Stochastic Parallel Gradient Descent Algorithm Research Articles

Theoretical Analysis on Active Polarization Control of Fiber Laser Based on Root Mean Square Propagation Algorithm

High-power linearly polarized fiber lasers are widely used in coherent beam combination, nonlinear frequency conversion, and gravitational wave detection. With the increase in output power, it is challenging for fiber lasers to maintain a high polarization extinction ratio (PER). Combined with intelligent techniques, active polarization control is a prospective method to obtain the laser output with high PER and high stability. We demonstrate a comprehensive model of an active polarization control system. The root mean square propagation (RMS-Prop) algorithm is used to control the non-polarization-maintaining (non-PM) fiber laser to generate linearly polarized laser. The parameters of the RMS-Prop algorithm are theoretically analyzed, including cost function, perturbation amplitude, and global learning rate. The simulation results show that PER is the optimal cost function. When the perturbation amplitude is 0.06 and the global learning rate is 0.6, the system can achieve the optimal control speed and accuracy. By comparison with the stochastic parallel gradient descent (SPGD) algorithm, the RMS-Prop algorithm has an advantage in obtaining higher PER.

Telescope Alignment Method Using a Modified Stochastic Parallel Gradient Descent Algorithm

To satisfy the demands of high image quality and resolutions, telescope alignment is indispensable. In this paper, a wavefront sensorless method based on a modified stochastic parallel gradient descent algorithm (SPGD) called the adaptive moment estimation SPGD (Adam SPGD) algorithm is proposed. Simulations are carried out using a four-mirror telescope, whose aperture is 6 m and fields of view are Φ2°. Three misalignments are shown as examples. Positions of the secondary mirror and third mirror are employed to compensate aberrations. The results show that merit functions and energy distributions of corrected images match with the designed ones. The mean RMS of residual wavefront errors is smaller than λ/14 (λ = 0.5 μm), indicating that the misalignments are well compensated. The results verify the effectiveness of our method.

Performance analysis of optimized equilibrium optimizer algorithm in coherent free-space optical communication system

Sensor-less adaptive optics (SLAO) is commonly employed in coherent free-space optical communication (CFSOC) system due to its capacity to mitigate the impact of atmospheric turbulence. The control algorithm determines the SLAO system's capacity to efficiently recorrect wavefront aberrations. In this study, we apply an Optimized Equilibrium Optimizer (OEO) algorithm as a control algorithm to the CFSOC system, the dynamic parameters and search framework of the Equilibrium Optimizer (EO) are modified to enhance the algorithm's resilience in strong atmospheric turbulence. Both theoretical analysis and simulation results demonstrate that the OEO algorithm exhibits exceptional calibration performance and robustness, effectively enhancing ME and reducing BER. In the simulation, the Stochastic Parallel Gradient Descent (SPGD) algorithm takes 10 times longer to achieve the same performance as the OEO algorithm. Meanwhile, the OEO algorithm and the other 6 algorithms were simulated with strong turbulence. Results demonstrated that the OEO algorithm outperforms other algorithms. The OEO algorithm is suitable for SLAO systems to enhance the communication quality of the CFSOC systems.

Efficient distributed architecture and optimized subarray control strategy to facilitate large-scale coherent beam combination

Traditional coherent beam combination (CBC) system architecture has revealed inadequacies in meeting the concurrent demands of large-scale deployment and high-bandwidth requirements. Addressing this challenge, we propose a distributed CBC system architecture based on the optimized stochastic parallel gradient descent (SPGD) algorithm. Our strategy segments the large-scale laser array into multiple independent smaller-scale subarrays, ensuring their efficient phase convergence through the introduction of corresponding reference lasers while avoiding interference when integrating different subarrays. Moreover, the piecewise SPGD algorithm is proposed and the intensity of the reference laser is modulated to further improve the convergence speed and accuracy within subarrays, enhancing the algorithm's compatibility across laser arrays of varying scales. We have validated the feasibility of the distributed CBC architecture through numerical analysis and assessed the strategy's performance in both static and dynamic environments using simulation software. The simulation findings indicate that, compared to traditional CBC systems, distributed architecture with 3, 7, and 19 subarrays and utilizing the piecewise SPGD algorithm, has experienced phase control bandwidth enhancements by factors of approximately 3.6, 10.4, and 32.5 respectively, maintaining superior average power output in dynamic noise environments. The proposed architecture and strategy also accommodate subarrays of variable scales and obviates the necessity for large-aperture optical components on the emitted plane, demonstrating exceptional scalability and adaptability.

