OAM-FSOC system based on improved WF

Abstract

The invention provides an OAM-FSOC wavefront distortion pre-compensation system based on an improved Nesterov momentum and a WF method. According to the system, wavefront distortion is pre-compensated through a wavefront-sensor-free AO correction unit based on the Nesterov momentum of an adaptive momentum attenuation parameter and an improved WF algorithm based on amplitude measurement. An amplitude value of a coding diffraction pattern is detected in real time by using a far-field camera, a wavefront controller based on an optimization algorithm calculates a distortion phase brought by turbulence according to the coding diffraction pattern amplitude value acquired by a CCD, and a spatial light modulator is driven to load a phase mask conjugated with the turbulence distortion phase, so that an OAM light beam can be compensated in advance before emission. After distortion pre-correction is carried out through the wavefront sensor-free AO system, the performance of the OAM-FSOC system can be obviously improved.

Description

Technical Field

[0001] The present invention belongs to the field of wireless coherent optical communication and relates to an Orbital Angular Momentum Free-Space Optical Communication (OAM-FSOC) system based on a wavefront distortion correction method of an improved Nesterov momentum and Wirtinger Flow (WF) algorithm. Background Art

[0002] In recent years, our understanding of vortex beams has deepened, reaching new heights. Researchers have discovered the orthogonal nature of orbital angular momentum (OAM) of photons. Theoretically, OAM has an infinite number of mode combinations, which can greatly improve the channel capacity and spectral efficiency of optical communications. An orbital angular momentum free-space optical communication system uses vortex beams as the transmission beam. Therefore, orbital angular momentum free-space optical communication (OAM-FSO) systems can achieve wireless communication with high information capacity, high spectrum utilization, and high transmission confidentiality. However, vortex beams are inevitably affected by atmospheric turbulence during free-space transmission. Atmospheric turbulence often leads to reduced performance of OAM-FSOC systems, which is typically manifested as significant energy leakage of the vortex beam, a drop in the main mode power to an extremely low value, an increase in the power of adjacent modes, and inter-mode crosstalk. Adaptive optics (AO) technology has been introduced into OAM-FSO systems as an effective compensation method to suppress turbulent interference. Orbital Angular Momentum (OAM) beams, which have unique spiral phase structures and phase singularity characteristics, are difficult to accurately measure their phase information using traditional adaptive optics systems consisting of wavefront sensors, wavefront processors, and wavefront correctors. In contrast, the sensor-less adaptive optics (SLAO) system uses a CCD camera instead of a wavefront sensor to capture the distorted phase and applies an appropriate phase recovery algorithm to achieve optimal control, thereby completing the correction of the wavefront distortion.

[0003] To address these issues, the present invention proposes an OAM-FSOC system based on an improved Nesterov momentum and WF algorithm. This system utilizes a sensorless AO correction unit, using Nesterov momentum with an adaptive momentum decay parameter and an improved WF algorithm based on amplitude measurement, to achieve pre-compensation of wavefront distortion. This method effectively reduces the computational burden of the optimization controller, improves operational efficiency, and further enhances the convergence rate and convergence capability of the sensorless adaptive optical system. Summary of the Invention

[0004] This invention aims to address the challenges faced by traditional WF algorithms when correcting for atmospheric turbulence wavefront distortion in OAM optical beams. These algorithms rely on a large number of light field intensity measurements, resulting in slow iterations and a tendency to fall into local minima. By incorporating an improved Nesterov momentum technique into the traditional WF algorithm, this invention effectively improves the algorithm's convergence performance and correction effectiveness.

[0005] The technical solution of the present invention is:

[0006] A wavefront correction method based on improved Nesterov momentum and the WF algorithm was applied to an OAM-FSOC precompensation system with a SLAO system. The OAM-FSOC precompensation system primarily consists of a transmitter, a SLAO system, and a receiver. First, the receiver emits a Gaussian beacon beam, which propagates through free space in the presence of atmospheric turbulence before entering the transmitter. At the transmitter, the distorted probe beam passes through a programmable liquid crystal display (LCD) to generate a coded diffraction pattern (CDP). A CCD camera then records the intensity distribution and transmits the data to a computer for phase retrieval. Finally, the computer system outputs an atmospheric turbulence precompensation phase mask, which is loaded onto a spatial light modulator (SLM). Finally, the OAM beam passes through the SLM, carrying a conjugate distorted wavefront. After the precompensated OAM beam passes through atmospheric turbulence, the conjugate distorted wavefront counteracts the turbulence effect.

