Wavefront Sensorless Adaptive Optics Correction Method Based On Deformable Mirror Eigen-modes

Classical adaptive optics (AO) system usually uses a customized wavefront sensor(such as Shark-Hartmann) to measure aberrations and a wavefront corrector (such asdeformable mirror) to make compensation. However, traditional AO system’s structure iscomplex and not applicable in some scenarios which cannot obtain a proper beacon, such asmultiphoton microscopy imaging system. In wavefront sensorless adaptive optics (WSAO)system, a distinct wavefront sensor is absent and the corrector is directly controlled by theinformation acquired from an image detector. With the advantages of small size and simplestructure, WSAO system has a broad application prospect.The wavefront correction methods in WSAO can be classified into two groups: onekind is model-free optimization algorithms, such as genetic algorithm, simulated annealingand stochastic parallel gradient descent (SPGD) algorithm. A metric function is needed toconverge with a large number of iterations for these algorithms. The iterative number ofSPGD algorithm is proportional to the square root of actuator numbers, so the convergencecan be very slow when using a large-actuator-number DM.Another kind is modal-based optimization algorithms whose optimized objects arespecific modes which make up wavefront aberration. The convergence can be dramaticallyaccelerated for large-actuator-number DM using modal-based algorithms. Martin Booth inOxford has proposed a non-iterative modal-based WSAO algorithm using Lukosz modeswhen they investigated high resolution microscopy imaging system. The requiredcorrection amount of each mode is directly solved from the relationship between Lukoszmode coefficients and metric function in this algorithm. Compared with SPGD algorithm,the real-time performance of WSAO system is improved greatly. However, DM cannotgenerate Lukosz modes accurately because of the limited DM fitting ability, and thecorrection accuracy will decline. To solve this problem, a WSAO algorithm based on DMeigen-modes which are deduced from influence functions of DM actuators is proposed. DMeigen-modes reflect the correction ability of DM itself and can be generated accurately byDM. The reconstruction accuracy of WSAO based on DM eigen-modes is higher because itavoids the fitting error of using classic Lukosz modes. The major contents of this paper arelisted as follows: 1. The basic principle of WSAO based on DM eigen-modes (referred to as“modal-based”) is described in detail, and the DM eigen-modes whose derivatives areorthogonal with each other are obtained from influence functions of DM.2. The related parameters in modal-based algorithm are simulated. The correctionability of Zernike aberrations is analyzed in open-loop and closed-loop mode. The influenceof image noise and image structure is discussed. The correction accuracy of WSAO basedon DM eigen-modes and Lukosz modes is compared. The convergence speed and accuracyin comparison with classic SPGD algorithm are also given.3. DM eigen-modes of OKO37-channel Membrane DM are obtained by experiment.The feasibility of modal-based algorithm is verified by experiment. In the same conditions,the correction accuracy of using DM eigen-modes is higher than that of using Lukoszmodes. The correction accuracy of modal-based algorithm and SPGD algorithm is similar,however, modal-based algorithm converges faster, thus has higher closed-loop correctionbandwidth and avoids stagnation in SPGD algorithm.4. A hybrid WSAO method based on modal-based and SPGD algorithm aftercomparing the two algorithms is proposed. In hybrid correction, wavefront error is firstcorrected by modal-based algorithm and then by SPGD algorithm. The experimental resultsshow that the actuator saturation problem in modal-based correction is avoided and theiterative number of SPGD algorithm is dramatically reduced.