Simulation and analysis of distortion correction of supercontinuum wavefront based on SPGD algorithm

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Coherent beam combining (CBC) of fiber laser array is a promising way to achieve high output power. Phase control is one key point to implement CBC. Appropriate feedback structures should be established to achieve phase control. Most feedback structures of CBC are established after the lasers emit to free space and consist of a set of lenses or mirrors. Those optical elements in free space may hinder array size and integration. In this paper, we demonstrated an all-fiber structured CBC method with distributed phase-locking. By adding an all-fiber measurement loop beside the main laser chain, the phase of main laser chain is appended to the measuring loop. Phases of each main laser chain are locked indirectly though the measurement loops by using stochastic parallel gradient descent (SPGD) algorithm. The principle of distributed phase-locking is also illustrated. Corresponding simulations are carried out and two-channel fiber lasers are coherently combined by this method. The experimental results show that the structure can achieve phase-locking effectively. Stable and distinct interference fringe is observed. Additionally, the structure proposed in this paper is straightforwardly building and expanding.