Superposition state orbital angular momentum online classification method based on stream computing framework

Abstract

The present application relates to superposition state orbital angular momentum online classification method based on stream computing framework, belongs to optical signal transmission field. The stream computing framework is built, the real-time collection and real-time calculation of orbital angular momentum sample are realized, the random turbulent disturbance simulation model is established, and different link optical transmission scenes are simulated. After obtaining the received light spot sample, through the data driven idea, the orbital angular momentum online classification model based on sequence extreme learning machine is constructed. The input of the model is the light spot feature, and the output of the model is the orbital angular momentum space mode category label. Considering the change of the current sample segment, the online classification model parameters are automatically updated, so as to avoid the manual parameter adjustment process, and the orbital angular momentum online classification is realized. The classification method formed by the present application can realize online learning of large-scale data set, break through the precision deficiency bottleneck caused by the physical model classification method, and can be suitable for different engineering application scenes.

Description

Technical Field

[0001] This invention belongs to the field of optical signal transmission technology, specifically relating to an online classification method for superposition state orbital angular momentum based on a stream computing framework. Background Technology

[0002] Orbital angular momentum (OAM) is an important physical property of light, describing the rotational motion of photons around the beam axis during transmission. Accurate identification of OAM is a core technology for understanding the physical properties of optical fields. In the field of optical communication, this technology can effectively demultiplex different orbital angular momentum modes, breaking through traditional transmission capacity limitations and providing technical support for building ultra-high-speed, high-capacity communication networks.

[0003] The authorized patent "A Method for Recognizing the Superposition of Orbital Angular Momentum Based on Conditional Generative Adversarial Networks" (202610026965.0) constructs a conditional generative adversarial network and introduces a skip connection mechanism into the generator's network structure. This preserves low-level detailed features, improves the quality of generated images, and effectively restores vortex beams that have been severely distorted by strong turbulence and long-distance propagation. The authorized patent "A Multi-Beam Radio Frequency OAM Positioning and Recognition Method and System Based on Deep Learning" (202311054861.3) uses optical orbital angular momentum as the basis for pre-training, trains radio frequency orbital angular momentum images using pre-trained weight information, and realizes the positioning and recognition functions of radio frequency orbital angular momentum. However, deep learning architectures often rely on complex parameter optimization strategies, have a high dependence on datasets, and are difficult to adapt to time-varying application scenarios.

[0004] The published patent "A Domain-Adaptive OAM Superimposed Mode Recognition and Turbulence Intensity Detection Method" (202411863416.6) proposes a domain-adaptive OAM superimposed mode recognition and turbulence intensity detection method. This method requires only a small amount of data to identify superimposed OAM modes and analyze the intensity of turbulence channels, significantly reducing training costs. It boasts advantages such as ease of operation, high cost-effectiveness, and strong real-time performance. The published patent "A Deep Learning-Based Orbital Angular Momentum Pattern Recognition Method" (202511391088.9) significantly improves the efficiency and accuracy of model training by introducing adaptive learning rate scheduling and gradient pruning techniques, effectively avoiding common convergence oscillation problems. The published patent "A Method for Orbital Angular Momentum Pattern Recognition Based on Improved ResNeSt-50" (202511897601.1) improves recognition accuracy by employing a deep neural network architecture based on ResNeSt-50 and integrating a split attention mechanism with multi-cardinality grouped convolution. The model exhibits strong robustness to biases in the spatial pattern generation process through comprehensive data augmentation strategies and adaptive channel adjustment. However, these methods require manual parameter tuning and are difficult to apply to increasingly large sample sets. Summary of the Invention

[0005] This invention provides an online classification method for orbital angular momentum of superposition states based on a stream computing framework. The aim is to enable online learning of large-scale datasets, overcome the bottleneck of insufficient accuracy caused by physical model classification methods, and is applicable to different engineering application scenarios. It has good theoretical significance and application value.

