An optical phased array phase compensation optimization method based on deep learning

Abstract

The application discloses an optical phased array phase compensation optimization method based on deep learning, which is applied to the technical field of optical phased array beam control and aims at solving the problem that traditional calibration methods need to rely on complex optical systems or multiple iterative calculations and cannot meet real-time compensation requirements in a dynamic environment. The application firstly acquires a one-to-one corresponding far-field light intensity distribution and an initial phase dataset; then constructs a neural network with a hybrid architecture including a convolution layer, a full connection layer and a physical connection layer; next, the neural network is trained based on the dataset; finally, the trained model is integrated into a phase compensation control system to predict an optimal decoupling phase value in real time, so as to eliminate phase distortion and improve the quality of the far-field light intensity.

Description

Technical Field

[0001] This invention belongs to the field of optical phased array beam control technology, and specifically relates to an optical phased array phase compensation optimization technology. Background Technology

[0002] Optical phased arrays achieve beam deflection and focusing by controlling the phase distribution of array elements. However, their performance is affected by factors such as manufacturing tolerances, temperature drift, and driving circuit noise, resulting in random phase errors between array elements. These errors cause wavefront distortion, reduce far-field light intensity concentration, disperse main lobe energy, and increase side lobe levels. Traditional calibration methods (such as interferometer measurements or iterative optimization algorithms) rely on complex optical systems or multiple iterative calculations, making it difficult to meet the real-time compensation requirements in dynamic environments.

[0003] Existing phase compensation techniques mainly include model-based optimization algorithms (such as the Gerchberg-Saxton algorithm and stochastic parallel gradient descent algorithm) and sensor feedback-based closed-loop control. The former has high computational complexity and is difficult to apply to large-scale arrays (such as those with more than 1024 channels); the latter requires additional integration of wavefront sensors, increasing system complexity and cost. In addition, traditional methods are poorly adaptable to nonlinear errors (such as the hysteresis effect of electro-optic modulators) and cannot complete high-precision compensation within milliseconds, limiting their application in high-speed beam scanning.

[0004] In recent years, deep learning has demonstrated powerful advantages in computational imaging and adaptive optics. Models such as convolutional neural networks (CNNs) and Transformers can learn complex nonlinear mapping relationships from massive amounts of data, providing new approaches for phase compensation in optical phased arrays. Compared to traditional methods, deep learning features end-to-end optimization, strong parallel computing capabilities, and fast inference speed, and is expected to achieve high-precision, low-latency real-time phase control, thereby driving performance breakthroughs in technologies such as laser communication and optical radar. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention proposes a deep learning-based optical phased array phase compensation optimization method. By directly embedding the liquid crystal dynamics equation into a neural network architecture, a hybrid model structure containing a physical connection layer is creatively designed, which is beneficial for improving phase compensation accuracy and far-field main lobe energy concentration.

[0006] The technical solution adopted in this invention is: a deep learning-based optical phased array phase compensation optimization method, comprising:

[0007] S1. Obtain a one-to-one corresponding far-field light intensity distribution and initial phase dataset; the initial phase data is given by the diffraction formula; the far-field light intensity distribution includes two parts: simulation and experiment; the simulation part is determined by the total free energy density of the liquid crystal and the field distribution equation, and the experimental part is obtained based on the optical phased array antenna system.

[0008] S2. Construct a neural network that includes convolutional layers, fully connected layers, and physically connected layers;

[0009] S3. The far-field light intensity distribution in step S1 is used as the input of the neural network. The output of the neural network is the predicted phase. The loss function is calculated between the predicted phase and the initial phase. The neural network is then optimized and trained by gradient descent.

[0010] S4. For each preset target deflection angle, first input the far-field ideal distribution into the trained neural network model, and then calculate the decoupled phase distribution.

[0011] S5. The wave control module performs adaptive phase compensation based on the decoupled phase distribution obtained in step S4.

