Relevant parameters for tip-tilt systems on large telescopes

In order to provide criteria for the design of tip-tilt systems on large telescopes, we derive analytic formulas for the aberrations of the tip-tilt corrected wave front as a function of the tracking algorithm and of the tracking frequency. We present a new definition for the required bandwidth of tip-tilt systems based upon the residual high-order aberrations, and we suggest a new, simple method to eliminate the influence of coma on the image centroid measurement. The effect of the science camera pixel size on the image quality is investigated. A simple approximation is given for the power spectrum of the image motion, and measured power spectra are compared to this approximation. We show that in order to measure the rms image motion properly, it is important to run the measurement over a sufficient period of time (> 10 min). In a second paper (Glindemann et al. 1997, PASP, 109, 688-696) in this journal, a tip-tilt system (CHARM) is presented where the parameters derived here are used to evaluate the system performance.