[0006] The technical solution adopted by this invention includes the following steps:

[0007] (1) A streaming computing framework was established, and real-time acquisition and calculation of orbital angular momentum (OAM) samples were realized through discretization of data streams;

[0008] (2) A simulation model of random turbulence disturbance was established. By generating a multi-phase screen, the equivalent simulation of the beam in different transmission media such as the atmosphere and ocean was realized. The influence of random turbulence on the Laguerre-Gaussian beam was analyzed, and the received beam spot sample was obtained. ;

[0009] (3) Using a data-driven modeling approach, an online classification model of orbital angular momentum based on sequence extreme learning machine was constructed. The input of the model is light spot samples. The model outputs orbital angular momentum space mode category labels. ;

[0010] (4) The output weights are obtained by calculating the online classification model of orbital angular momentum. ;

[0011] (5) Input a new spot sample Using an online classification model based on orbital angular momentum, the OAM spatial mode category label of the current light field intensity sample is calculated. This enables online classification of orbital angular momentum.

[0012] The convection computing framework described in step (1) of this invention is as follows:

[0013] The stream computing framework uses Spark technology and establishes an interaction mode between the client and the server. On the server side, the distributed file system HDFS is used for data storage. Users send data requests to the server through the client, and the server performs function calls in the background. In the Spark processing module, a series of data operations on the Resilient Distributed Dataset (RDD) are completed through transformation functions, and the entire module is executed through action functions to obtain classification results. The server returns the results to the client, completing the data response.

[0014] The establishment of the stochastic turbulence disturbance simulation model in step (2) of this invention is as follows:

[0015] By generating multiple phase screens, equivalent simulations of beam transmission through different media such as the atmosphere and ocean are achieved. Through fast Fourier transform, random turbulent phase screens can be obtained. Using multiple intermediate planes to form a phase screen sequence, the expression for the Laguerre-Gaussian LG beam passing through each phase screen layer is obtained:

[0016] (1)

[0017] in, and These represent the Fourier transform and the inverse Fourier transform, respectively. and These represent the light field intensity at the source and after propagation through a phase screen, respectively. Indicates the light field intensity at the receiving plane. Represents the imaginary unit. Represents the random turbulence transformation operator. The distance between each phase screen layer, , , , Representing coordinates, a Monte Carlo simulation is performed to obtain the light spot sample at the receiving end. By considering different topological charge numbers, the superposition state OAM mode is obtained.

[0018] The online classification model of orbital angular momentum in step (3) of this invention is as follows:

[0019] A three-layer neural network structure consisting of an input layer, hidden layers, and an output layer is constructed. The training process is divided into two stages: initial learning and online learning. In the initial learning stage, the input layer is... There are 1 node, and the hidden layer is 1. There are 1 node in the output layer and 1 node in the spot sample. Orbital angular momentum space mode category tags Composition of sample data The mapping expression between the two is:

[0020] (2)

[0021] in, and These are the input weights and biases, respectively. To output weights, represent The One input parameter, represent The One output parameter, For the activation function, to further simplify the expression, the set of orbital angular momentum space mode category labels is represented as follows: The hidden layer random matrix is ​​represented as:

[0022] (3)

[0023] Therefore, the mapping expression can be simplified to a matrix form, as follows:

[0024] (4)

[0025] Output weights These are important parameters during the training phase, and can be computed using the Moore-Penrose generalized inverse, specifically represented as:

[0026] (5)

[0027] in, Hidden layer random matrix The generalized inverse of MP can be represented as ;

[0028] During the online learning phase, the output weights are updated using an iterative optimization method. Time period sample fragment Upon arrival, the number of input layer nodes in the Extreme Learning Machine increases, and the objective function of the mapping expression becomes minimizing the approximation error of all current sample segments, expressed as:

[0029] (6)

[0030] in, and They represent Time-time hidden layer random matrix and orbital angular momentum space modal category label set.

[0031] In step (4) of this invention, the output weights are calculated by optimizing the parameters of the online classification model for orbital angular momentum. :

[0032] Considering the linear relationship between the hidden layer and the output layer, in Based on the network parameters over a time period, calculate Time period output weight expression:

[0033] (7)

[0034] Since matrix multiplication satisfies the associative law, we divide the whole into two parts for calculation and introduce... Intermediate variables in time period Output weights The first part of the expression can be simplified to obtain Intermediate variables in time period The expression is:

[0035] (8)

[0036] Consider output weights The latter part of the expression, expanded using the matrix multiplication principle, yields:

[0037] (9)

[0038] Therefore, we obtain The output weight for each time period is:

[0039] (10)

[0040] Through iteration, the first... Output weights corresponding to fragments The expression is:

[0041] (11)

[0042] in, The online classification model of orbital angular momentum does not require retraining and has good data adaptability.