[0012] The beneficial effects of this invention are as follows: This invention constructs a deep neural network model and trains it based on the initial phase and far-field light intensity dataset of the constructed optical phased array. This allows the model to learn the nonlinear mapping relationship between the far-field grating lobe distribution of the optical phased array and the ideal wavefront. The ideal far-field distribution is then input into the trained deep neural network to obtain the decoupled conjugate phase, and adaptive phase compensation under dynamic environments is achieved using a wave control module. This includes the following advantages:

[0013] 1. Deep Fusion of Physical Constraints and Data-Driven Approach: By directly embedding the liquid crystal dynamics equations into a neural network architecture, a hybrid model structure including a physical connection layer was creatively designed. This structure not only retains the powerful feature learning capabilities of deep learning but also ensures that the prediction results strictly conform to the actual physical laws of optical phased arrays by introducing physical constraints such as second-nearest neighbor second-order cross-nonlinear relationships. This fusion method solves the problem of poor physical interpretability in traditional pure data-driven models, which is beneficial for improving phase compensation accuracy and far-field main lobe energy concentration.

[0014] 2. Breakthrough Improvements in Real-Time Performance and Generalization Ability: A combination of lightweight network structure and adaptive optimization strategies significantly improves computational efficiency while maintaining high accuracy. Through the cascading use of 3×3 small convolutional kernels and the optimized design of a 1024-dimensional fully connected layer, the number of model parameters is reduced by 40% compared to traditional methods. Furthermore, a joint training mechanism based on simulation and experimental data, coupled with a dynamically decaying learning rate strategy, makes the model robust to real-world interference factors such as manufacturing tolerances and circuit noise, enabling it to adapt to phased array systems of varying sizes. Attached Figure Description

[0015] Figure 1 This is a schematic diagram of the optical phased array antenna system on which the method of the present invention is based;

[0016] Figure 2 This is a flowchart of the deep learning-based optical phased array phase compensation optimization method of the present invention;

[0017] Figure 3 This is a schematic diagram of the structure of a convolutional neural network used for phase distortion and prediction compensation of optical phased arrays in an embodiment. Detailed Implementation

[0018] To facilitate understanding of the technical content of this invention by those skilled in the art, the following description, in conjunction with the accompanying drawings, further illustrates the invention.

[0019] The deep learning-based optical phased array phase compensation optimization method of this invention is based on an optical phased array antenna system such as... Figure 1 As shown, it includes a laser source, a linear polarizer, an optical phased array, a CCD camera, and a neural network processing unit. The laser source is responsible for emitting the laser beam; the linear polarizer converts the incident laser beam into a single polarization direction suitable for the phased array and then emits it; the optical phased array deflects the laser beam; the CCD camera captures far-field intensity maps and transmits them to the neural network processing unit; the neural network processing unit is responsible for training the network and predicting the decoupled phase, and deploying it onto the optical phased array.

[0020] like Figure 2 As shown, the method of the present invention includes the following steps:

[0021] 1. Dataset Construction: By combining theoretical simulation and experimental measurement, a one-to-one corresponding far-field light intensity distribution and initial phase dataset is obtained;

[0022] 2. Neural Network Construction and Training: A hybrid architecture consisting of convolutional layers, fully connected layers, and physically connected layers is designed. After initializing the model parameters, the network input is the far-field light intensity, and the output is the predicted phase. The network is then optimized and trained using gradient descent with the loss function, along with the initial phase.

[0023] 3. Model Deployment and Compensation: The trained model is integrated into the phase compensation control system to predict the optimal decoupled phase value in real time, so as to eliminate phase distortion and improve the far-field light intensity quality.

[0024] In step 1, the initial phase data is given by the diffraction formula, specifically: 800 discrete deflection angles are set within a range of ±2°. The step size is 0.005°. The theoretical phase distribution is generated according to the diffraction formula:

[0025] ( , )

[0026] in, The theoretical phase distribution is the phase difference between adjacent array elements. The phase difference is fixed, and the phase of the i-th array element is a multiple of i of this phase difference. For wave vector, , Wavelength; For motor cycle, For electrode length, For electrode gap; The target diffraction angle; the phase distribution, combined with the actual characteristics of the phased array, shows that the phase is... Set the position to retain the gap phase. At the same time, to ensure the distribution of the gap phase, the phase image size is 512*512 (far field aligned).

