Research On Laser Beam Shaping Technique Based On Stochastic Parallel Gradient Descent Algorithm

In the applications of laser, the beams with high energy concentration areusually needed. However, poor quality of the beam from laser, surface machiningerrors of the optical elements, and alignment errors of the optical system will causethe wave-front distortions. For the applications of high-energy laser, there is anotherproblem of thermal deformation. In addition, the energy of laser will disperse furtherbecause of the external conditions such as atmospheric turbulence during beamtransmission. All the matters will seriously affect the laser beam focusing, resultingin lower utilization of energy. Whereas the problem, laser beam shaping isparticularly essential. Beam shaping means to modulate the wave-front phase of alaser beam by use of wave-front correction devices, thereby change the lightintensity distribution of the beam, so as to improve the beam quality and meet theneeds of practical applications.Among beam shaping techniques, the adaptive style based on the deformationmirror can optimize the system performance index directly by using some controlalgorithm, and obtain the surface shape and control voltages of the deformablemirror, for the purpose of real-time shaping. The stochastic parallel gradient descent(SPGD) algorithm is a commonly used optimized control algorithm, which is easy tobe implemented and has a fast convergence rate. Further more, if the convergence index and parameters of the algorithm are appropriate, the convergence precision canbe ensured. Therefore, the algorithm has greater application values, and becomes acurrent research hotspot.In this paper, firstly, the research background, development process and specificimplementation methods of laser beam shaping technique are surveyed, as well asthe research status of SPGD algorithm at home and abroad. Then, the mathematicalbasis, basic principles, implementation process and convergence characteristics ofSPGD algorithm are analyzed amply in theory. Then, the composition of the laserbeam shaping system based on SPGD algorithm are introduced, with the principlesand applications of deformable mirror, the shaping device, as the emphases. On thisbasis, the beam shaping based on SPGD is researched with numerical simulations,and the contents include the flat-topped and focused beam shaping of Gaussian beam,as well as the validation of algorithm’s convergence properties. The results ofsimulations verify the feasibility of SPGD to beam shaping. Finally, a set of focusedbeam shaping experimental system based on SPGD is designed and built, with themicro-machined membrane deformable mirror (MMDM) as the shaping device. Andthe experiment is achieved respectively with three performance evaluation functions:radius of the focused spot, encircled energy ratio with geometric center as the center,and encircled energy ratio with centroid as the center. As a result, the shaped beam iswell. By comparing the convergence rates and shaping effects of the three cases,there is a conclusion that it is best to choose encircled energy ratio of centroid as theperformance evaluation function, with certain guiding significance to the practicalapplications.