CN114815436B - Mutual coupling compensation method of optical phased array elements based on neighborhood sampling principal component analysis - Google Patents

Abstract

The invention discloses an optical phased array element mutual coupling compensation method based on neighborhood sampling principal component analysis, which includes two processes of dimensionality reduction and iteration, and dimensionality reduction includes the following steps: S1, calculating the corresponding S2, obtain the neighborhood sampling matrix X; S3, calculate the covariance matrix C of X; S4, calculate the eigenvalues and eigenvectors of C, and splicing the eigenvectors by rows to obtain the matrix U; S5, the eigenvalues from large Go to the small sort, sort the eigenvectors in the U matrix correspondingly, and get the space transformation matrix P; S6, use the P matrix to multiply the voltage vector to the left to get a new vector

The iteration includes the following steps: S7. Obtain the updated voltage vector and load it on the array element of the phased array; S8. Collect the value J of the evaluation function, and compare the value J according to the change amount δJ of the evaluation function

Update the first K values of . The invention can greatly reduce the iterative dimension of the optimization process, increase the convergence speed, and improve the robustness of the system operation.

Description

Mutual coupling compensation method for optical phased array elements based on neighborhood sampling principal component analysis

Technical Field

The invention belongs to the technical field of optical phased array control and adaptive optical optimization algorithm, and specifically relates to an optical phased array element mutual coupling compensation method based on neighborhood sampling principal component analysis.

Background Art

Optical phased array is an ideal method to achieve non-mechanical beam deflection and is used in many fields, such as light detection and ranging, free space communication, target tracking and remote sensing. However, many optical phased arrays face the problem of mutual coupling between array elements, such as the lateral electric field of liquid crystal phased array and thermal crosstalk of silicon-based phased array, which will cause phase error of near-field wavefront, thereby deteriorating the quality of far-field deflected beam. These coupling problems caused by device structure are difficult to solve by improving manufacturing process or materials alone. Therefore, the commonly used method is to compensate for the phase difference through some iterative adaptive optimization algorithms, such as genetic algorithm, particle swarm algorithm, random parallel gradient descent algorithm, etc. However, the iterative convergence rate of these algorithms will be greatly reduced with the increase of the number of array elements. This is because these iterative algorithms optimize each array element of the phased array independently, so the dimension of the iterative variable is equal to the number of array elements, and it is very difficult to find the global optimal solution through iteration in high-dimensional space, and it may even fall into the local optimal solution and fail to converge. Therefore, the slow iterative convergence speed has become the main obstacle to the application of optimization algorithms in practical systems.

In order to improve the convergence speed of the optimization algorithm, there are currently three main methods. The first method is array element decoupling, that is, the coupling relationship between the array elements is modeled by numerical calculation methods, so as to separate the influence of a single array element on the evaluation function. However, in actual systems, it is very difficult to accurately model the coupling relationship between the array elements, so this method mostly remains at the theoretical level and is rarely used in actual engineering. The second method is phase difference modeling, that is, the phase difference of the system is modeled according to the phase difference theory, the relationship between the phase difference and the evaluation function is established, and then the cause of the phase difference is optimized in a targeted manner. This method can improve the optimization speed of the system, but the established model can only be applied to specific scenarios. Different scenarios require different models, and it is difficult to accurately model the phase difference in some scenarios. The third method is machine learning modeling, which builds the error model of the phased array device through a large number of sample training, and then optimizes the device. However, this method requires a large number of samples for pre-training models, and the model is not universal between different devices.

In general, there is still a lack of a practical algorithm that can perform adaptive iterative optimization and phase compensation for the phase error caused by the coupling problem between optical phased array elements, while ensuring fast convergence speed and supporting online operation while taking into account versatility.

Summary of the invention

The purpose of the present invention is to overcome the shortcomings of the prior art and provide an optical phased array element mutual coupling compensation method based on neighborhood sampling principal component analysis, which can greatly reduce the iteration dimension of the optimization process, avoid falling into the local optimal solution, increase the convergence speed, and improve the robustness of the system operation.

