When high performance is expected, vibrations are becoming a burning issue in adaptive optics systems. For mitigation of these vibrations, in this paper, we propose a method to identify the vibration model. The nonlinear least squares algorithm named the Levenberg-Marquardt method is adapted to acquire the model parameters. The experimental validation of the high performance of vibration mitigation associated with our identification method has been accomplished. Benefiting from this method, vibrations have been significantly suppressed using linear quadratic Gaussian control, where the root-mean-square of the residual vibrations has been reduced down to a portion of a microradian. Moreover, the experimental results show that with the model identified, vibrations ranging from wide low-frequency perturbation to high-frequency vibration peaks can be dramatically mitigated, which is superior to classical control strategies.

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An optimization-based correction method is developed to control simultaneously two deformable mirrors in a wavefront-sensor-less adaptive beam cleanup system, where the wave-front aberrations could not be compensated by a single deformable mirror. Stochastic parallel gradient decent algorithm is chosen as the optimization algorithm. In this control method, different aberrations are assigned to each deformable mirror according to their different correction quality. The method is proved to be effective by numerical simulations as well as experiments. Experimental results showed that the area containing 84% energy of the laser beam in the far-field can reach 3.0 times diffraction limited.

A simple but effective decoupling control algorithm based on Zernike mode decomposition for adaptive optics systems with dual deformable mirrors is proposed. One of the two deformable mirrors is characterized with a large stroke (woofer) and the other with high spatial resolutions (tweeter). The algorithm works as follows: wavefront gradient vector is decoupled using the Zernike modes at first, and then the control vector for the woofer is generated with low order Zernike coefficients to eliminate high order modes. At the same time the control vector for the tweeter is reset by a constraint matrix in order to avoid coupling error accumulation. Simulation indicates the algorithm could get better performance compared with traditional Zernike mode decomposition control algorithms. Experiments demonstrate that this algorithm can effectively compensate for phase distortions and significantly suppress the coupling between the woofer and tweeter.

We present a slab laser amplifier beam cleanup experimental system based on a 39-actuator rectangular piezoelectric deformable mirror. Rather than use a wave-front sensor to measure distortions in the wave-front and then apply a conjugation wave-front for compensating them, the system uses a Stochastic Parallel Gradient Descent algorithm to maximize the power contained within a far-field designated bucket. Experimental results demonstrate that at the output power of 335W, more than 30% energy concentrates in the 1x diffraction-limited area while the beam quality is enhanced greatly.

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For the accurate extraction of cavity decay time, a selection of data points is supplemented to the weighted least square method. We derive the expected precision, accuracy and computation cost of this improved method, and examine these performances by simulation. By comparing this method with the nonlinear least square fitting (NLSF) method and the linear regression of the sum (LRS) method in derivations and simulations, we find that this method can achieve the same or even better precision, comparable accuracy, and lower computation cost. We test this method by experimental decay signals. The results are in agreement with the ones obtained from the nonlinear least square fitting method.