Active phase locking of a three-aperture array using a corner cube lateral transfer reflector.

We present a novel technique for coherent beam combining of a three-aperture array. In our method, a retroreflector samples the beam from the edge of each aperture and redirects the sampled beams back through the gap in the center. The sampled beams contain both angle and phase information for the three-aperture array, which can be used to lock the phase and tip/tilt. In a proof-of-concept experiment, we phase-lock the three-aperture array by maximizing the power through a pin hole of the far-field pattern of the sampled array via the stochastic parallel gradient descent algorithm. This approach eliminates the need for bulky sampling optics, which is particularly advantageous for the large-diameter arrays required for long distance inter-satellite free-space optical communication.

Coherent beam combining of two all-PM thulium-doped fiber chirped pulse amplifiers

In this paper, we report a coherent beam combining (CBC) system that involves two thulium-doped all-polarization maintaining (PM) fiber chirped pulse amplifiers. Through phase-locking the two channels via a fiber stretcher by using the stochastic parallel gradient descent (SPGD) algorithm, a maximum average power of 265 W is obtained, with a CBC efficiency of 81% and a residual phase error of λ/17. After de-chirping by a pair of diffraction gratings, the duration of the combined laser pulse is compressed to 690 fs. Taking into account the compression efficiency of 90% and the main peak energy proportion of 91%, the corresponding peak power is calculated to be 4 MW. The laser noise characteristics before and after CBC are examined, and the results indicate that the CBC would degrade the low frequency relative intensity noise (RIN), of which the integration is 1.74% in [100 Hz, 2 MHz] at the maximum combined output power. In addition, the effects of the nonlinear spectrum broadening during chirped pulse amplification on the CBC efficiency are also investigated, showing that a higher extent of pulse stretching is effective in alleviating the spectrum broadening and realizing a higher output power with decent combining efficiency.Graphical

Experimental demonstration of scene-based cophasing in optical synthetic aperture imaging using the SPGD algorithm

Large-aperture telescopes based on optical synthetic aperture imaging are investigated for recent high-resolution spaceborne observations. An enabling technique of aperture synthesis is a cophasing method to suppress a piston-tip-tilt error between sub-apertures. This paper proposes a scene-based cophasing technique using the stochastic parallel gradient descent (SPGD) algorithm, assuming application to high-resolution Earth observation. A significant advantage of the SPGD algorithm is a model-less cophasing capability based on extended scenes, but the simultaneous scene-based piston-tip-tilt correction between multiple apertures has not been demonstrated. In this paper, we developed a tabletop synthetic aperture imaging system with 37 sub-apertures and demonstrated extended-scene-based piston-tip-tilt control by optimizing applied voltages to 111 actuators simultaneously. The demonstration experiments used not only static scenes but also a time-varying dynamic scene for observation targets. In every measurement, the proposed scene-based approach reduced the initially defined piston-tip-tilt errors, and the image sharpness significantly improved, although the correction rate in the dynamic scene observation was slower. Finally, this paper discusses the influence of scene dynamics on image-based cophasing.