[0007] The detailed principles of the optimization algorithm of the Nesterov momentum based on adaptive momentum decay parameter and the improved WF algorithm based on amplitude measurement proposed in the present invention are as follows:

[0008] The traditional WF algorithm is used to solve non-convex problems in quadratic programming, namely:

[0009] y τ =|<a τ ,z>| 2,τ=1,2,3,...,m(1)

[0010] In the formula, is the decision variable, is a known sampling vector, It is the measured value obtained through observation. It is converted into the loss function form through the least squares method. This function is used to evaluate the difference between the predicted value and the true value. The loss function is zero if and only if y = x, so the solution to this non-convex problem is:

[0011]

[0012] That is, to find a solution z that minimizes f(z), but the function f is non-convex, so the solution that minimizes f(z) is often not unique. The WF algorithm uses two steps to find an approximate optimal solution that meets the conditions:

[0013] (1) Initialization is performed by spectral method, because for a specific random model, the initial value z0 is obtained by iterating the sequence {z τ} will eventually converge to the solution of the problem. First calculate the scaling constant λ, which is related to the observed value y τ and observation vector a τ Then we obtain the semi-positive Hermitian matrix constructed based on the observation vector and observation value: The eigenvector corresponding to the maximum eigenvalue of Use λ to Scaling is performed so that the initial estimate vector and the true solution are of the same order of magnitude, Then the vector z0 is the initial estimation vector.

[0014]

[0015] (2) Using a method similar to gradient descent, the initial vector z0 obtained in step (1) is used as input for iteration:

[0016]

[0017] During the iteration process, μ t+1 represents the iteration step size. Since the estimated vector gradually approaches the true solution during the iteration process, the initial iteration step size is usually selected to be small and gradually increased as the iteration progresses. To prevent the step size from being too large and thus failing to converge to the true solution, the iteration step size is fixed to a specific value after a certain number of iterations:

[0018]

[0019] A large number of studies have shown that the parameter t0 is 330, μ maxWhen the value is 0.4, the iteration process can proceed at the fastest speed.

[0020] When using the WF algorithm to solve the phase for compensating the wavefront distortion of the OAM beam, y τ represents the intensity information of the measured diffraction pattern, z represents the distortion phase information carried by the distorted probe beam, and a τ represents the coded pattern on the LCD, and <> represents the process of the distorted probe beam generating a diffraction pattern through the LCD.

[0021] In the initialization phase of the traditional WF algorithm, when the initial estimate z0 is obtained by the spectral method, the constructed matrix Y will be affected by the heavy-tailed probability distribution, which may make the initial estimate z0 too far away from the true solution. Therefore, in the improved algorithm, we use the median truncated orthogonal initialization that can make the initial estimate closer to the true solution. The orthogonal initialization is inspired by the orthogonality between high-dimensional random vectors, that is, the initial estimate z0 is required to be equal to the measurement vector a. τ The subsets of are highly orthogonal to each other, where I0 is an index set with a cardinality of |I0|<m. To prevent outliers from negatively affecting the initialization results, a truncation mechanism is introduced. When constructing the matrix Y, the selected measurement vector a τ Certain cutoff conditions {ψ τ ≤αλ}. This condition is intended to eliminate the influence of outliers. Here, α represents the preset parameter, λ = med(ψ) / 0.455, and med(·) represents the function used to calculate the median.

[0022] The main eigenvector z0 is obtained by the matrix Y in formula (7), where is the complement of I0, and then the main eigenvector is scaled z0=λz0, where the estimated norm λ is obtained according to formula (8).

