Magnetic fluid deformable mirror based wavefront sensorless adaptive optics systems

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.

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.

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.

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.

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.

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.

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.

<sec> With the development of laser technology, the application scope of nondiffracting beams, such as Bessel beams, Mathieu beams, cosine beams, and parabolic beams, which remain invariant along their propagation, continues to expand. During its propagation, the main lobes of these beams tend to bend towards off-axis position, which is called self-accelerating (or self-bending) property. A Bessel-like beam with self-acceleration can realize the propagation of the main lobe along a curved trajectory while maintaining the non-diffraction. Because of the above property, Bessel-like beams have been utilized in various areas such as guiding particles along arbitrarily curved trajectories, self-accelerating beams in nonlinear medium, plasma guidance, and laser-assisted guiding of electric discharges around objects. </sec><sec> In this paper, we propose a method of bending the trajectory of Bessel-like beams by using a magnetic fluid deformable mirror (MFDM) instead of traditional spatial light modulator (SLM) and Pancharatnam-Berry (PB) phase manipulation. The MFDM provides a method without pixelation, where all parameters can be rapidly modified for fine-tuning. Furthermore, compared with the conventional deformable mirror, the MFDM has the advantages of a continuous and smooth mirror surface, large shape deformation, low manufacture cost, easy extension, and large inter-actuator stroke. Therefore, it is easy for the MFDM to generate the ideal shape of an axicon. Firstly, according to geometric analysis, the asymmetrical mirror profile to produce a self-accelerating Bessel-like optical beam is proposed. The proposed mirror profile can be used to compensate for the difference in optical path length for each annular slice of the axicon. If a collimated Gaussian beam is incident on the mirror combining the axicon and the asymmetrical mirror profiles, which can obtain Bessel-like beams with arbitrarily curved trajectories. Secondly, the resultant of the self-accelerating Bessel-like beams along parabolic trajectories is validated by the simulation in MATLAB. Finally, a prototype of MFDM consisting of the dual-layer arrays of miniature electromagnetic coils, a Maxwell coil and the magnetic fluid filled in a circular container is fabricated for the experiment. The experimental results show that the Bessel-like beams propagate along the parabolic trajectories, with the MFDM used, and the accuracy of the curved trajectories is verified. The proposed method in this paper opens a new experimental way to the study of Bessel-like beam; the theoretical approach can also be generalized mathematically for other non-paraxial beam propagation. </sec>

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.

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.

We investigate numerically the feasibility of phase aberration correction in a wavefront sensorless adaptive optical system, based on the imperialist competitive algorithm (ICA). Considering a 61-element deformable mirror (DM) and the Strehl ratio as the cost function of ICA, this algorithm is employed to search the optimum surface profile of DM for correcting the phase aberrations in a solid-state laser system. The correction results show that ICA is a powerful correction algorithm for static or slowly changing phase aberrations in optical systems, such as solid-state lasers. The correction capability and the convergence speed of this algorithm are compared with those of the genetic algorithm (GA) and stochastic parallel gradient descent (SPGD) algorithm. The results indicate that these algorithms have almost the same correction capability. Also, ICA and GA are almost the same in convergence speed and SPGD is the fastest of these algorithms.

A phase controller for coherent beam combining (CBC) of fibre lasers has been designed and manufactured based on a stochastic parallel gradient descent (SPGD) algorithm and a field programmable gate array (FPGA). The theoretical analysis shows that the iteration rate is higher than , and the average compensation bandwidth of CBC for 5 or 20 channels is or , respectively. The tests show that the phase controller ensures reliable phase locking of lasers: When the phases of five lasers are locked by the improved control strategy with a variable gain, the energy encircled in the target is increased by than that in the single output, the phase control accuracy is better than , and the combining efficiency is 92 %.

Brain tumour diagnosis is significant for both physicians and patients, but the low contrast and the artefacts of MRI glioma images always affect the diagnostic accuracy. The existing mainstream image enhancement methods are insufficient in improving contrast and suppressing artefacts simultaneously. To enrich the field of glioma image enhancement, this research proposed a glioma image enhancement method based on histogram modification and total variational using stochastic parallel gradient descent (SPGD) algorithm. Firstly, this method modifies the cumulative distribution function on the image histogram and performs gamma correction on the image according to the modified histogram to obtain a contrast‐enhanced image. Then, the method suppresses the artefacts of glioma images by total variational and wavelet denoising algorithm. To get better enhancement images, the optimal parameters in the proposed method are searched by the SPGD algorithm. The statistical studies performed on 580 real glioma images demonstrate that the authors’ approach can outperform the existing mainstream image enhancement methods. The results show that the proposed method increases the discrete entropy of the image by 8.9% and the contrast by 2.8% compared to original images. The enhanced images are produced by the proposed method with a natural appearance, appealing contrast, less degradation, and reasonable detail preservation.

In order to improve the recognition ability of tunnel cracks in the UAV platform with a vision imaging system in the UAV platform with a vision imaging system, this paper proposes a tunnel crack segmentation algorithm using SPGD-and-generative adversarial network fusion. The SPGD algorithm can enhance the detail and edge information of a tunnel crack image, which improves the clarity of the tunnel crack image. The new generative adversarial network (GAN) is designed by using an improved U-Net generator and full convolutional network (FCN) discriminator to form a new network; the improved generative adversarial network can effectively segment tunnel crack images after stochastic parallel gradient descent (SPGD) algorithm processing, especially the texture feature extraction and segmentation of small tunnel cracks, which can improve the rate of recognition of tunnel cracks. Based on collected tunnel crack image data, we selected 12 typical tunnel crack images and verified the rationality and advanced nature of the proposed recognition algorithm by comparing it with other recognition methods. The results show that the recognition rate of the proposed tunnel crack recognition algorithm was significantly improved.

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.