Sidelobe suppression for accelerating beams

Although the control of trajectory, amplitude and beam-width in accelerating beams have been extensively investigated, sidelobes manipulation of such beams, which is required in many applications, has been surprisingly under-researched. This paper presents an approach for the generating of accelerating beams with significantly reduced sidelobes. The proposed method encompasses a two-step angular spectrum design, including employing a general model to establish the phase distribution and applying a stochastic parallel gradient descent (SPGD) algorithm to optimize the binary amplitude modulation. Experimental results confirm that the sidelobe intensity of accelerating beams can be reduced by over 50% with our method, thereby enhancing their applicability in many fields, such as micro-machining, particle manipulation, and optical communication.

Generation of needle-shaped beam with super-resolution spot and large depth of focus using diffractive optics

The finite depth of focus (DOF) of a focusing lens gives rise to the degradation of lateral resolution at defocused positions. Consequently, the generation of a needle-shaped beam with sub-diffraction size and extended DOF can break through this limitation, but few studies have effectively balanced these two characteristics. In this paper, we propose a method based on the stochastic parallel gradient descent (SPGD) algorithm for designing multi-ring diffractive optical elements (DOEs) to produce the needle-shaped beam, which maintains a super-resolution and uniform spot within a large extended DOF range. Numerical simulations and experimental results have validated that our method can extend the DOF by 14 times longitudinally and reduce the lateral resolution to 73% of Airy spot, while maintaining up to 92% uniformity of the beam diameter. Furthermore, we demonstrate that the DOF of the needle-shaped beam extends with the increase of the number of rings and phase levels within the DOE. Our work provides an effective strategy for the design of DOF-extended DOE and it is anticipated to find potential applications in microscopy and three-dimensional imaging, photolithography, and optical manipulation.

Photonic integrated coherent beam combiner based on MMI and the SPGD algorithm.

Atmospheric turbulence severely degrades the optical wavefront of a propagating beam, which greatly reduces the coupling efficiency of free-space optical (FSO) receivers. Among the various methods to mitigate the effects, the use of a multi-channel receiver is more convenient and economical. After passing through the multi-channel receiver, multiple single-mode fibers (SMFs) are output and need to be combined. In this paper, we propose photonic integrated coherent beam combiners based on multimode interference (MMI) and the stochastic parallel gradient descent (SPGD) algorithm, which avoids detecting the light out of each channel and adding the data signal in the electrical domain. First, we propose a 4-channel coherent beam combiner based on a 4×1 MM, and about 21 iterations of the SPGD algorithm are required to enhance the combined optical power to a maximum of 96%. Furthermore, we demonstrate a combination of 16 beams using five 4×1 MMIs, which requires 140 iterations to enhance the combined power to 89%. This study offers theoretical insights to enhance the integration of FSO communication systems.

Design method for laser beam aggregation based on SPGD

This paper proposes a design method for laser beam aggregation based on SPGD, effectively addressing the issue of beam aggregation inconsistency caused by external interferences during the multi-path laser beam combination process. This further enhances the energy density of the combined laser spot. By applying a random binary disturbance vector based on control parameters and employing the stochastic parallel gradient descent (SPGD) algorithm for model control and parallel iteration, the control parameters are halved. This accelerates the iteration speed, enabling rapid aggregation of the combined laser beams and maximizing the energy density of the laser spot.

All-purpose automatic image stacking for sparse aperture telescopes using dynamic metric stochastic parallel gradient descent algorithm

Image stacking is the first step of alignment of the sparse aperture telescopes. We propose an all-purpose automatic image stacking technique using dynamic metric stochastic parallel gradient descent algorithm (DM-SPGD). With the image stacking modeled as an optimization problem, the dynamic metric functions consisting of a distance metric and an energy metric are defined. According to the judgment of the spot state, the two metrics, both computed from the focal spot at each step, are switched dynamically to perform SPGD optimization. By use of the dynamic metric functions, DM-SPGD can exactly and quickly correct any-amplitude tip/tilt errors, regardless of the array arrangements, aperture numbers and coherence as verified by simulation. In addition, jitter and changes in piston brought about by the environment have no effect on the image stacking. Multiple closed-loop image stacking experiments are performed, demonstrating that the offsets of randomly distributed spots can be all controlled below 0.5 pixels within 300 iterations (within 30 s).