The objective of the present invention is achieved through the following technical solution: an optical phased array element mutual coupling compensation method based on neighborhood sampling principal component analysis includes two processes of dimensionality reduction and iteration, and the dimensionality reduction process includes the following steps:

其中N为相控阵的阵元总数；S1. According to the target angle of deflection, the driving voltage corresponding to each element of the phased array is calculated through the phased array formula and the voltage-phase relationship, and the driving voltage of all elements is recorded as an N-dimensional column vector

Where N is the total number of elements in the phased array;

将它们与

按列拼接，得到邻域采样矩阵

记为X，其中K为电压向量总数；S2. Set K-1 sampling points in a neighborhood of the target angle and calculate the voltage vector corresponding to each sampling point

Combine them with

Concatenate by columns to get the neighborhood sampling matrix

Denoted as X, where K is the total number of voltage vectors;

S3, calculate the covariance matrix C=XX ^T of the neighborhood sampling matrix X;

S4, calculating the eigenvalues of the covariance matrix C and the eigenvectors corresponding to the eigenvalues, and concatenating the eigenvectors row by row to obtain the matrix U;

S5. Sort the eigenvalues of the covariance matrix C from large to small, and sort the eigenvectors in the U matrix accordingly to obtain the spatial transformation matrix P;

对其进行空间变换，得到新的向量

S6. Use the P matrix to multiply the voltage vector

Transform it spatially to get a new vector

The iterative process includes the following steps:

的前K个维度施加随机微扰

对更新后的

使用空间变化矩阵P的逆矩阵进行反变换，得到更新后的电压向量

并将

加载到相控阵的阵元上；S7, yes

Apply random perturbations to the first K dimensions of

For the updated

Use the inverse matrix of the space-varying matrix P to perform an inverse transformation to obtain the updated voltage vector

and will

Loaded onto the elements of the phased array;

的前K个值进行更新，更新公式为：

其中

表示第n次迭代的数据，γ为迭代步长。S8, collect the value J of the evaluation function, and adjust the

The first K values of are updated, and the update formula is:

in

Represents the data of the nth iteration, and γ is the iteration step size.

Furthermore, the specific implementation method of step S1 is as follows: the phased array formula refers to the relationship between the phase shift ΔΦ between adjacent elements of the phased array and the target angle θ, that is, ΔΦ=2π/λ·dsinθ, where λ is the wavelength of the incident laser and d is the center spacing of the phased array elements; the voltage-phase relationship refers to the relationship curve between the phase shift ΔΦ of the phased array and the driving voltage, which is measured experimentally and is used to map the phase shift ΔΦ to a voltage value, thereby obtaining the driving voltage required for each element.

Furthermore, a neighborhood of the target angle in step S2 refers to an angle range of [θ-δθ, θ+δθ] centered at the target angle θ, where δθ satisfies: |sin(θ+δθ)-sin(θ)|＜λ/(Nd), where λ is the wavelength of the incident laser and d is the center spacing of the phased array elements.

The beneficial effects of the present invention are as follows: the present invention extracts the structural information of the optical phased array through principal component analysis, and approximates it with a small number of dimensions, and realizes compensation of the phase difference caused by the mutual coupling of the array elements by adaptively optimizing the driving voltage of the optical phased array elements in a low-dimensional space; on this basis, through multiple sampling in the neighborhood of the target angle, the coupling information in different dimensions is obtained, and the accuracy of linear approximation is improved. It can greatly reduce the iteration dimension of the optimization process, avoid falling into the local optimal solution, improve the convergence speed, and improve the robustness of the system operation; at the same time, the algorithm does not depend on any specific device structure or application scenario, and can be applied to any phased array system with inter-element coupling problems, and has strong universality.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flow chart of an optical phased array element mutual coupling compensation method based on neighborhood sampling principal component analysis of the present invention.

DETAILED DESCRIPTION

The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

As shown in FIG1 , a method for compensating mutual coupling of optical phased array elements based on neighborhood sampling principal component analysis of the present invention includes two processes, dimensionality reduction and iteration. In the dimensionality reduction process, principal component analysis is used to extract structural information of the optical phased array, and a spatial transformation matrix is generated by sorting eigenvalues and eigenvectors, and the matrix is approximated with a few dimensions in the new space, thereby reducing the dimensionality of high-dimensional data. On this basis, coupling information in different dimensions is obtained by multiple samplings in the neighborhood of the target angle, thereby improving the accuracy of linear approximation. In the iteration process, a random parallel gradient descent algorithm is used to iteratively optimize the data after dimensionality reduction, thereby compensating for the phase error caused by mutual coupling of optical phased array elements.