[0043] The step (5) of this invention involves inputting a new light spot sample. Using an online classification model based on orbital angular momentum, the OAM spatial mode category label of the current light field intensity sample is calculated. The specific expression is:

[0044] (12)

[0045] in, , This enables online classification of orbital angular momentum.

[0046] This invention establishes a simulation model for random turbulent optical transmission. Through numerical simulation, it simulates the light field intensity distribution of a beam at the transmitter and receiver under turbulent conditions, obtaining a set of received light spot samples. Using a data-driven approach, an online classification model for orbital angular momentum based on a sequential extreme learning machine is constructed. The model automatically updates its online classification parameters, thus avoiding manual parameter tuning and achieving online classification of superposition-state orbital angular momentum. The classification method developed in this invention enables online learning of large-scale datasets, overcoming the accuracy limitations of physical model-based classification methods, and is applicable to various engineering application scenarios.

[0047] The beneficial effects of this invention are

[0048] (1) The present invention designs a stream computing framework to realize real-time acquisition and real-time calculation of orbital angular momentum samples.

[0049] (2) This invention considers the influence of random turbulence on optical parameters and simulates random turbulence conditions through a random phase screen to obtain a set of received light spot samples. An online classification model of orbital angular momentum for sequential extreme learning machine is established through the idea of ​​data-driven approach, which breaks through the bottleneck of insufficient accuracy caused by physical model.

[0050] (3) Considering the changes in the current sample fragments, the parameters of the online classification model are automatically updated, thereby avoiding the manual parameter tuning process and achieving complete automation. This has good engineering application value for the information processing of complex systems. Attached Figure Description

[0051] Figure 1 This is a schematic diagram of the stream computing framework of the present invention;

[0052] Figure 2 This is a simulation model diagram of random turbulent optical transmission according to the present invention;

[0053] Figure 3 This is a flowchart of the online classification method of the present invention;

[0054] Figure 4 This is a comparison chart of the classification accuracy of this invention;

[0055] Figure 5This is a diagram showing the online classification results of the superposition state orbital angular momentum of this invention. Detailed Implementation

[0056] An online classification method for orbital angular momentum of superposition states based on a stream computing framework includes the following steps:

[0057] (1) A streaming computing framework was established, and real-time acquisition and calculation of orbital angular momentum (OAM) samples were realized through discretization of data streams;

[0058] (2) A simulation model of random turbulence disturbance was established. By generating a multi-phase screen, the equivalent simulation of the beam in different transmission media such as the atmosphere and ocean was realized. The influence of random turbulence on the Laguerre-Gaussian beam was analyzed, and the received beam spot sample was obtained. ;

[0059] (3) Using a data-driven modeling approach, an online classification model of orbital angular momentum based on sequence extreme learning machine was constructed. The input of the model is light spot samples. The model outputs orbital angular momentum space mode category labels. ;

[0060] (4) The output weights are obtained by calculating the online classification model of orbital angular momentum. ;

[0061] (5) Input a new spot sample Using an online classification model based on orbital angular momentum, the OAM spatial mode category label of the current light field intensity sample is calculated. This enables online classification of orbital angular momentum.

[0062] The convection computing framework described in step (1) of this invention is as follows:

[0063] The stream computing framework uses Spark technology and establishes an interaction mode between the client and the server. On the server side, the distributed file system HDFS is used for data storage. Users send data requests to the server through the client, and the server performs function calls in the background. In the Spark processing module, a series of data operations on the Resilient Distributed Dataset (RDD) are completed through transformation functions, and the entire module is executed through action functions to obtain classification results. The server returns the results to the client, completing the data response.

[0064] The establishment of the stochastic turbulence disturbance simulation model in step (2) of this invention is as follows:

[0065] By generating multiple phase screens, equivalent simulations of beam transmission through different media such as the atmosphere and ocean are achieved. Through fast Fourier transform, random turbulent phase screens can be obtained. Using multiple intermediate planes to form a phase screen sequence, the expression for the Laguerre-Gaussian LG beam passing through each phase screen layer is obtained:

[0066] (1)

[0067] in, and These represent the Fourier transform and the inverse Fourier transform, respectively. and These represent the light field intensity at the source and after propagation through a phase screen, respectively. Indicates the light field intensity at the receiving plane. Represents the imaginary unit. Represents the random turbulence transformation operator. The distance between each phase screen layer, , , , Representing coordinates, a Monte Carlo simulation is performed to obtain the light spot sample at the receiving end. By considering different topological charge numbers, the superposition state OAM mode is obtained.