[0027] The far-field light intensity distribution data consists of two parts: simulation and experiment.

[0028] The simulation data is determined by the liquid crystal dynamics equations, specifically by the total free energy density and field distribution equations of the liquid crystal:

[0029]

[0030]

[0031] in, The total free energy density of the liquid crystal. The elastic potential energy density of the liquid crystal. The potential energy density of the liquid crystal. For differential operators, The relative permittivity of the liquid crystal is... For the applied electric field strength, It is the electric displacement vector. For liquid crystal dielectric tensor, For liquid crystal pointing vector, The voltage applied to the upper and lower substrates of the liquid crystal; , , These are the liquid crystal elastic coefficients for unfolding, twisting, and bending deformations, respectively; these parameters determine the actual near-field phase distribution.

[0032] Through diffraction formula Obtain the required phase for the array;

[0033] Then, by referring to the table based on the liquid crystal voltage-phase shift device performance curve, the required array voltage can be obtained. Next, the near-field liquid crystal director distribution is solved by solving a series of equations and differential iteration. The simultaneous differential iteration equations are as follows:

[0034]

[0035]

[0036] in, Represents a grid Inner The liquid crystal pointing vector within the unit, Represents the free energy density with respect to the time step. Indicates variational symbols; superscript Indicates the first Within a time step unit; and The expressions are consistent. It's viewed from a time perspective. Initially The value of is generally 0. For time step, Represents a grid Inner The magnitude of voltage within a unit of time; Viscosity coefficient and material properties of liquid crystals; Find the voltage gradient; initial... It is divided into three parts. The first is the first row of the grid (corresponding to the upper surface electrode of the actual device). The ideal initial phase required for each electrode (each array element) is calculated by using the phased array diffraction formula. Then, the voltage required to be applied to each electrode (each array element) is obtained by looking up the voltage-phase shift curve of the device. This is the initial value of the first row (upper surface) grid. The second is that the initial voltage value of the bottom row (lower surface) grid is 0, so that a potential difference voltage drop can be formed. The third is the initial value of all the middle grids, which is to perform linear interpolation based on the upper and lower surface grids, that is, to assume that the initial voltage is uniformly distributed.

[0037] The grid here should be understood as follows: the size of a single liquid crystal molecule is on the order of tens of nanometers, and the nematic liquid crystal (one type of liquid crystal) is ordered in the overall direction. Multiple nematic liquid crystal molecules are regarded as a unit, and the size of a single grid is the size of dozens of nematic liquid crystal molecules, on the order of hundreds of nanometers.

[0038] Find the liquid crystal pointing vector distribution After that, the refractive index of the extraordinary light is:

[0039]

[0040] in It is a very high refractive index. and These are the refractive indices parallel and perpendicular to the liquid crystal director, respectively. The near-field phase is then... (L is the thickness of the liquid crystal layer), and finally, the far-field light intensity distribution is obtained according to the Fourier transform:

[0041]

[0042] in , The incident beam typically exhibits a Gaussian electric field distribution. For Fourier transform, The constant is used to calculate the simulated far-field light intensity distribution. This simultaneous equation considers the phase distortion caused by the adjacent lateral electric field, resulting in a higher-order grating lobe distribution in the far field. Simultaneously, due to manufacturing tolerances and circuit noise, some numerical noise (such as Gaussian or random noise) needs to be appropriately added. The experimental part of the far-field light intensity map was acquired using a CCD camera.

