Investigation On Stochastic Parallel Gradient Descent Algorithm For Deformable Mirror Control

With the increasing requirements for high-resolution imaging,the requirement for adaptive optics technology has increased in various fields,including astronomical observation,biological microscopy,human eye imaging and atmospheric communication.Adaptive optical systems based on traditional piezoelectric deformation mirrors are complex with low optical energy utilization,high voltage drives and high costs,which limit their applications in the civil field.In recent years,there has been a lot of research on wave-front sensorless adaptive optics technology,which does not require a wave-front detector.The system has a compact structure and high energy utilization,which has attracted more and more attention.It only replaces wave-front detection with an algorithm,reducing system cost.The stochastic parallel gradient descent(SPGD)algorithm is its typical representative.SPGD algorithm is an optimization algorithm based on random signals and the global funct ion of the system.It is a commonly used algorithm in wave-front sensorless adaptive optical system.However,due to the randomness and iterative requirements,the algorithm converges slowly and the imaging result is unsatisfactory,which is the main reason that the current wave-front sensorless system exists mainly in laboratory and cannot be used in practical applications.In order to promote its application in the fields of communication,biological microscopic imaging,laser atmospheric transmission,etc.,it is necessary to improve the algorithm convergence speed and accuracy.In the work,an adaptive optical system based on a 69-unit voice coil deformation mirror is constructed,and the SPGD control algorithm is studied.The main tasks include:The control algorithms of the voice coil deformable mirror are summarized in this thesis.First,we describe the working principle of the voice coil deformable mirror and the control basis of the deformable mirror surface—the response function and control matrix.Then,the closed-loop control algorithms based on the control matrix are summarized,including PID control,SPGD algorithm and simulated annealing(SA)algorithm.Next,the electro-optic performance of the 69-unit voice coil deformable mirror was investigated,which was important for its high-precision control in the wave-front sensorless adaptive optical system.The tests mainly include the driver linearity and hysteresis,the surface flattening ability of deformable mirror,the fitting ability to Zernike surface shape,and the response time.The linearity of the voice coil driver is 4.17%,the average hysteresis error is 0.46%.The flattening rms of the deformable mirror is 8.48 nm,and the fitting of 3-8Zernike shapes is performed,and the average PV value of the largest fitting shape is36.557μm.The test results show that the voice coil deformable mirrors have excellent linearity,low hysteresis,high accuracy,and fast response.A closed-loop correction experiment was conducted,and the corrected wave-front rms converges to 24.5nm.The SPGD control algorithm based on the voice coil deformable mirror is optimized and improved to promote its practical application.By simulation,in order to improve the convergence speed of the wave-front sensorless adaptive optics system based on SPGD algorithm without reducing accuracy,the relationship between the amplitude of random perturbation and the gain factor in the SPGD algorithm are studied and optimized.First,a full-range simulation study on the relationship between random disturbance amplitude and gain coefficient is conducted to obtain the best relationship curve,it’s different with the existing SPGD algorithm,which empirically fixes the value of one parameter and then searches the other parameter.This study obtains all the optimal relationship curves of the two key parameters of SPGD algorithm.In the actual correction process,they can directly and accurately find their optimal values according to the size of the distortion.It is beneficial to improve the convergence speed and accuracy of the wave-front sensorless system.Experiment shows that adaptive optics system has a parameter preference area that is related to the initial distortion magnitude.With the theoretical verification and the comparison with simulated annealing algorithm,the results show that the convergence accuracy of the SPGD algorithm is 6.32% higher than that of the SA algorithm.At the same time,an extended target calibration experiment based on the SPGD algorithm is conducted to discuss the convergence of the SPGD algorithm under the different cost functions.The results show that the correction accuracy of the image VAR evaluation is better than the wave-front rms evaluation and image SMD evaluation by 5.6% and 3.8%.