Errors in the Estimation Method for the Rejection of Vibrations in Adaptive Optics Systems

In recent years the problem of the mechanical vibrations impact in adaptive optics (AO) systems has been renewed. These signals are damped sinusoidal signals and have deleterious effect on the system. One of software solutions to reject the vibrations is an adaptive method called AVC (Adaptive Vibration Cancellation) where the procedure has three steps: estimation of perturbation parameters, estimation of the frequency response of the plant, update the reference signal to reject/minimalize the vibration. In the first step a very important problem is the estimation method. A very accurate and fast (below 10 ms) estimation method of these three parameters has been presented in several publications in recent years. The method is based on using the spectrum interpolation and MSD time windows and it can be used to estimate multifrequency signals In this paper the estimation method is used in the AVC method to increase the system performance. There are several parameters that affect the accuracy of obtained results, e.g. CiR number of signal periods in a measurement window, N number of samples in the FFT procedure, H time window order, SNR, b number of ADC bits, y damping ratio of the tested signal. Systematic errors increase when N, CiR, H decrease and when y increases. The value for systematic error is approximately 10(-10) Hz/Hz for N = 2048 and CiR = 0.1. This paper presents equations that can used to estimate maximum systematic errors for given values of H, CiR and N before the start of the estimation process.