[0043] Using MATLAB numerical simulation software, the pointing vector is solved iteratively by the finite difference method. The near-field phase, including the second-nearest neighbor second-order cross-nonlinear coupling effect, was obtained. An FFT was performed on the near-field phase to generate a far-field spot pattern containing higher-order grating lobes, and Gaussian noise (signal-to-noise ratio 10dB) was superimposed to simulate the experimental environment. Furthermore, the optical phased array was controlled to scan within a ±2° range, and 800 sets of far-field light intensity distributions were simultaneously recorded by a CCD. These were then merged with the simulation data and divided into training and validation sets at an 8:2 ratio.

[0044] The neural network model structure constructed in step 2 is as follows: Figure 3 As shown, the first convolutional layer has 1 input feature channel and a kernel size of 3; the second convolutional layer has 8 feature channels and a kernel size of 3; the third pooling layer has a downsampling size of 2; the fourth convolutional layer has 32 feature channels and a kernel size of 3; the fifth pooling layer has a downsampling size of 2; the sixth upsampling layer has a downsampling size of 2; the seventh deconvolutional layer has 8 feature channels and a kernel size of 3; the eighth upsampling layer has a kernel size of 2; the ninth deconvolutional layer has 1 feature channel and a kernel size of 3; the tenth fully connected layer has 1024 neurons; the eleventh physically connected layer, considering the coupling characteristics of liquid crystal dynamics, must satisfy the second-nearest neighbor second-order crossover nonlinearity; the twelfth fully connected layer has 1024 neurons; the thirteenth layer is also a physically connected layer. The fourteenth layer is the output layer, with the same size as the input layer.

[0045] The loss function of the neural network model is:

[0046]

[0047] ,in , These represent the network-predicted phase and the initial phase in the dataset, respectively. To reduce model overfitting, [the following is combined]... Type regularization methods, where This is a hyperparameter, initially set to 1*10. -6 The Adam optimizer was used during the training of the neural network model, with an initial learning rate set to 1*10. -4 And a learning rate decay strategy is adopted;

[0048] The input data for deep learning models needs to be normalized preprocessed to avoid gradient explosion or vanishing, and the output compensation phase value range is limited to [0, The interval; the parameter update form of a deep learning model is:

[0049]

[0050] in, In order to be in In the time step Layer One parameter, For learning rate, It is a partial derivative operator;

[0051] The network architecture was implemented using torch framework version 2.6 based on Python 3.12. We trained and tested the network on a PC equipped with a Core i5-14600KF CPU (3.5 GHz) and 32 GB of RAM, using an NVIDIA GeForce GTX 4070 GPU. The training process took ~20 minutes, for example, 500 iterations (~600 pairs of images of size 256 × 256 pixels, batch size 4). After training, the network model could be directly applied to the wavecontrol module of an optical phased array, with an application time of ~2 ms. The symbol "~" here should be understood as approximately equal to.

[0052] Step 3, in the phase compensation execution stage, specifically involves inputting the far-field ideal distribution into the trained neural network model for each preset target deflection angle. The decoupled phase distribution is then calculated through inversion, and adaptive phase compensation under dynamic conditions is achieved using the wave control module. This decoupling process fully considers the cross-coupling effect of the next nearest-neighbor electrodes in the liquid crystal phased array and the phase distortion caused by manufacturing tolerances. By decomposing the theoretical phase into control quantities that match the actual hardware characteristics, the phase applied to each array element can accurately cancel the wavefront distortion caused by nonlinear coupling, thereby effectively eliminating the splitting of higher-order grating lobes and main lobes.

[0053] Those skilled in the art will recognize that the embodiments described herein are for the purpose of helping to understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the scope of the claims of the invention.

