Application of Deep Neural Network in Wavefront Sensing Based on Transport of Intensity Equation
The Transport of Intensity Equation(TIE)offers an effective method for wavefront sensing,utilizing the variations in near-field defocused intensity distribution patterns across multiple propagation distances to reconstruct the phase aberrations introduced by turbulent media,such as the atmosphere.YANG Huizhe et al have explored TIE-based wavefront sensing for satellite-ground laser communication systems,addressing challenges related to the Point-Ahead Angle(PAA).Their simulations and bench experiments,using a Zernike-based linear reconstruction method,demonstrated effectiveness under high Signal-to-Noise Ratio(SNR)conditions.However,linear wavefront reconstruction faces significant nonlinear errors,rendering it ineffective in low SNR environments,which are common in low laser power scenarios typical of laser communication systems.To address these challenges,this paper proposes a Deep Neural Network(DNN)training model.The model utilizes the differences in intensity distributions observed at two distinct propagation distances as the input data.The outputs of the model are the first 4 to 79 orders of the Zernike coefficients corresponding to the phase aberrations.The input and output data used for DNN training are simulated through two processes based on the actual satellite-ground laser communication systems.The first process is the uplink propagation of a collimated laser beam through the atmospheric turbulence,while the second process is the reimaging of the backscattered patterns from these different altitudes.To generate a diverse set of datasets,three variable parameter sets are employed:the atmospheric coherence lengths of 0.05,0.10,and 0.15 meters;the turbulence layer heights of 0,5,and 10 kilometers;and the laser powers of 5,10,20,50,100,200,and 300 watts.This results in 63 unique combinations.Each combination contains 10,000 random phase screens,yielding a total of 630,000 training data.By comparing the Wavefront Errors(WFE)between the original and reconstructed phases,different model architectures,loss functions,and optimizers are evaluated.Ultimately,ResNet34 is chosen as the backbone network.A linear weight pooling method is proposed for the neck network,along with the Weighted Mean Absolute Error(WMAE)function and the SophiaG optimizer.Simulation results provide compelling evidence that the DNN approach significantly outperforms the traditional linear reconstruction methods.Notably,it substantially reduces the laser power requirements essential for effective wavefront sensing.For instance,at a laser power level of 5 W,the reconstruction accuracy achieved by the DNN model matches that of linear methods operating at a substantially higher power of 200 W.Furthermore,as the laser power exceeds 20 W,the detection error for the DNN approach stabilizes at approximately 200 nm RMS,reaching the accuracy limits of the 79th order Zernike polynomial.Moreover,the execution time is also a crucial indicator of its practicality,especially in real-time adaptive optics systems.Testing one thousand datasets on a single PC with an NVIDIA A 5 000 GPU yielded a total processing time of 0.52 seconds for the DNN,resulting in an average processing time of approximately 0.52 milliseconds per dataset,thereby meeting the real-time requirements of adaptive optics systems with a KHz sampling frequency.In contrast,under the same hardware conditions the linear reconstruction method needs approximately 27.31 milliseconds per dataset.The DNN method is about 52 times faster than the linear reconstruction method,highlighting the significant advantages of DNNs in practical applications.Although the DNN method demonstrates excellent performance in wavefront sensing accuracy and execution efficiency,it still has some shortcomings.First,the reliance on training data is a common issue for DNNs.The performance of DNNs is highly dependent on the quality and diversity of the training data.If the actual turbulent conditions differ significantly from the training data,the model's performance can decline sharply.Therefore,it is necessary to further enhance the diversity of the training data to cover a broader range of turbulent conditions and noise levels.Second,the model's interpretability is limited.DNNs are often regarded as black boxes,making their internal decision-making processes difficult to explain using physical laws.In this paper,we designed the linear weight pooling and a weighted mean absolute error loss function based on the physical context of the task.However,further efforts are required to integrate DNNs with the physical models to improve the model's interpretability and robustness.
Wavefront sensingDeep neural networkTransport of intensity equation
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