[0068] The online classification model of orbital angular momentum in step (3) of this invention is as follows:

[0069] A three-layer neural network structure consisting of an input layer, hidden layers, and an output layer is constructed. The training process is divided into two stages: initial learning and online learning. In the initial learning stage, the input layer is... There are 1 node, and the hidden layer is 1. There are 1 node in the output layer and 1 node in the spot sample. Orbital angular momentum space mode category tags Composition of sample data The mapping expression between the two is:

[0070] (2)

[0071] in, and These are the input weights and biases, respectively. To output weights, represent The One input parameter, represent The One output parameter, For the activation function, to further simplify the expression, the set of orbital angular momentum space mode category labels is represented as follows: The hidden layer random matrix is ​​represented as:

[0072] (3)

[0073] Therefore, the mapping expression can be simplified to a matrix form, as follows:

[0074] (4)

[0075] Output weights These are important parameters during the training phase, and can be computed using the Moore-Penrose generalized inverse, specifically represented as:

[0076] (5)

[0077] in, Hidden layer random matrix The generalized inverse of MP can be represented as ;

[0078] During the online learning phase, the output weights are updated using an iterative optimization method. Time period sample fragment Upon arrival, the number of input layer nodes in the Extreme Learning Machine increases, and the objective function of the mapping expression becomes minimizing the approximation error of all current sample segments, expressed as:

[0079] (6)

[0080] in, and They represent Time-time hidden layer random matrix and orbital angular momentum space modal category label set.

[0081] In step (4) of this invention, the output weights are calculated by optimizing the parameters of the online classification model for orbital angular momentum. :

[0082] Considering the linear relationship between the hidden layer and the output layer, in Based on the network parameters over a time period, calculate Time period output weight expression:

[0083] (7)

[0084] Since matrix multiplication satisfies the associative law, we divide the whole into two parts for calculation and introduce... Intermediate variables in time period Output weights The first part of the expression can be simplified to obtain Intermediate variables in time period The expression is:

[0085] (8)

[0086] Consider output weights The latter part of the expression, expanded using the matrix multiplication principle, yields:

[0087] (9)

[0088] Therefore, we obtain The output weight for each time period is:

[0089] (10)

[0090] Through iteration, the first... Output weights corresponding to fragments The expression is:

[0091] (11)

[0092] in, The online classification model of orbital angular momentum does not require retraining and has good data adaptability.

[0093] The step (5) of this invention involves inputting a new light spot sample. Using an online classification model based on orbital angular momentum, the OAM spatial mode category label of the current light field intensity sample is calculated. The specific expression is:

[0094] (12)

[0095] in, , This enables online classification of orbital angular momentum.

[0096] The invention will be further illustrated below with specific experimental examples.

[0097] 1. A stream computing framework was established.

[0098] Specific forms such as Figure 1As shown, Spark technology was used to store and process the received light spot samples, establishing a client-server interaction model. On the server side, a distributed file system (Hadoop Distributed System, HDFS) was used for data storage. Users send data requests to the server through the client, and the server performs function calls in the background. In the Spark processing module, transformation functions complete a series of data operations on Resilient Distributed Datasets (RDDs), and action functions execute the entire module to obtain the classification results. The server returns the results to the client, completing the data response.

[0099] 2. A simulation model of random turbulent optical transmission was established.

[0100] Specific forms such as Figure 2 As shown, equivalent simulations of beam transmission through different media such as the atmosphere and ocean are achieved by generating multiple phase screens. Random turbulent phase screens can be obtained through Fast Fourier Transform. Using a sequence of phase screens composed of multiple intermediate planes, the expression for the Laguerre-Gaussian (LG) beam passing through each phase screen is obtained:

[0101] (1)

[0102] in, and These represent the Fourier transform and the inverse Fourier transform, respectively. and These represent the light field intensity at the source and after propagation through a phase screen, respectively. Indicates the light field intensity at the receiving plane. Represents the imaginary unit. Represents the random turbulence transformation operator. The distance between each phase screen layer, , , , Representing coordinates. A Monte Carlo simulation is performed to obtain a set of light field intensity samples at the receiver. By considering different topological charge numbers, we obtain the superposition state OAM mode.