[0023]

[0024] λ=med(ψ) / 0.455(8)

[0025] In the iterative stage, the quadratic loss function of the traditional WF algorithm is The establishment of is based on the intensity value of the diffraction pattern, that is, The fourth form of , requires a large number of observations in the calculation, which leads to higher storage data requirements and larger calculations. In order to reduce this cost, the amplitude value ψ based on the diffraction pattern is adopted. τ =| τ ,z>|,τ=1,2,3,...,m established new loss function ​While the new loss function sacrifices smoothness, it still exhibits significant statistical and computational advantages. With good initialization, the new loss function exhibits geometric properties similar to convex functions in the optimal solution region, enabling linear convergence when using gradient descent. In particular, its quadratic growth property in the optimal solution region makes the proposed momentum term feasible.

[0026] When dealing with large data problems, the gradient descent method has a slow iteration speed and is prone to falling into local extremes. Therefore, in the improved algorithm, Nesterov momentum is introduced into the WF algorithm to accelerate the iteration process. The WF algorithm only considers the current gradient information during the iteration process, but after introducing the momentum term, it considers both historical gradient information and current gradient information, and the gradient direction is corrected. The Nesterov Accelerated Gradient (NAG) algorithm proactively adds the gradient information of the intermediate points when updating the momentum. Compared with the general momentum acceleration algorithm, it can more efficiently correct the gradient direction, reduce the oscillation during the optimization process, and thus accelerate convergence. The core formula of the NAG algorithm is:

[0027]

[0028] The purpose of introducing the momentum term in the WF algorithm is to combine historical gradient information and correct the current gradient direction. However, since the influence of historical gradient information on the current gradient is constantly changing during the iteration process, the fixed momentum decay coefficient cannot reflect this change during the iteration process. Therefore, the momentum decay rate can be dynamically adjusted according to the difference between the current gradient and the historical gradient direction. The cosine similarity is used to measure the current gradient direction and the historical momentum:

[0029]

[0030] Among them G t is the gradient matrix of the midpoint, M t-1 is the historical momentum matrix, is the gradient matrix G of the midpoint t The conjugate transpose of . ||·|| F To find the Frobenius norm of a matrix.

[0031] When the cosine similarity is less than the threshold τ0 = 0.8, the midpoint gradient is too far away from the historical momentum direction, and the influence of historical momentum should be reduced. When the cosine similarity is greater than the threshold, the momentum attenuation parameter is increased. The update formula of the momentum parameter β is:

[0032]

[0033] Therefore, the process of obtaining the distortion phase of the probe beam by the improved WF algorithm is as follows:

[0034] (1) Initial estimate is obtained by median truncated orthogonal initialization:

[0035]

[0036] (2) The final solution z is obtained by the gradient descent algorithm of Nesterov momentum with adaptive momentum decay parameter:

[0037] y t+1 =z t +β t (z t+1 -z t )

[0038]

[0039] BRIEF DESCRIPTION OF THE DRAWINGS

[0040] In order to make the purpose, technical solutions and beneficial effects of the present invention more clear, the present invention provides the following drawings for illustration:

[0041] Figure 1 Block diagram of the OAM-FSOC system with an adaptive optics system without a wavefront sensor.

[0042] Figure 2 Iterative flowchart for improving the WF algorithm.

[0043] Figure 3 Light intensity distribution diagram of OAM beams with different modal values before and after compensation.

[0044] Figure 4 Phase distribution diagram of OAM beams with different modal values before and after compensation.

[0045] Figure 5 Mode purity ratio of the OAM beam with modal value l = 3 before and after compensation.

[0046] Figure 6 RMSE changes with the number of iterations under different algorithm compensations. DETAILED DESCRIPTION