The dimensionality reduction process only needs to be run once for each target angle optimization, and includes the following steps:

S1. According to the target angle of deflection, the driving voltage corresponding to each element of the phased array is calculated through the phased array formula and the voltage-phase relationship, and the driving voltage of all elements is recorded as an N-dimensional column vector

Where N is the total number of elements in the phased array;

The specific implementation method is as follows: the phased array formula refers to the relationship between the phase shift ΔΦ between adjacent elements of the phased array and the target angle θ, that is, ΔΦ=2π/λ·dsinθ, where λ is the wavelength of the incident laser and d is the center spacing of the phased array elements; the voltage-phase relationship refers to the relationship curve between the phase shift ΔΦ of the phased array and the driving voltage, which is measured experimentally and is used to map the phase shift ΔΦ to a voltage value, thereby obtaining the driving voltage required for each element.

将它们与

按列拼接，得到邻域采样矩阵

记为X，其中K为电压向量总数；目标角度的一个邻域是指以目标角度θ为中心，位于[θ-δθ，θ+δθ]的角度范围，其中δθ满足：|sin(θ+δθ)-sin(θ)|＜λ/(Nd)，其中λ为入射激光的波长，d为相控阵阵元中心间距。S2. Set K-1 sampling points in a neighborhood of the target angle and calculate the voltage vector corresponding to each sampling point

Combine them with

Concatenate by columns to get the neighborhood sampling matrix

Denoted as X, where K is the total number of voltage vectors; a neighborhood of the target angle refers to the angle range of [θ-δθ, θ+δθ] centered at the target angle θ, where δθ satisfies: |sin(θ+δθ)-sin(θ)|＜λ/(Nd), where λ is the wavelength of the incident laser and d is the center spacing of the phased array elements.

S3. Calculate the covariance matrix C=XX ^T of the neighborhood sampling matrix X, where the superscript T represents transposition. The obtained covariance matrix C is an N-dimensional real symmetric matrix, whose diagonal elements are the variances of each dimension of X, and the non-diagonal elements are the covariances;

S4. Calculate the eigenvalues {λ ₁ ,λ ₂ ...λ _N } of the covariance matrix C and the eigenvectors ξ ₁ ,ξ ₂ ...ξ _N corresponding to the eigenvalues, and concatenate the eigenvectors row by row to obtain the matrix U. From the properties of real symmetric matrices, it can be seen that C satisfies:

D＝UCU ^T

Where U is a matrix composed of the eigenvectors of C as row vectors; D is a diagonal matrix, and the diagonal elements are each eigenvalue of C in turn, that is:

S5. Sort the eigenvalues {λ ₁ , λ ₂ ..λ _N } of the covariance matrix C from large to small, and sort the eigenvectors in the U matrix accordingly, to obtain a spatial transformation matrix P, so that the eigenvectors corresponding to the larger eigenvalues are arranged in the front rows of the P matrix;

对其进行空间变换，得到新的向量

S6. Use the P matrix to multiply the voltage vector

Transform it spatially to get a new vector

相当于定义了这样一种空间变换，即将

的每个元素映射到这组新的基底上，新基底中每个维度上的值对应为

的每个元素。根据协方差矩阵C的定义，特征向量对应的特征值越大，代表该维度上数据的方差越大，其在空间变换后涵盖的信息量也越大。因此，通过对特征值进行排序，将信息量较大的特征向量对应的维度排到靠前的位置，实现对相控阵结构信息的线性近似，亦即保留了主要的信息；在迭代过程中只对这些维度进行优化，相较于直接对原始电压向量的N维空间进行优化，即为实现了降维；其余维度由于对应较小的特征值，因此涵盖的信息量较小，是相对次要的信息，予以忽略有助于提高优化的效率。The principle of the dimensionality reduction process of S1 to S6 is: the eigenvectors form a new set of orthogonal bases, and the matrix P is used in S6 to multiply the original voltage vector

This is equivalent to defining such a spatial transformation.

Each element of is mapped to this new basis, and the value of each dimension in the new basis corresponds to

Each element of . According to the definition of the covariance matrix C, the larger the eigenvalue corresponding to the eigenvector, the larger the variance of the data on that dimension, and the larger the amount of information it covers after spatial transformation. Therefore, by sorting the eigenvalues, the dimensions corresponding to the eigenvectors with larger amounts of information are placed in the front positions, and the linear approximation of the phased array structure information is achieved, that is, the main information is retained; in the iterative process, only these dimensions are optimized, which is compared to directly optimizing the N-dimensional space of the original voltage vector, which is to achieve dimensionality reduction; the remaining dimensions correspond to smaller eigenvalues, so the amount of information covered is smaller, which is relatively minor information, and ignoring them helps improve the efficiency of optimization.

The present invention introduces neighborhood sampling in S2 because for the same optical phased array, different angles correspond to different voltage vectors, and the degree of mutual coupling between array elements is also different. Therefore, each additional voltage vector introduces new dimensional information to the principal component analysis.

