Adaptive phase aberration correction based on imperialist competitive algorithm

Supercontinuum laser, as a new type of laser source, compared with monochromatic or quasi-monochromatic light, has incandescent wide spectra and the brightness of the laser. However,the beam quality in high power is usually bad and greatly affected by atmospheric turbulence in the transmission process. Therefore, how to improve the beam quality to ensure the energy transmission and image quality has become a popular topic. According to the measurement results of the near field wavefront characteristics of the supercontinuum laser in different wavelength, we know that the wavefront phase of the light source is relatively stable and change slowly over time. The types of wavefront distortion at each wavelength are basically the same, mainly made up of defocus and astigmatism. In order to conform to the wavefront characteristics of supercontinuum laser, the input of simulation is low-order static distortion wavefront generated by using Zernike polynomia with defocus and astigmatism. Stochastic Parallel Gradient Descent (SPGD) algorithm with the thorlabs DMP40 deformable mirror and CCD camera as the imaging sensor, is used to construct a simulation model for wavefront correction of low-order static distortion aberrations. Since B-SPGD algorithm is superior to U-SPGD in terms of convergence speed and correction effect, as well as adaptability to the near field wavefront distortion [1], we use B-SPGD algorithm to construct the simulation program for wavefront correction simulation research. The ability and convergence of SPGD algorithm to correct wavefront distortion are studied, mainly about the random disturbance amplitude and influence coefficient of the core parameters. In order to get close to the evaluation standard of laser in practical application, Strehl Ratio(SR) is selected as the performance evaluation function. According to the effective diameter of deformable mirror and the distance between electrodes, the influence function of deformable mirror is normalized to the unit circle to meet the requirements of simulation calculation. In order to improve the stability of SPGD algorithm and reduce the possibility of SPGD algorithm falling into local extreme values, we use Hessian matrix to optimize SPGD algorithm. After simulation and analysis of distortion correction of Supercontinuum laser wavefront, deformable mirror controlled by SPGD algorithm has good correction capability for low-order static aberration.

Magnetic fluid deformable mirror (MFDM) is a new type of wavefront corrector that features large deformation strokes, smooth continuous mirror surface, low manufacturing cost, and easy scalability. Considering the idea of taking full advantages of the MFDM's stroke strengths and the limitations of the adaptive optics (AO) system with the wavefront sensor, this paper proposes a MFDM based wavefront sensorless adaptive optics system. In order to make the MFDM produce desired deformation to eliminate unknown aberrations, this paper introduces the stochastic parallel gradient descent (SPGD) algorithm in the control system. Experimental results show that this SPGD algorithm can effectively control the MFDM to compensate for the unknown aberration in a parallel laser beam so that a perfect focused spot is produced on the CCD image.

In this paper, an aberration correction algorithm for wavefront sensorless adaptive optics system is presented, which is based on the approximately linear relation between the mean square of the aberration gradients and the second moment of far-field intensity distribution. To demonstrate algorithm's performance, an experiment system of aberration corrections for Fresnel zone plates imaging is set up. The correction results show the excellent performance of this method in correction speed, and correction capability. Comparing with conventional stochastic parallel gradient descent (SPGD) algorithm, the correction speed with this method is improved about four times for the similar correction effect.

Sensor-less adaptive optics (AO) technology is an effective method to compensate the wave front distortion caused by atmospheric turbulence in free space optical communication (FSOC) system. In general, a lot of iterations are required to update the control voltage vector step by step for the stochastic parallel gradient descent (SPGD) algorithm which is a conventional and often considered model-free algorithm. The newly developed model-based algorithms have certain constraints and difficulties for the construction of the models. Therefore, in order to develop a rapid wave front distortion compensation algorithm with better performance, we present a hybrid method which combines a model-based algorithm presented by Martin J. Booth and SPGD algorithm to correct the low-order aberration and high-order aberration respectively. Simulations show that this hybrid method can compensate wave front aberrations with higher convergence speed than that of SPGD algorithm and finally reach higher Strehl ratio (SR) and better bit error rate (BER) with same iterations, particularly under strong turbulence. This result means that our hybrid method can improve coupling efficiency and quality of FSOC system.

A low cost adaptive optical system for improving solid-state laser beam quality has been set up. This system consists of a deformable mirror, a high voltage amplifier, a set of solid-state laser system, a CCD camera, a control software and corresponding optimization algorithm. This adaptive optical system doesn't employ a wave-front sensor to detect the phase information, but optimize the light intensity within a fixed aperture in the focal plane by a 19-element piezoelectricity deformable mirror. In order to find the optimum surface profile of the deformable mirror, which is applied to correct the phase aberrations in a solid-state laser system, a global genetic algorithm is introduced. The far-field light intensity signal, which is measured by a CCD camera, is used as a fitness function of the genetic algorithm. In this paper, the performance and efficiency of this wave-front sensor-less adaptive optical system based on the genetic algorithm are presented. Both the simulation results and the experimental results are given and discussed.

