SPGD Algorithm Research Articles

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.

Hybrid algorithm for initial phase calibration of optical phased array.

The synthesis of laser coherence and the accuracy of beam scanning, which are based on an optical phased array (OPA), are severely constrained by phase noise. This limitation hampers their applications in various fields. Currently, the most widely utilized calibration method is adaptive optics, which can effectively mitigate phase noise and enhance the quality of the output beam. However, because of the multiple array elements of the OPA and the large optimization range for each element, the adaptive optimization method experiences slow convergence and a high risk of falling into local optima. We propose a narrowing search range algorithm that can quickly reduce phase noise by narrowing the search range of the optimal value. After initial optimization, the SPGD algorithm was used. This study was verified through simulations and experiments utilizing the OPA of various array elements. These findings indicate that the hybrid algorithm expedites the calibration process, requires simple experimental equipment, and can be broadly utilized.

Accelerating optical phased array calibration with improved SPGD algorithm

As a new type of beam pointing control technology, optical phased array has broad application prospects in the fields of laser radar and beam synthesis. However, the phase error in practical application brings great difficulties to beam detection and deflection, which must be calibrated. In this paper, a SPGD algorithm combined with Adam algorithm (ASPGD) is proposed and compared with the traditional optimization algorithm. The results show that the improved SPGD algorithm can double the convergence speed and increase the cosine similarity value by about 10%.

Numerical Simulation of Performance Improvement of Coherent Lidar Based on SPGD Algorithm

Numerical Simulation of Performance Improvement of Coherent Lidar Based on SPGD Algorithm

Over-the-Air Phased Array Calibration Based on SPGD Algorithm

Over-the-Air Phased Array Calibration Based on SPGD Algorithm

Multi-order hybrid vector mode decomposition in few-mode fibers with DL-based SPGD algorithm

Multi-order hybrid vector mode decomposition in few-mode fibers with DL-based SPGD algorithm

Advanced root mean square propagation with the warm-up algorithm for fiber coupling.

Fiber coupling plays an important role in applications such as free-space optical communication (FSOC) and self-referencing interferometry. However, the coupling efficiency is often affected by turbulence and platform vibrations, which requires dynamic coupling with optimization algorithms. In this paper, to further mitigate the effects of sudden disturbances and to expand the effective range of fiber coupling systems, we propose a new method called the advanced root mean square propagation with warm-up (ARW) algorithm. By adaptively adjusting both the gain rate and the perturbation rate with warm-up operations, the ARW algorithm can achieve higher effective range and acceptable steady-state coupling efficiency simultaneously. Simulation and experimental results demonstrate that the proposed method requires only 36.4% of the iterations of the SPGD algorithm to deal with sudden disturbances. Moreover, the effective range of the ARW algorithm is 530.50µrad in the specific coupling platform, which is 20% higher than the effective range of SPGD.

Piston correction of sparse aperture systems using hybrid optimization algorithm

In a sparse aperture imaging system, the piston error affects the co-phase of subapertures and reduces the imaging resolution. Based on the image quality evaluation function, the piston error correction can be converted into a class of optimization problems. In this paper, a metaheuristic algorithm is used to implement global search based on stochastic parallel gradient descent algorithm. A hybrid algorithm is obtained by combining the stochastic parallel gradient descent algorithm with the Gray Wolf algorithm. The hybrid algorithm is developed at the best three positions of the population (the head wolf) using the gradient direction of the SPGD algorithm, and the other populations keep moving toward the best three head wolves. This hybrid algorithm balances exploration and exploitation better in the piston error correction of sparse aperture systems. The hybrid algorithm has a good optimization speed while satisfying the correction accuracy. The performance of this hybrid algorithm is verified in simulations with three-aperture and seven-aperture systems.

Improved SPGD Algorithm for Optical Phased Array Phase Calibration

A chip-level optical beam steerer is an inevitable choice for next-generation light detection and ranging (LiDAR). The research on optical phased array (OPA) is the most intriguing. However, the complexity of control and calibration speed limit the full potential as the number of channels increases. In this paper, an improved stochastic parallel gradient-descent algorithm combined with the Nesterov accelerated gradient method (NSPGD) is presented and applied in a 512-channel OPA. This algorithm can reduce the phase calibration time of large-scale OPA and demonstrates a better convergence performance than traditional SPGD. Compared with the traditional SPGD and hill-climbing (HC) algorithm, optimized convergence performance of NSPGD is shown. The side mode suppression ratio (SMSR) of over 10dB for 512-channel OPA is obtained with the NSPGD algorithm, and the convergence speed is twice that of traditional SPGD. In addition, a temperature-controlled OPA is also studied to stabilize the whole calibration system.

