Until last week, the telescope control software used a relationship between the Z-focus position of the SMU and antenna leg temperatures. This was in the absence of a better estimate for the temperature of the antenna hardware, although future work on the dish temperature sensor system should provide another option and despite the (re-?)discovery last week that the Z-focus was better correlated with ambient air temperature than with antenna leg temperature.

This document examines in more detail the thermal cycles of the JCMT legs and air in order to facilitate future improvements in the SMU thermal correction algorithms.

The leg temperatures (L) lag the air temperatures (T) throughout the day, as seen in the following plot (ignore the red line):

In it we follow these temperatures through 01 Oct 2002, and the locus is followed clockwise from midnight to midnight. L lags several hours behind T. A whole month's worth of data is shown below:

where clockwise loci of different amplitudes may be seen. At any given time of the day, however, it is instructive to plot L against T : the plot below shows the 31 data from October representing the mean temperatures in the 15minutes around 02:00 HST each day :

The best-fit straight line is shown and the slope noted. These slopes are plotted against hour of the day below :

and show an obvious diurnal cycle. The upshot is that where a previous algorithm used a liner relationship between Z-focus offset and L :
            DZT = DZT_CONST + ( DZT_COEFF * MEAN_TEMPERATURE )
a new relationship between dZ and T should be expected to be linear with T but with different coefficients for different times of the day - something not incorporated into the code. In fact the switch from using L to using T assumed a slope of unity, which may be roughly correct on average but is precisely correct only twice per day ! (The 'stopped clock' syndrome). For nighttime work a value of between 0.5 and 0.6 would be more useful, and presumably this will emerge empirically from analysis of future recorded focus data.