[0047] In order to make the technical solutions, advantages and purposes of the present invention more clear, the present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0048] like Figure 1As shown, the OAM-FSOC pre-compensation system with a SLAO system of the present invention includes a transmitting and receiving module. The transmitting module includes a laser, a modulator, and a turbulence screen generation module. In the present invention, the modulation module uses binary phase shift keying (BPSK) to modulate the signal onto a laser carrier to obtain a modulated vortex beam signal. The modulated optical signal passes through a spatial light modulator and carries a wavefront conjugated with atmospheric turbulence distortion. The turbulence screen generation module is derived using the power spectrum inversion method based on Kolmogorov turbulence statistics theory. The SLAO system includes a programmable LCD device, a CCD camera, a spatial light modulator, and a control module based on an improved Nesterov momentum and WF algorithm. The control module uses a new algorithm to calculate the distorted wavefront generated by a Gaussian beam after passing through atmospheric turbulence, and generates a phase mask conjugated with the distorted wavefront, which is loaded onto the spatial light modulator. The receiving module transmits a Gaussian beacon beam, which transmits turbulence distortion information to the transmitter after passing through atmospheric turbulence. After the pre-compensated vortex beam passes through atmospheric turbulence, the conjugate distorted wavefront and the turbulence effect are offset, mixed by a local oscillator, then demodulated by a photodetector and demodulator, and finally processed by DSP to obtain the actual signal.

[0049] In the OAM beam correction system, the beam quality can be evaluated using the root mean square error (RMSE) of the corrected light intensity distribution and the mode purity (MP). The smaller the RMSE value and the larger the mode purity, the better the beam quality.

[0050]

[0051] Among them, u0 represents the intensity distribution of the light field without atmospheric turbulence distortion, u τ represents the intensity distribution of the conjugate distortion compensated light field obtained after τ iterations.

[0052] The mode purity (MP) of an OAM beam is an important metric that measures the energy contribution of the target mode within the beam. It is typically calculated by decomposing the optical field into orthogonal fundamental modes. First, the inner product of the optical field to be measured is performed with each fundamental mode to obtain the corresponding projection coefficients. The power of each mode and the total power of all modes are then calculated. Ultimately, the mode purity (MP) is defined as the ratio of the target mode power to the sum of the total mode powers.

[0053]

[0054] In the present invention, the relevant parameters are set:

[0055] First, assuming that the light beam is distorted when passing through the turbulent phase screen, in the numerical simulation, the modified Von Karman spectrum is used to generate the phase screen through the power spectrum inversion method. In the case that the phase screen lacks low-frequency components, the subharmonic compensation method is adopted to compensate for the low-frequency components.

[0056] To correct the turbulence distortion, the OAM beam is pre-compensated by passing it through a spatial light modulator (SLM) loaded with a phase mask that is conjugate to the turbulence distortion.

[0057] We first verified the correction performance of the improved WF algorithm for the wavefront distortion of OAM beams with different modal values. Figure 3 As shown in the figure, after the new algorithm is used to compensate for a single-mode OAM beam, the intensity distribution takes on a uniform circular shape, with most of the energy concentrated in the ring, effectively improving the intensity distribution. Although the ring gradually increases with increasing modal value, the distorted OAM beam intensity information can still be corrected, demonstrating that the new algorithm is well suited for OAM beams with different modal values and has good stability. For multiplexed OAM beams, after several energy comparisons using the new algorithm, the intensity distribution takes on a uniform petal shape, and the distorted multiplexed beam is also well corrected.

[0058] exist Under the condition of terrestrial atmospheric turbulence, the phase distribution diagram of OAM beams with different modal values before and after compensation by the new algorithm is shown as follows: Figure 4 As shown in Figure 2, for OAM beams with different modes l = 3 and l = 5, the new algorithm effectively corrects the distorted wavefront phase, resulting in a uniform phase distribution and clear isophase lines. When OAM beams of different modes are multiplexed, the distorted phase can also be corrected. The multiplexed OAM beam with l = -3,3 exhibits a pattern of intersecting light and dark after correction using the new algorithm.

[0059] Then, the OAM mode l=3 is taken as an example to illustrate the crosstalk suppression effect of the new algorithm in the case of single-channel communication. Figure 5 The mode purity of the OAM beam corrected by the new algorithm is shown, and the atmospheric structure constants are: Before the algorithm was used for compensation, the distorted OAM beam experienced severe crosstalk, resulting in low mode purity in the primary mode and diffusion into adjacent modes. After the new algorithm was used for compensation, the mode purity of the primary mode was significantly improved, reaching a normalized mode purity value exceeding 0.9. The proportion of adjacent modes was minimal, effectively suppressing inter-mode crosstalk.