The covariance matrix C is an N-dimensional real symmetric square matrix, whose rank is equal to the number of neighborhood sampling points K, and is also equal to the number of non-zero eigenvalues; since the spatial transformation matrix is composed of eigenvectors, the larger the number of sampling points K, the more eigenvectors corresponding to non-zero eigenvalues can be obtained, and the more accurate the approximation of the phased array structure information, but the slower the calculation speed. In practical applications, the number of sampling points should be reasonably selected to seek a balance between accuracy and speed.

The iterative process needs to be repeated until the preset convergence condition is reached, that is, the optimization is completed, including the following steps:

的前K个维度施加随机微扰

对更新后的

使用空间变化矩阵P的逆矩阵进行反变换，得到更新后的电压向量

并将

加载到相控阵的阵元上；S7, yes

Apply random perturbations to the first K dimensions of

For the updated

Use the inverse matrix of the space-varying matrix P to perform an inverse transformation to obtain the updated voltage vector

and will

Loaded onto the elements of the phased array;

的前K个值进行更新，更新公式为：

其中

表示第n次迭代的数据，γ为迭代步长。评价函数，是指对当前远场光强分布状况的一个评价函数，常用的评价函数包括偏转效率、边模抑制比和主瓣半高全宽等，可根据实际需求进行选用。S8, collect the value J of the evaluation function, and adjust the

The first K values of are updated, and the update formula is:

in

Represents the data of the nth iteration, and γ is the iteration step. The evaluation function refers to an evaluation function for the current far-field light intensity distribution. Commonly used evaluation functions include deflection efficiency, side mode suppression ratio, and main lobe half-height full width, which can be selected according to actual needs.

The iteration is stopped until the preset convergence conditions are met, such as the expected convergence value or the set number of iterations, or the change in the evaluation function caused by the perturbation reaches the set value.

Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims (2)

1. The optical phased array element mutual coupling compensation method based on neighborhood sampling principal component analysis is characterized by comprising two processes of dimension reduction and iteration, wherein the dimension reduction process comprises the following steps of:

s1, calculating driving voltage corresponding to each array element of a phased array according to a target angle of deflection through a phased array formula and a voltage-phase relation, and recording the driving voltage of all the array elements as an N-dimensional column vector

Wherein N is the total number of array elements of the phased array; the specific implementation method comprises the following steps: the phased array formula refers to a relation between the phase shift quantity delta phi between adjacent phased array elements and a target angle theta, namely delta phi = 2 pi/lambda dsin theta, wherein lambda is the wavelength of incident laser, and d is the center-to-center distance of the phased array elements; the voltage-phase relation is a relation curve between phased array phase shift quantity delta phi and driving voltage, and is measured by experiments and used for mapping the phase shift quantity delta phi into a voltage value so as to obtain driving voltage required by each array element;

s2, setting K-1 sampling points in one adjacent area of the target angle, and calculating each sampling point pairVoltage vector of the application

They are combined with->

Splicing according to columns to obtain a neighborhood sampling matrix +.>

Denoted as X, where K is the total number of voltage vectors;

s3, calculating covariance matrix C=XX of neighborhood sampling matrix X ^T ；

S4, calculating a characteristic value of the covariance matrix C and a characteristic vector corresponding to the characteristic value, and splicing the characteristic vector according to rows to obtain a matrix U;

s5, sorting the eigenvalues of the covariance matrix C from large to small, and sorting eigenvectors in the U matrix correspondingly to obtain a space transformation matrix P;

s6, using the P matrix to multiply the voltage vector

Spatially transforming it to obtain a new vector +.>

The iterative process comprises the following steps:

s7, pairing

Random perturbation is applied to the first K dimensions of (2)>

For updated->

Inverse transformation is performed using the inverse of the spatial variation matrix P to obtain an updated voltage vector +.>

And will->

Loading the array elements of the phased array;

s8, acquiring a value J of the evaluation function, and according to the change delta J of the evaluation function

The first K values of (a) are updated by the following update formula:

Wherein->

Data representing the nth iteration, γ being the iteration step.

2. The optical phased array element mutual coupling compensation method based on the neighborhood sampling principal component analysis according to claim 1, wherein one neighborhood of the target angle in the step S2 is an angle range centered on the target angle θ and located in [ θ - δθ, θ+δθ ], where δθ satisfies: and (2) sin (theta+delta theta) -sin (theta) | < lambda/(Nd), wherein lambda is the wavelength of incident laser, and d is the center-to-center distance of the array elements of the phased array.

Images