.49 0.17 0.46

07-95 9675 0.19 0.61 0.26 0.56

08-95 10462 0.22 0.60 0.23 0.54

all 85962 0.17 0.76 0.47 0.64

Routine measurements were carried out 3 to 4 nights every week. To avoid the surface layer (SL) influence (Vernin & Muñoz-Tuñón 1994), the DIMM at site A was located on a 5-m tower designed by the Galileo Project. The DIMM situated on site B belongs to Isaac Newton Group and was installed on top of the WHT terrace.

As mentioned previously, both longitudinal and transverse FWHM are recorded and subsequently used to determine the validity of the measurements and to improve them. During an observing run, when a systematic discrepancy is noticed between FWHM_l and of more than 12%, which is the relative error expected from the number of images processed and other noise (see Vernin & Muñoz-Tuñón 1995), the data are discarded, otherwise they are averaged.

 
Figure 2:   The distribution function of measured seeing corresponding to two months at site A is shown by a continuous line. The dotted line (left) refers to the deduced log-normal distribution resulting from the measurement of the second moment. The dotted line (right) represents the result of the deconvolution assuming an additive Gaussian noise

 
Figure 3:   Mean, median, minimum and rms seeing values for each month at site A. The statistic of observed time with the seeing monitor during the campaign at site A is plotted

The distribution function of a positive random variable, like seeing, is expected to be log-normal (see e.g. Lee 1960). In Fig. 2 (click here) (left) we display with a solid line the distribution function of measured seeing for two different months, along with the deduced log-normal distribution (dotted line) one would expect from the measurement of the second moment. It is clear that the deduced log-normal distribution is broader and smoother compared to the observed one. We already know that there is spurious noise, due to the low number of images processed to provide an individual seeing measurement (N = 200), which certainly may affect the shape of the distribution function.

Let us suppose that this noise is additive and does not depend on the seeing value; then the probability density function (pdf) of the measured seeing, , is the convolution of the true pdf of the seeing, , and the noise pdf, :

A simple deconvolution is made assuming a Gaussian behaviour of the noise. In Fig. 2 (click here) (right) we plot with a dotted line the deconvolved pdf, evaluating an rms noise compatible with the number of processed images. One notes the fit improvement which proves that our seeing data are compatible with an expected log-normal distribution of the seeing and a Gaussian additive noise.