[0060] In order to demonstrate the superiority of the proposed new algorithm, the RMSE under different algorithm compensations is compared and analyzed. RMSE can intuitively represent the convergence accuracy during the iterative process. Figure 6As shown in the figure, the GS algorithm converges quickly, but its convergence accuracy is limited. Compared with the GS algorithm, the traditional WF algorithm and the improved WF algorithm converge slowly at the beginning, but then converge rapidly, and their convergence accuracy is significantly higher than that of the GS algorithm. The improved WF algorithm converges significantly faster than the traditional WF algorithm.

[0061] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person familiar with the technology can understand and think of any changes or replacements within the technical scope disclosed by the present invention, which should be included in the scope of the present invention.

Claims

1. An OAM-FSOC system based on improved WF, characterized by: The system primarily comprises a transmitter, a receiver, and a sensorless AO correction unit. The transmitter includes a spatial light modulator (SLM), a modulator, and a laser; the sensorless AO correction unit includes a programmable LCD (LCD), a far-field camera (CCD), and a computer system for running an improved WF algorithm; and the receiver includes a laser, a local oscillator (LO), a photodetector, a demodulator, and a digital signal processor (DSP). First, the receiver transmits a probe beam through free space in the presence of atmospheric turbulence before entering the transmitter. At the transmitter, the distorted probe beam passes through the programmable LCD to simulate a coded diffraction pattern (CDP). The CCD camera captures the intensity information and transmits it to a computer for calculation using the improved algorithm. Finally, the computer system outputs an atmospheric turbulence pre-compensation phase mask, which is loaded onto the SLM. Finally, the OAM beam passes through the SLM, carrying a conjugate distorted wavefront. After the pre-compensated OAM beam passes through atmospheric turbulence, the conjugate distorted wavefront offsets the turbulence effect.

2. The improved WF algorithm according to claim 1, characterized in that: The following steps are involved: Step 1: The operation process of the traditional WF algorithm is as follows First, according to the intensity information y of the diffraction pattern obtained by measurement τ and the coding pattern a on the LCD τ A minimum quadratic loss function based on the diffraction pattern intensity is constructed, where z is the distorted phase information carried by the distorted probe beam that needs to be calculated. y τ =|<a τ ,z>| 2 ,τ=1,2,3,...,m (1) l(x,y)=(yx) 2 (2) Then, an initial solution close to the true solution for iterative operation is obtained by initialization through the spectral method, that is, the scaling constant λ is calculated, and the eigenvector corresponding to the maximum eigenvalue of the semi-positive definite matrix Y is Finally, the initial solution z0 for iteration is obtained. Finally, the final solution is obtained by iterative calculation using a gradient descent method, that is, the calculated distortion phase caused by atmospheric turbulence, where μ t+1 Represents the iteration step size. Step 2: Since the minimum quadratic loss function constructed based on the diffraction pattern intensity value requires a large number of measurement samples, resulting in excessive computational and storage burdens, it is improved to construct the amplitude information ψ based on the diffraction pattern τ The minimum quadratic loss function is obtained, and the quadratic growth property of the new loss function in the neighborhood of the optimal solution lays the foundation for introducing the momentum term to accelerate iteration. ψ τ =| τ ,z>|,τ=1,2,3,...,m (8)​ Step 3: Since the initial solution obtained by spectral initialization is affected by outliers in the measurement sample, resulting in insufficient accuracy of the initialization result, an improved orthogonal initialization method based on median truncation is used, where λ = med(ψ) / 0.455, med(·) is the function for calculating the median, and α is a preset parameter. To satisfy the truncation condition ψ τ The set of coding patterns with ≤αλ. Step 4: Since the gradient descent method has the problem of slow iteration speed and easy to fall into the local optimal solution, it is improved to the gradient descent method based on Nesterov momentum with adaptive attenuation parameter to accelerate the iteration process and improve the iteration accuracy.

3. The probe beam according to claim 1, characterized in that The probe beam used is a Gaussian beam.

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