Convolutional Neural Network Combined With Stochastic Parallel Gradient Descent to Decompose Fiber Modes Based on Far-Field Measurements

Modal decomposition (MD) of fiber modes based on direct far-field measurement combining the convolutional neural network (CNN) with a stochastic parallel gradient descent (SPGD) algorithm is investigated both numerically and experimentally. For obtaining the modal coefficients of fiber modes guided in a large-mode-area fiber, the fiber modes are decomposed into a finite number of Hermite gaussian modes, the initial conditions of the modal coefficients are obtained through the CNN, and further optimization of them are carried out through the SPGD. The ambiguity problem that may happen in the CNN owing to the existence of the pair-beam field is resolved by properly labelling the phase differences with a single-valued parameter set in consideration of the mode-order indices. The feasibility and effectiveness of the proposed MD method is verified both numerical simulations and experimental demonstrations with both recorded image data and online real-time image data. The correlation error incurred by the proposed method is below 6.6×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> and 8.7×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> in the numerical simulations and the experimental demonstrations, respectively. The online real-time operation of the proposed method is also experimentally demonstrated at a decomposing rate of ∼2 Hz.

High-Power Orbital Angular Momentum Beam Generation Using Adaptive Control System Based on Mode Selective Photonic Lantern

We demonstrate an all-fiber adaptive spatial control system with a mode selective photonic lantern as the core device to generate orbital angular momentum (OAM) modes. A 3×1 mode selective photonic lantern has been designed and fabricated, which can easily guide OAM modes. The stochastic parallel gradient descent (SPGD) algorithm is used to control the phase of each input channel. A stable OAM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> mode with a mode purity of 0.98 is obtained in a 30/130 μm fiber, and a 50W stable quasi-OAM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> mode beam is achieved after power scaling in a 42/250 μm output fiber. This system cannot only compensate the atmosphere turbulence effects on transmission distortion, but also be improved to generate switchable OAM modes with different topological charges, which provides great possibility of application in practical communication system.

An adaptive enhancement method based on stochastic parallel gradient descent of glioma image

AbstractBrain 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.

A Novel SPGD Algorithm for Wavefront Sensorless Adaptive Optics System

Stochastic parallel gradient descent (SPGD) is the most frequently used optimization algorithm for correcting wavefront distortion in the wavefront sensorless adaptive optics(WFS-Less AO)system. However, the convergence speed of the SPGD algorithm becomes slow rapidly as increasing of distortion, and the probability of falling into local optimum is rising owing to the fixed gain coefficient. It cannot meet the requirement of real-time wavefront distortion correction. Therefore, a novel algorithm is proposed in this paper, called as adaptive gain stochastic parallel gradient descent (AGSPGD) based on the AMSGrad optimizer in the deep learning, to improve the convergence speed of the algorithm and to reduce the probability of falling into local optimum. The AGSPGD algorithm adopts the first-order moment and the second-order moment of the performance index, which are combined to dynamically adjust the gain. The numerical simulations are completed in this paper. The results of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$D/r_0=2.5$</tex-math></inline-formula> conditions demonstrate that the AGSPGD can reduce the number of iterations by 25%, and the probability of the algorithm falling into local optimum is reduced from 16% to 4%. In addition, the AGSPGD still outperforms the SPGD as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$D/r_0$</tex-math></inline-formula> increasing.

Residual network-based aberration correction in a sensor-less adaptive optics system

The performance of free-space optical communication (FSOC) is often affected by atmospheric turbulence. The sensor-less adaptive optics (SLAO) system is an effective method for overcoming the effects of atmospheric turbulence. The performance of the control algorithm in the SLAO system directly determines whether the SLAO system can effectively correct wavefront aberrations. In this study, we introduce a residual network (ResNet) as a control algorithm to replace the traditional control algorithm. By lowering the number of iterations, this strategy enhances the real-time performance of the FSOC system. The final ResNet model can achieve an accuracy of 0.98 for training and 0.92 for testing. The simulation results show that stochastic parallel gradient descent (SPGD) algorithm takes 700 times longer and requires at least 500 iterations to achieve the same performance as ResNet. And we verify the feasibility of the ResNet model by setting up an experiment.

