A successful beam cleanup of a 5-mJ/200-μs pulsed solid-state laser system operating at 532-nm wavelength is demonstrated. In this beam cleanup system, a wave-front sensor-less adaptive optics （AO） system is set up with a 20-element bimorph mirror （BM）, a high-voltage amplifier, a chaxge-coupled device camera, and a control software implementing the stochastic parallel gradient descent （SPGD） algorithm. The brightness of the laser focal spot is improved because the wave-front distortions have been compensated. The performance of this system is presented and the experimental results are analyzed.
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.