Beam combination of fiber laser array is an effective technique contributed to improve the brightness of fiber lasers. In order to realize high-efficiency CBC, challenges like phase distortion (mainly including piston and tilt phase aberrations) should be taken into consideration. Resent years, tilt phase aberrations control has been come true by adaptive fiber optics collimator using the stochastic parallel gradient descent (SPGD) algorithm. However, the convergence rate of tilt control system still cannot satisfy the needs of practical application. In order to increase the tilt control bandwidth, a new idea is put forward that applying the orthogonal single frequency dithering (OSFD) technique into tilt control, and numerical simulation has been completed. A hexagonal laser array with 7 elements has been simulated, and each element has a pair of initial tilt angles in horizontal and vertical direction. The initial tilt angles comply with normal distribution. In the same condition, tilt phase control has been realized through SPGD and OSFD individually, and the convergence steps (defined as the iteration steps that improve the normalized PIB above 0.9) with appropriate parameters are respectively about 20 (SPGD) and 7 (OSFD). Furthermore, tilt phase control of large number hexagonal array is simulated, and the results are as follows: for 19/37 elements, the least convergence steps are about 80/160(SPGD) and 19/55(OSFD). Comparing with SPGD algorithm, it is obvious that the OSFD has higher convergence rate and greater potential for tilt control application in large number coherent fiber laser array.

IERUS Technologies, Inc. and the University of Alabama in Huntsville have partnered to perform characterization and development of algorithms and hardware for adaptive optics. To date the algorithm work has focused on implementation of the stochastic parallel gradient descent (SPGD) algorithm. SPGD is a metric-based approach in which a scalar metric is optimized by taking random perturbative steps for many actuators simultaneously. This approach scales to systems with a large number of actuators while maintaining bandwidth, while conventional methods are negatively impacted by the very large matrix multiplications that are required. The metric approach enables the use of higher speed sensors with fewer (or even a single) sensing element(s), enabling a higher control bandwidth. Furthermore, the SPGD algorithm is model-free, and thus is not strongly impacted by the presence of nonlinearities which degrade the performance of conventional phase reconstruction methods. Finally, for high energy laser applications, SPGD can be performed using the primary laser beam without the need for an additional beacon laser. The conventional SPGD algorithm was modified to use an adaptive gain to improve convergence while maintaining low steady state error. Results from laboratory experiments using phase plates as atmosphere surrogates will be presented, demonstrating areas in which the adaptive gain yields better performance and areas which require further investigation.

To speed up the convergence rate of Stochastic Parallel Gradient Descent(SPGD) algorithm that was used to control a deformable mirror for wavefront shaping and to enhance the capability of real-time wave-front shaping,a simulation model was established by using wave-front distortion described by 12 Zernike polynomials and a 32-unit deformable mirror.Two constant matrixes were obtained with the orthogonality of Zernike polynomials in a unit circle,which simplizes computations and speeds up the running time of the algorithm.After 660 iterations,the Strehl ratio is 0.8.Comparison results of 6 kinds of SPGD algorithms with Matlab7.8.0 show that indirect-fixed-bilateral SPGD algorithm can be used in the conditions of low Strehl ratio,and indirect-varied-bilateral SPGD algorithm can be used in the conditions of high Strehl ratio,which will speed up the convergence rate of SPGD algorithm and provide the theoretical guidance for laser shaping.

The adaptive polarization conversion system which converts the non-polarization maintaining laser to polarization maintaining one based on stochastic parallel gradient descent (SPGD) algorithm is reported in this paper. Using polarization controller to control polarized component in X and Y direction directly, adopting SPGD optimization technology to optimize the output extinction ratio, it finally realizes polarization conversion of non-polarization maintaining laser to polarization maintaining one. In theory, the model of adaptive polarization conversion is built based on the principle of the controller and the SPGD algorithm. In experiment, we first realized adaptive conversion of non-polarization maintaining laser to polarization maintaining one with an extinction ratio of 14.1 dB. Then we used the system to change the polarization direction of the linearly polarized laser from any direction (0-360) to the expected direction with high extinction ratio, and the average extinction ratio is about 12 dB.

