The rejection of vibrations in adaptive optics systems using a DFT-based estimation method

Adaptive optics systems are commonly used in many optical structures to reduce perturbations and to increase the system performance. The problem in such systems is undesirable vibrations due to some effects as shaking of the whole structure or the tracking process. This paper presents a frequency, amplitude and phase estimation method of a multifrequency signal that can be used to reject these vibrations in an adaptive method. The estimation method is based on using the FFT procedure. The undesirable signals are usually exponentially damped harmonic oscillations. The estimation error depends on several parameters and consists of a systematic component and a random component. The systematic error depends on the signal phase, the number of samples N in a measurement window, the value of CiR (number of signal periods in a measurement window), the THD value and the time window order H. The random error depends mainly on the variance of noise and the SNR value. This paper shows research on the sinusoidal signal phase and the estimation of exponentially damped sinusoids parameters. The shape of errors signals is periodical and it is associated with the signal period and with the sliding measurement window. For CiR=1.6 and the damping ratio 0.1% the error was in the order of 10-5 Hz/Hz, 10-4 V/V and 10-4 rad for the frequency, the amplitude and the phase estimation respectively. The information provided in this paper can be used to determine the approximate level of the efficiency of the vibrations elimination process before starting it.