Wide-Field Telescope Alignment Using the Model-Based Method Combined with the Stochastic Parallel Gradient Descent Algorithm

To acquire images with higher accuracy of wide-field telescopes, deformable mirrors with more than 100 actuators are used, making the telescope alignment more complex and time-consuming. Furthermore, the position of the obscuration caused by the secondary mirror in the experiment system is changed with the difference of fields of view, making the response matrix of the deformable mirror different in various fields of view. To solve this problem, transfer functions corresponding to different fields of view are calculated according to the wavefront edge check and boundary conditions. In this paper, a model-based method combined with the stochastic parallel gradient descent (SPGD) algorithm is used. The experiment results show that our method can correct the aberrations with a high accuracy in both on-axis and off-axis fields, indicating that the effective actuators are well chosen corresponding to different fields of view.

Adaptive Gradient Estimation Stochastic Parallel Gradient Descent Algorithm for Laser Beam Cleanup

For a high-power slab solid-state laser, obtaining high output power and high output beam quality are the most important indicators. Adaptive optics systems can significantly improve beam qualities by compensating for the phase distortions of the laser beams. In this paper, we developed an improved algorithm called Adaptive Gradient Estimation Stochastic Parallel Gradient Descent (AGESPGD) algorithm for beam cleanup of a solid-state laser. A second-order gradient of the search point was introduced to modify the gradient estimation, and it was introduced with the adaptive gain coefficient method into the classical Stochastic Parallel Gradient Descent (SPGD) algorithm. The improved algorithm accelerates the search for convergence and prevents it from falling into a local extremum. Simulation and experimental results show that this method reduces the number of iterations by 40%, and the algorithm stability is also improved compared with the original SPGD method.

Modal reconstruction of transverse mode-locked laser beams

Transverse mode-locking in an end-pumped solid state laser by amplitude modulation with an acousto-optic modulator was investigated. Using the stochastic parallel gradient descent algorithm the modal power coefficients and the modal phases of the transverse mode-locked (TML) laser beam were reconstructed from the measured spatial and spatio-temporal intensity distributions, respectively. The distribution of the reconstructed modal power coefficients revealed that the average mode order of the transverse mode-locking process could be increased by a factor of about 8 compared to previous works, corresponding to an increase in the normalized oscillation amplitude by a factor of about 3. Furthermore, we found that besides a non-Poissonian modal power distribution, strong aberrations of the modal phases occurred in the experiment, resulting in a deformation of the oscillating spot. Additionally, we demonstrated the generation of up to four spots oscillating simultaneously on parallel traces by operating the TML laser on a higher mode order in the orthogonal direction to the transverse mode-locking process. TML lasers are of interest, e.g., for beam scanning purposes, as they have the potential to enable spot resolving rates in the multi-GHz regime.