High Accuracy Aberration Correction Based on Combination Spgd Algorithm for Free-Space Optical Communication

High Accuracy Aberration Correction Based on Combination Spgd Algorithm for Free-Space Optical Communication

Adaptive Laser Aiming Through 2 km Horizontal Atmosphere with Precise-Delayed SPGD Algorithm

Adaptive Laser Aiming Through 2 km Horizontal Atmosphere with Precise-Delayed SPGD Algorithm

Experimental Demonstration of Central-Lobe Energy Enhancement Based on Amplitude Modulation of Beamlets in 19 Elements Fiber Laser Phased Array

Coherent beam combination of fiber laser phased array is a promising technique to achieve high-brightness laser output. In this paper, we focus on central-lobe energy enhancement of the combined beam in the far-field by theoretically and experimentally investigating the relationship between the power-in-the-bucket (PIB) of the combined beam in the far-field and the beamlets amplitude modulation in the near-field. We employ a 19-elements fiber laser phased array integrating adaptive fiber-optic collimators with a beamlet filling factor of 0.903 and achieve phase-locking and beamlet pointing correction among fiber lasers using the SPGD algorithm. The amplitude modulation applied to the tiled sub-apertures is used to control the shape of the emissive array's amplitude envelope to further change the PIB of the combined beam under the same total output power. According to theoretical analysis, the fiber laser phased array achieves PIB = 0.51 for a zero truncation ratio (Tr), which is increased to PIB = 0.57 for Tr = 1.3. Experimentally, we observe PIB = 0.49 for Tr = 0 and PIB= 0.56 for Tr = 1.3. The experimental results are in good agreement with the theoretical analysis, suggesting that the amplitude modulation is helpful for further improving the energy density of central-lobe.

3-channel Tiled-aperture Coherent-beam-combining System Based on Target-in-the-loop Monitoring and SPGD Algorithm

3-channel Tiled-aperture Coherent-beam-combining System Based on Target-in-the-loop Monitoring and SPGD Algorithm

FPGA -based SPGD algorithm implementation of adaptive optical system

FPGA（field programmable gate array）具有可重复编程、算法实现灵活等优势，以97单元变形镜为原型，提出基于FPGA的SPGD（stochastic parallel gradient descent algorithm）控制算法通用快速实现方案。采用TimeGen软件对SPGD算法进行时序分析，并采用Vivado软件分别对SPGD算法随机扰动电压生成、性能指标计算和控制电压的计算与输出进行FPGA配置和编程，将每个模块的计算结果与Matlab结果进行对比、分析。研究结果证明了该文所提方案的合理性和可行性，为下一步基于FPGA的SPGD算法硬件实现和应用提供基础。

基于改进型SPGD算法的涡旋光波前畸变校正

基于改进型SPGD算法的涡旋光波前畸变校正

Coherent beam combining based on the SPGD algorithm with a momentum term

The stochastic parallel gradient descent with a momentum term (named MomSPGD) algorithm is innovatively presented and applied for coherent beam combining to substitute for the traditional SPGD algorithm. The feasibility of coherent synthesis system using the MomSPGD algorithm is validated through numerical simulations and experiments. The results of the simulations and the experiment indicate that the proposed algorithm can improve convergence speed and immunity of the synthesis system compared with the traditional SPGD algorithm.

Adaptive SMF Coupling Based on Precise-Delayed SPGD Algorithm and Its Application in Free Space Optical Communication

The adaptive coupling of laser beam from space into single-mode fiber (SMF) plays an important role in the fiber-based free space optical communication technology. This paper investigates a kind of adaptive SMF coupling system based on a novel corrector named adaptive fiber coupler, and an improved control algorithm named precise-delayed stochastic parallel gradient descent (PD-SPGD). Compared to the SPGD algorithm used previously, PD-SPGD can compensate for the inherent response delay of the controlled system by setting a precise time delay between the disturbed voltages and the performance metrics. The experimental results show that this new algorithm increases the iteration rate from 3 to 8 kHz and decreases the convergence time from 6.3 to 2.5 ms when the static angular errors was corrected. As a result, the control bandwidth of the sinusoidal angular jitters is more than doubled. At the end, a preliminary atmospheric compensation experiment over a 520 m near-ground propagation path is conducted to verify the effectiveness of the method mentioned above.

Arbitrary temporal shape pulsed fiber laser based on SPGD algorithm

A novel adaptive pulse shaping method for a pulsed master oscillator power amplifier fiber laser to deliver an arbitrary pulse shape is demonstrated. Numerical simulation has been performed to validate the feasibility of the scheme and provide meaningful guidance for the design of the algorithm control parameters. In the proof-of-concept experiment, information on the temporal property of the laser is exchanged and evaluated through a local area network, and the laser adjusted the parameters of the seed laser according to the monitored output of the system automatically. Various pulse shapes, including a rectangular shape, ‘M’ shape, and elliptical shape are achieved through experimental iterations.

基于SPGD算法的光纤激光偏振控制理论与实验研究

基于SPGD算法的光纤激光偏振控制理论与实验研究

Coherent beam combining of a narrow-linewidth long-pulse Er3+-doped multicore fiber amplifier.

Active phase locking of a multicore erbium-doped fiber amplifier is demonstrated for 180 ns narrow-linewidth pulses at 1545 nm. A spatial light modulator is used at the input of the amplifier to control the optical phase of 7 beams injected in the hexagonally-arranged cores, ensuring efficient combining through a SPGD algorithm. At the output, combining is performed using a diffractive optical element. This experiment establishes multicore amplifiers as a promising way to scale the energy of Brillouin-limited pulsed amplifiers for LIDAR applications. We also present a simple lensless technique to measure phase shifts between pairs of adjacent channels that could be implemented in future active coherent combining systems.