Tracking Stability of the WHT

 Tracking errors Any imperfections of the telescope's tracking system will contribute to the width of  long exposure images. These may include slow tracking errors as well as vibrations of the telescope structure at higher frequencies. The WHT autoguider system operates at a closed loop bandwidth of approximately 0.1 Hz.  Tracking errors occurring at higher frequencies are uncorrected, so that the spectrum of image motion at frequencies higher than 0.1 Hz is relevant to the long exposure PSF width.

The JOSE wavefront sensor data provides measurements of the power spectrum of image motion. The first order Zernike terms measure the component of image motion which is common to all subapertures of the wavefront sensor, ie. the mean tilt of the wavefront over the whole telescope pupil. Tilts result from both tracking errors and from large scale atmospheric seeing distortions.

The figure below shows  the averaged power spectrum of the first order Zernike terms  for the JOSE data set. In general the telescope and atmospheric contributions to the spectrum cannot be distinguished. However, a narrow spike in the power spectrum due to a known oscillation of the WHT structure  is visible at 2.7 Hz. Although this resonance contributes little power on average, the oscillation can have a significant effect on image width if it is strongly excited, for example by wind buffeting of the telescope structure. Such high frequency telescope oscillations are difficult to detect during normal astronomical observations. In future it may be possible to monitor the telescope drive encoders automatically, and to alert the observer to excess tracking errors at high frequencies.

The power spectrum shows that there is significant power in image motions at frequencies higher than the autoguider bandwidth (0.1 Hz). However, the total variance for the Zernike tilts measured by the JOSE sensor is on average less than expected for the Tatarski structure function of atmospheric fluctuations with infinite outer scale (figure).  This indicates that the outer scale of turbulence is not much greater than the 4.2-m aperture of the WHT.  Furthermore, there are no very large contributions from uncorrected tracking errors.

Mean power spectrum of image motion (Zernike tilts) for the WHT, derived from the JOSE data set.

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