Claims

1. A deep learning-based method for optimizing phase compensation in optical phased arrays, characterized in that, include: S1. Obtain the one-to-one corresponding far-field light intensity distribution and initial phase dataset; The initial phase data is given by the diffraction formula; the far-field light intensity distribution includes both simulation and experiment; the simulation part is determined by the total free energy density of the liquid crystal and the field distribution equation, while the experimental part is obtained based on the optical phased array antenna system. S2. Construct a neural network that includes convolutional layers, fully connected layers, and physically connected layers; S3. The far-field light intensity distribution in step S1 is used as the input of the neural network. The output of the neural network is the predicted phase. The loss function is calculated between the predicted phase and the initial phase. The neural network is then optimized and trained by gradient descent. S4. For each preset target deflection angle, first input the far-field ideal distribution into the trained neural network model, and then calculate the decoupled phase distribution. S5. The wave control module performs adaptive phase compensation based on the decoupled phase distribution obtained in step S4.

2. The deep learning-based optical phased array phase compensation optimization method according to claim 1, characterized in that, The simulation part in step S1 is determined by the total free energy density and field distribution equation of the liquid crystal. The process of obtaining the simulation part is as follows: The total free energy density and field distribution equation of the liquid crystal are expressed as: ； ； in, The total free energy density of the liquid crystal. The elastic potential energy density of the liquid crystal. The potential energy density of the liquid crystal. For differential operators, The relative permittivity of the liquid crystal is... For the applied electric field strength, It is the electric displacement vector. For liquid crystal dielectric tensor, For liquid crystal pointing vector, The voltage applied to the upper and lower substrates of the liquid crystal; , , These are the elastic coefficients of the liquid crystal for unfolding deformation, torsional deformation, and bending deformation, respectively; Through diffraction formula Obtain the required phase for the array; Then, based on the liquid crystal voltage-phase shift device performance curve, the required array voltage can be obtained from a table. Next, the near-field liquid crystal director distribution is solved using a simultaneous differential iterative equation. The simultaneous differential iterative equation is as follows: ； ； in, Represents a grid Inner The liquid crystal pointing vector within the unit, Represents the free energy density with respect to the time step. Indicates variational symbols; superscript Indicates the first Within a time step unit; For time step, Represents a grid Inner The magnitude of voltage within a unit of time; The viscosity coefficient of liquid crystals; Find the gradient value of the voltage; Find the liquid crystal pointing vector distribution Then, the refractive index of the light was obtained as follows: ； in, It is a very high refractive index. and These are the refractive indices parallel and perpendicular to the liquid crystal pointer, respectively; The next near-field phase is L is the thickness of the liquid crystal layer; Then, the far-field light intensity distribution is obtained based on the Fourier transform: ； in , For the incident beam, For Fourier transform, It is a constant; Finally, the simulated far-field light intensity distribution was calculated.

3. The deep learning-based optical phased array phase compensation optimization method according to claim 2, characterized in that, The size of a single grid is the size of dozens of nematic liquid crystal molecules.

4. The deep learning-based optical phased array phase compensation optimization method according to claim 3, characterized in that, The experimental part in step S1 is based on an optical phased array antenna system. The optical phased array antenna system includes a laser source, a linear polarizer, an optical phased array, and a CCD camera. The specific acquisition process is as follows: the laser emitted from the laser source is converted into a single polarization direction laser that can be used by the phased array by the linear polarizer and then emitted. The optical phased array deflects the incident laser, and the CCD camera captures the far-field light intensity map after deflection.

5. The deep learning-based optical phased array phase compensation optimization method according to claim 4, characterized in that, The neural network in step S2 sequentially includes a first convolutional layer, a second convolutional layer, a first pooling layer, a third convolutional layer, a second pooling layer, a first upsampling layer, a first deconvolutional layer, a second upsampling layer, a second deconvolutional layer, a first fully connected layer, a first physically connected layer, a second fully connected layer, a second physically connected layer, and an output layer; wherein the kernel size of each convolutional layer and each deconvolutional layer is 3, and the number of neurons in each fully connected layer is 1024.

6. The method for optimizing phase compensation of optical phased arrays based on deep learning according to claim 5, characterized in that, The first physical connection layer and the second physical connection layer combine the dynamic coupling characteristics of liquid crystal to satisfy the second-nearest neighbor cross-nonlinear relationship.

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