Phase control scheme of the coherent beam combining system for generating perfect vectorial vortex beams assisted by a Dammann vortex grating.

Based on Dammann vortex grating and adaptive gain stochastic parallel gradient descent algorithm, we theoretically proposed a phase control technology scheme of the coherent beam combining system for generating perfect vectorial vortex beams (VVBs). The simulated results demonstrate that the discrete phase locking for different types of VVBs (including vortex beams, vector beams, and generalized VVBs) can be successfully realized. The intensity distributions, polarization orientation, Pancharatnam phases, and beam widths of different |Hm,n〉 states with the obtained discrete phase distribution further prove that the generated beams are perfect VVBs. Subsequently, the phase aberration residual for different VVBs is evaluated using the normalized phase cosine distance function, and their values range from 0.01 to 0.08, which indicates the obtained discrete phase distribution is close to the ideal phase distribution. In addition, benefitting from the high bandwidth of involved devices in the proposed scheme, the influence of dynamic phase noise can be negligible. The proposed method could be beneficial to realize and switch flexible perfect VVBs in further applications.

Deep learning–based vortex decomposition and switching based on fiber vector eigenmodes

Abstract Structured optical fields, such as cylindrical vector (CV) and orbital angular momentum (OAM) modes, have attracted considerable attention due to their polarization singularities and helical phase wavefront structure. However, one of the most critical challenges is still the intelligent generation or precise control of these modes. Here, we demonstrate the first simulation and experimental realization of decomposing the CV and OAM modes by reconstructing the multi-view images of projected intensity distribution. Assisted by the deep learning–based stochastic parallel gradient descent (SPGD) algorithm, the modal coefficients and optical field distributions can be retrieved in 1.32 s within an average error of 0.416 % showing high efficiency and accuracy. Especially, the interference pattern and quarter-wave plate are exploited to confirm the phase and distinguish elliptical or circular polarization direction, respectively. The generated donut modes are experimentally decomposed in the CV and OAM modes, where purity of CV modes reaches 99.5 %. Finally, fast switching vortex modes is achieved by electrically driving the polarization controller to deliver diverse CV modes. Our findings may provide a convenient way to characterize and deepen the understanding of CV or OAM modes in view of modal proportions, which is expected of latent applied value on information coding and quantum computation.

Adaptive Optical Closed-Loop Control Based on the Single-Dimensional Perturbation Descent Algorithm.

Modal-free optimization algorithms do not require specific mathematical models, and they, along with their other benefits, have great application potential in adaptive optics. In this study, two different algorithms, the single-dimensional perturbation descent algorithm (SDPD) and the second-order stochastic parallel gradient descent algorithm (2SPGD), are proposed for wavefront sensorless adaptive optics, and a theoretical analysis of the algorithms' convergence rates is presented. The results demonstrate that the single-dimensional perturbation descent algorithm outperforms the stochastic parallel gradient descent (SPGD) and 2SPGD algorithms in terms of convergence speed. Then, a 32-unit deformable mirror is constructed as the wavefront corrector, and the SPGD, single-dimensional perturbation descent, and 2SPSA algorithms are used in an adaptive optics numerical simulation model of the wavefront controller. Similarly, a 39-unit deformable mirror is constructed as the wavefront controller, and the SPGD and single-dimensional perturbation descent algorithms are used in an adaptive optics experimental verification device of the wavefront controller. The outcomes demonstrate that the convergence speed of the algorithm developed in this paper is more than twice as fast as that of the SPGD and 2SPGD algorithms, and the convergence accuracy of the algorithm is 4% better than that of the SPGD algorithm.