[0103] 3. An online classification model for orbital angular momentum was established.

[0104] A three-layer neural network structure consisting of an input layer, hidden layers, and an output layer is constructed. The training process is divided into two phases: initial learning and online learning. Figure 3 As shown. In the initial learning phase, the input layer is... There are 1 node, and the hidden layer is 1. The output layer has 1 node. (Spot sample) Orbital angular momentum space mode category tags Composition of sample data The mapping expression between the two is:

[0105] (2)

[0106] in, and These are the input weights and biases, respectively. To output weights, represent The One input parameter, represent The One output parameter, For activation functions. To further simplify the expression, the set of orbital angular momentum space mode category labels is represented as: The hidden layer random matrix is ​​represented as

[0107] (3)

[0108] Therefore, the mapping expression can be simplified to a matrix form, as follows:

[0109] (4)

[0110] Output weights These are important parameters during the training phase and can be computed using the Moore-Penrose (MP) generalized inverse, specifically represented as...

[0111] (5)

[0112] in, Hidden layer random matrix The generalized inverse of MP can be represented as .

[0113] During the online learning phase, the output weights are updated using an iterative optimization approach. Time period sample fragment Upon arrival, the number of input layer nodes in the Extreme Learning Machine increases, and the objective function of the mapping expression becomes minimizing the approximation error of all current sample segments, which can be expressed as:

[0114] (6)

[0115] in, and They represent Time-time hidden layer random matrix and orbital angular momentum space modal category label set.

[0116] 4. Iteratively calculate the output weights.

[0117] Considering the linear relationship between the hidden layer and the output layer, in Based on the network parameters over a time period, calculate Time period output weight expression

[0118] (7)

[0119] Since matrix multiplication satisfies the associative law, the entire matrix can be divided into two parts for calculation, which introduces... Intermediate variables in time period Output weights The first part of the expression can be simplified to obtain Intermediate variables in time period The expression is

[0120] (8)

[0121] Consider output weights The latter part of the expression, expanded using the matrix multiplication principle, yields:

[0122] (9)

[0123] Therefore, we obtain The output weight for each time period is

[0124] (10)

[0125] Through iteration, the first... Output weights corresponding to fragments The expression is

[0126] (11)

[0127] in, The online classification model for orbital angular momentum does not require retraining and has good data adaptability.

[0128] 5. Calculate new orbital angular momentum labels using an online prediction model for orbital angular momentum.

[0129] Input new spot sample Using the orbital angular momentum online classification model, the OAM spatial mode category label of the current light field intensity sample can be calculated. The specific expression is

[0130] (12)

[0131] in, , This enables online classification of orbital angular momentum.

[0132] The invention will be further illustrated with specific examples, such as... Figure 4 As shown, there are 480 training samples and 120 test samples, with each sample segment consisting of 20 samples. It can be seen that the classification accuracy of the OS-ELM method in this case is significantly higher than that of the SVM method, improving the online classification accuracy of orbital angular momentum. The online classification results of superposition state orbital angular momentum are shown below. Figure 5 As shown. Using a random turbulent optical transmission simulation model, the set of received light spot samples is obtained as follows: Figure 5 As shown in (a), the orbital angular momentum label of the currently received light spot sample is obtained by calculating the output expression through the online classification model of orbital angular momentum. Figure 5 As shown in (b), Online classification of orbital angular momentum was achieved.

Claims

1. An online classification method for orbital angular momentum of superposition states based on a stream computing framework, characterized in that, Includes the following steps: (1) A streaming computing framework was established, and real-time acquisition and calculation of orbital angular momentum (OAM) samples were realized through discretization of data streams; (2) A simulation model of random turbulence disturbance was established. By generating a multi-phase screen, the equivalent simulation of the beam in different transmission media such as the atmosphere and ocean was realized. The influence of random turbulence on the Laguerre-Gaussian beam was analyzed, and the received beam spot sample was obtained. ; (3) Using a data-driven modeling approach, an online classification model of orbital angular momentum based on sequence extreme learning machine was constructed. The input of the model is light spot samples. The model outputs orbital angular momentum space mode category labels. ; (4) The output weights are obtained by calculating the online classification model of orbital angular momentum. ; (5) Input a new spot sample Using an online classification model based on orbital angular momentum, the OAM spatial mode category label of the current light field intensity sample is calculated. This enables online classification of orbital angular momentum.

