Observations

In order to assess the short exposure PSF experimentally, observations of individual unresolved stars were undertaken at the NOT. These observations were made at the Cassegrain focus of the telescope during technical time at the very end of the night of 2000 May 12 and on the night of 2000 May 13 by Craig Mackay, John Baldwin and Graham Cox. The JOSE camera used for the observations comprised a $512\times512$ front-illuminated frame-transfer CCD with $15$ $\mu m$ square pixels run by an AstroCam 4100 controller. The controller allowed windowing of the area of readout and variable pixel readout rates up to $5.5$ $MHz$. The detector read noise was typically $50$--$60$ electrons for these observations. The $f/11$ beam at the focus was converted to $f/30$ using a single achromat to give an image scale of $41$ $mas$ $pixel^{-1}$ ($25$ $pixels$ $as^{-1}$).

The observations were taken through the I-band filter from the HiRac instrument at the NOT. The bandpass of this filter is similar to a top-hat in shape, with a centre wavelength of $810$ $nm$ and a bandwidth of $125$ $nm$. All of the short exposures were taken at frame rates higher than $150$ $Hz$ and without autoguiding to ensure that the temporal behaviour of the periods of good seeing was adequately characterised.

The diffraction-limited PSF of the $2.56$ $m$ telescope with $0.70$ $m$ secondary obstruction has a FWHM of $64$ $mas$ at the observing wavelength of $810$ $nm$. The pixel scale of $41$ $mas$ $pixel^{-1}$ was a compromise between the area of sky which could be observed at high frame rate and the degradation of the image FWHM due to the finite pixel size.

Four stars were observed at the end of the first night of technical time at the NOT in May 2000. Two of these stars ($\alpha$ Aquilae and $\gamma$ Aquilae) were sufficiently bright that the CCD camera reached saturation in the best exposures, and these runs have been excluded from further analyses. A small number of frames (less than 1%) in all the runs were mis-recorded by the camera, and these frames have also been excluded from further analysis. Table 3.2 describes the two usable observing runs from the first night.

Table 3.2: High frame-rate observations performed at the end of the first night of NOT technical time in May 2000.

Target	Frame rate / Hz	Number of exposures	Seeing FWHM / as	Strehl ratio for best 1% of exposures
epsilon Aquilae	185	6000	0.38	0.26
V656 Herculis	185	6000	0.49	0.21

The seeing was good and the short exposure images clearly showed a single bright speckle at some instants. In order to assess the atmospheric conditions, the individual short exposures were summed without re-centring to produce an average image, equivalent to a conventional long exposure with duration equal to the total time for the run. The FWHM of the star in this image represents a measure of the atmospheric seeing conditions, and is listed in column $4$ of Table 3.2. The FWHM measurements are consistent with an $r_{0}$ of $0.34$--$0.44$ $m$ at the $810$ $nm$ observing wavelength for Kolmogorov turbulence with an infinite outer scale. The telescope diameter would then equal $6$ or $7$ times $r_{0}$. Previous atmospheric measurements at La Palma have typically favoured an outer scale of a few metres (see e.g. Nightingale & Buscher (1991); Wilson et al. (1999)), and under these conditions a slightly smaller value of $r_{0}$ would be consistent with the long exposure FWHM.

A list of the observations on the second night is given in Table 3.3. Each run typically comprised between $5000$ and $24000$ frames over a period of $30$--$160$ $s$. Target stars, both single stars and binaries, were chosen principally lying in the declination range $10^{\circ}$--$20^{\circ}$ and close to the meridian, so that most of the data was taken at zenith angles $<20^{\circ}$. Zenith angles up to $50^{\circ}$ were explored later in the night, and the effects of atmospheric dispersion became significant, since no corrective optics were employed. As on the first night, a small number of short exposures in each run were mis-recorded, and these exposures were excluded from further analysis.

Table 3.3: Observations on the second night of NOT technical time in May 2000.

Target	Frame rate / Hz	Number of exposures	Seeing FWHM / as	Strehl ratio for best 1% of exposures
alpha Leonis	185	6000	0.71	0.079
gamma Leonis	159	5000	0.65	0.092
gamma Leonis	182	5000	0.54	0.099
zeta Bootis	152	24000	0.58a	0.20
zeta Bootis	152	24000	0.64a	0.17
CN Bootis	152	2000	0.58	0.084
alpha Herculis	191	6000	0.42	0.21
alpha Herculis	191	6000	0.38	0.21
beta Delphini	373	10000	0.52	0.20b
beta Delphini	257	10000	0.40	0.18b
beta Delphini	190	10000	0.60	0.16b
alpha Delphini	180	10000	0.47	0.18b
alpha Delphini	180	10000	0.57	0.20b

^a Approximate value after accounting for tracking error
^b The Strehl ratio was reduced by atmospheric dispersion at high zenith angle

Figure 3.7 shows the wind speed during the observations at the NOT in May 2000. These measurements were taken at the top of the NOT weather mast situated at the right hand side of Figure 3.1, a few tens of metres from the telescope.

Figure 3.7: The wind speed measured at the NOT weather station during the observations in May 2000. The times that four runs were taken are indicated by the star names on the graph. The wind speed was typically in the range $1$--$6$ $m$ $s^{-1}$ for these observations.