HRCam data

After the preliminary screening 1662 observation records were retained.
The general statistics of the FWHM measurements is

 
Average: 		 0.65 arcsec

Median: 		  0.61 arcsec

Rms: 		     0.18 arcsec

Minimum: 		 0.35 arcsec

One should note here that the median values are more significant of general performance than arithmetic averages. Image quality and seeing statistics follow an approximately log-normal distribution (see fig. ) in which the average is significantly larger than the median. Therefore plain regression techniques, which assume a Gaussian distribution, cannot be applied directly on distributions of FWHM values and we will here use the method of collapsing the data to median values binned over small intervals of a dependent variable before applying fitting techniques.

  
Figure: Histogram of FWHM data from HRCam: note the typical log-normal distribution.

A first verification establishes that the HRCam FWHM distribution does not appear to show a significant dependency on wind speed:

 
Median for U < 5 m/s: 		 0.61 arcsec

Median for 5 < U < 10 m/s: 		 0.64 arcsec

Median for 10 < U < 15 m/s: 		 0.64 arcsec

Median for U > 15 m/s: 		 0.58 arcsec

The temperature data measured at several locations around the telescope and in the dome (see table ) confirm that the CFHT dome environment is almost permanently characterized by a stable thermal stratification. In the vast majority of the observations the air temperature above the primary mirror is lower than the one near the top ring, which in turn is lower than the external air temperature - see fig. . This stratification effectively "damps" free convection flow patterns and any related turbulence. Indeed one does not find any seeing that could be attributed to 's between air and floor and dome surfaces.

The temperature of the primary mirror stays generally very close to the one of air just above it: the average of the mirror surface-air temperature difference is + 0.05K, with a rms of 0.47K. As shown by fig. , and are visibly correlated (the correlation coefficient is 0.75) while this hardly appears to be the case of the pairs consisting of and , although the correlation coefficient is nevertheless 0.14 .

  
Figure: Scatter plot of versus

Fig. shows a scatter plot of FWHM values with respect to . In order to avoid bias from the airmass effect only observations with are taken (984 records). Binned medians are also shown.
For a trend to larger median FWHM is noticeable.
For no influence is noted, if one excepts a group of values for which is less than -1K, which belong all to a same observation sequence. Therefore the higher average seeing of this sequence may well be due to increased natural seeing accidentally occurring at the time.

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Figure: Scatter plot of HRCam FWHM versus the temperature difference between the mirror surface and the surrounding air. Binned median values and the are also shown.

Fig. shows a scatter plot of FWHM values with respect to the temperature difference between the dome interior and the outside air. Again only observations with are considered. Note that because of the dome floor cooling system, the dome interior is amost always colder than the outside air.
For no dependency is appearing.
For there may seem to be a trend toward increased seeing, but too few data points exist to derive any significant conclusion.

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Figure: Scatter plot of HRCam FWHM versus the dome-outside temperature difference .

In order to find correlation coefficients that would fit equations () and (), it is necessary to get first an estimate of the fixed telescope/instrument error . By correlating with respect to a subset of FWHM values for which the temperature dependent effects are absent, one can estimate the mean natural seeing and the fixed error due to the instrument. This subset, which includes only FWHM values corresponding to K and K (858 records), is plotted in fig. . Noting that, when and are nil, equation () becomes

a least square fit on the binned median values of the selected subset gives a fixed error due to the instrument
arcsec

while the median natural seeing is evaluated as
arcsec

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Figure: HRCam FWHM versus in absence of mirror and dome seeing

To find a parameterization for the FWHM versus relationship, we consider a subset with (fig. ). Noting that in this case, equation (), combined with () gives

For , a least square fit gives = 0.38 which results in the following parameterization for the mirror seeing contribution:

This fit is also plotted on fig. .
For the slope is practically nil, while for K, the data are inconclusive, as explained above.

So far then, recalling that no dependency appears with respect to the temperature difference between the dome interior and the outside air, the HRCam performance appears represented by the following relationship:

Other possible dependencies were sought by analyzing the values of natural seeing extracted by means of equation ()

versus other temperature differences obtainable from the sensors listed in table . None could be determined. For instance, fig. shows a plot of values computed from () with respect to the temperature gradient along the tube : no correlation is apparent.

Noting that we had not taken into account the mirror orientation in the parameterization for mirror seeing (), we have analyzed also a subset of values in which is > 0.5K with respect to - fig.. Also in this case no correlation is apparent.

Finally, the median of over the entire data set (1662 records) is 0.39 arcsec, very close to the value of 0.397 arcsec evaluated previously.
Equation () can thus be considered as verified for the HRCam observations.

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Figure: HRCam computed natural seeing with respect to the temperature gradient along the tube .

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Figure: Check for unaccounted effects of telescope orientation on mirror seeing: HRCam computed natural seeing with respect to (only data with 0.5K)