2. The online classification method for superposition state orbital angular momentum based on a stream computing framework according to claim 1, characterized in that, The convection computing framework in step (1) is as follows: The stream computing framework uses Spark technology and establishes an interaction mode between the client and the server. On the server side, the distributed file system HDFS is used for data storage. Users send data requests to the server through the client, and the server performs function calls in the background. In the Spark processing module, a series of data operations on the Resilient Distributed Dataset (RDD) are completed through transformation functions, and the entire module is executed through action functions to obtain classification results. The server returns the results to the client, completing the data response.

3. The online classification method for superposition state orbital angular momentum based on a stream computing framework according to claim 1, characterized in that, The establishment of the random turbulence disturbance simulation model in step (2) is as follows: By generating multiple phase screens, equivalent simulations of beam transmission through different media such as the atmosphere and ocean are achieved. Through fast Fourier transform, random turbulent phase screens can be obtained. Using multiple intermediate planes to form a phase screen sequence, the expression for the Laguerre-Gaussian LG beam passing through each phase screen layer is obtained: (1) in, and These represent the Fourier transform and the inverse Fourier transform, respectively. and These represent the light field intensity at the source and after propagation through a phase screen, respectively. Indicates the light field intensity at the receiving plane. Represents the imaginary unit. Represents the random turbulence transformation operator. The distance between each phase screen layer, , , , Representing coordinates, a Monte Carlo simulation is performed to obtain the light spot sample at the receiving end. By considering different topological charge numbers, we obtain the superposition state OAM mode.

4. The online classification method for superposition state orbital angular momentum based on a stream computing framework according to claim 1, characterized in that, The online classification model for orbital angular momentum in step (3) is as follows: A three-layer neural network structure consisting of an input layer, a hidden layer, and an output layer is constructed. The training process is divided into two stages: initial learning and online learning. In the initial learning phase, the input layer is There are 1 node, and the hidden layer is 1. There are 1 node in the output layer and 1 node in the spot sample. Orbital angular momentum space mode category tags Composition of sample data The mapping expression between the two is: (2) in, and These are the input weights and biases, respectively. To output weights, represent The One input parameter, represent The One output parameter, For the activation function, to further simplify the expression, the set of orbital angular momentum space mode category labels is represented as follows: The hidden layer random matrix is ​​represented as: (3) Therefore, the mapping expression can be simplified to a matrix form, as follows: (4) Output weights These are important parameters during the training phase, and can be computed using the Moore-Penrose generalized inverse, specifically represented as: (5) in, Hidden layer random matrix The generalized inverse of MP can be represented as ; During the online learning phase, the output weights are updated using an iterative optimization method. Time period sample fragment Upon arrival, the number of input layer nodes in the Extreme Learning Machine increases, and the objective function of the mapping expression becomes minimizing the approximation error of all current sample segments, expressed as: (6) in, and They represent Time-time hidden layer random matrix and orbital angular momentum space modal category label set.

5. The online classification method for superposition state orbital angular momentum based on a stream computing framework according to claim 1, characterized in that, In step (4), the output weights are calculated by optimizing the parameters of the online classification model of orbital angular momentum. : Considering the linear relationship between the hidden layer and the output layer, in Based on the network parameters over a time period, calculate Time period output weight expression: (7) Since matrix multiplication satisfies the associative law, we divide the whole into two parts for calculation and introduce... Intermediate variables in time period Output weights The first part of the expression can be simplified to obtain Intermediate variables in time period The expression is: (8) Consider output weights Expanding the latter part of the expression using the matrix multiplication principle, we get: (9) Therefore, we obtain The output weight for each time period is: (10) Through iteration, the first... Output weights corresponding to fragments The expression is: (11) in, The online classification model of orbital angular momentum does not require retraining and has good data adaptability.

6. The online classification method for superposition state orbital angular momentum based on a stream computing framework according to claim 1, characterized in that, The step (5) involves inputting a new light spot sample. Using an online classification model based on orbital angular momentum, the OAM spatial mode category label of the current light field intensity sample is calculated. The specific expression is: (12) in, , This enables online classification of orbital angular momentum.

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