Instead of acquiring the previous aberrations of an optical wavefront with a sensor, wavefront sensor-less (WFSless) adaptive optics (AO) systems compensate for wavefront distortion by optimizing the performance metric directly. The stochastic parallel gradient descent (SPGD) algorithm is pervasively adopted to achieve performance metric optimization. In this work, we incorporate CoolMomentum, a method for stochastic optimization by Langevin dynamics with simulated annealing, into SPGD. Numerical simulations reveal that, compared with the state-of-the-art SPGD variant, the proposed CoolMomentum-SPGD algorithm achieves better convergence speed under various atmospheric turbulence conditions while requiring only two tunable parameters.

In wave-front-sensor-less adaptive optics (WFS-less AO) systems, the Jacopo Antonello (JA) method belongs to the model-based class and requires few iterations to achieve acceptable distortion correction. However, this method needs a lot of measurements, especially when it deals with moderate or severe aberration, which is undesired in free-space optical communication (FSOC). On the contrary, the stochastic parallel gradient descent (SPGD) algorithm only requires three time measurements in each iteration, and is widely applied in WFS-less AO systems, even though plenty of iterations are necessary. For better and faster compensation, we propose a WFS-less hybrid approach, borrowing from the JA method to compensate for low-order wave front and from the SPGD algorithm to compensate for residual low-order wave front and high-order wave front. The correction results for this proposed method are provided by simulations to show its superior performance, through comparison of both the Strehl ratio and the convergence speed of the WFS-less hybrid approach to those of the JA method and SPGD algorithm.

Stochastic parallel gradient descent (SPGD) algorithm is one of the most promising methods for effective coherent beam combination. However, the algorithm also has some disadvantages, such as slow convergence speed and local extremum. This paper proposes an AdaDelSPGD algorithm, which combines an AdaDelta algorithm with a SPGD algorithm, and improves the traditional AdaDelta algorithm with adaptive gain coefficient. It is worth noting that the adaptive gain coefficient can be adjusted in real time to improve the convergence rate. The effectiveness of the proposed algorithm is verified by relevant simulation experiments, and the results show that the proposed algorithm can significantly improve the convergence speed. Following the experiments with the fiber laser-phased array multiplex communication system, we can draw the conclusion that the addition of communication modulation reduces the beam quality, and the higher the modulation frequency, the worse the beam quality. However, adding the SPGD algorithm can improve the beam quality. The AdaDelSPGD algorithm proposed in this paper can further improve the beam quality, and the bit error rate of communication is also decreased after testing. This provides a foundation for further research on the fiber laser-phased array multiplex communication system.

The adaptive interferometer has been recently proposed to realize the metrology of unknown freeform surfaces with several restructured algorithms for feedback control. The adaptive moment estimation (Adam) stochastic parallel gradient descent (SPGD) algorithm is employed in this paper for fringes release. The proposed algorithm makes considerable progress in relieving conflict of the convergence rate, speed, and parameters intervention. Simulations and experiments show its 37% time saving and 99% convergence rate, with arbitrarily configured parameter increment, compared with the SPGD algorithm. It would have great potential in in-process tests in freeform surface fabrication or large-volume testing.

Owing to the restriction of the stimulated Brillouin scattering (SBS) and other nonlinear effects, the output power of the single frequency amplifier is ar a level of about hundred watts. Multi-wavelength and non-single frequency seed laser will mitigate the SBS and improve the output power of the fiber laser amplifier. The coherent beam combining of the non-single frequency and/or multi-wavelength laser will greatly increase the total output power of the coherent beam combining as compared with the coherent beam combining of a single frequency laser. Based on the stochastic parallel gradient descent (SPGD) algorithm, coherent combining of four channel four-wavelength lasers is realized. In the close loop state, the mean power of the main-lobe is four times higher than that of the open-loop, approaching 75% of its ideal value. The coherent combining of the multi-wavelength and non-single frequency laser is demonstrated and an approach to the high power coherent beam combining is provided.

An adaptive optics (AO) system based on a stochastic parallel gradient descent (SPGD) algorithm is proposed to reduce the speckle noises in the optical system of a stellar coronagraph in order to further improve the contrast. The principle of the SPGD algorithm is described briefly and a metric suitable for point source imaging optimization is given. The feasibility and good performance of the SPGD algorithm is demonstrated by an experimental system featured with a 140-actuator deformable mirror and a Hartmann-Shark wavefront sensor. Then the SPGD based AO is applied to a liquid crystal array (LCA) based coronagraph to improve the contrast. The LCA can modulate the incoming light to generate a pupil apodization mask of any pattern. A circular stepped pattern is used in our preliminary experiment and the image contrast shows improvement from 10−3 to 10−4.5 at an angular distance of 2λ/D after being corrected by SPGD based AO.