FPGA-based laser coherent synthesis SPGD algorithm voltage tuning method and system
By constructing a hyperplane H and a rotation matrix W, the problem of limited output voltage range of the DA module was solved, and the stability and convergence of the multi-beam coherent combining system were improved.
Patent Information
- Application Number
- CN202511909650.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-17
- Publication Date
- 2026-03-24
AI Technical Summary
In the prior art, the output voltage range of the DA module is limited by hardware, resulting in no range constraint on voltage iteration, which easily exceeds the range, causing instantaneous phase fluctuations and light intensity fluctuations in the phase modulator, affecting the stability of multi-beam coherent synthesis.
A positive interactive complement space is constructed between the hyperplane H and the voltage increment of each channel. The initial voltage vector is projected onto the hyperplane through the rotation matrix W to generate a parallel perturbation voltage vector. This ensures that the perturbation and update process is carried out within the hyperplane, avoiding the voltage from exceeding the range of the DA module.
It improves the stability and convergence speed of the multi-beam coherent combining system, reduces the probability of voltage exceeding the range of the DA module, and enhances the stability of phase locking and coherent combining.
Smart Images
Figure CN121722202A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to active phase control technology in the field of fiber laser coherent combining, specifically to a voltage optimization method and system for the SPGD algorithm of laser coherent combining based on FPGA. Background Technology
[0002] In the field of fiber laser coherent combining, active phase control technology is the core for achieving efficient coherent combining of multiple beams. Among them, the multi-channel phase control technology based on the Stochastic Parallel Gradient Descent (SPGD) algorithm using a Field Programmable Gate Array (FPGA) is widely used. This technology uses an FPGA as the hardware carrier of the SPGD algorithm. The FPGA outputs an analog voltage to drive the phase modulator, changing the phase of each laser channel. Simultaneously, a photodetector is used to collect the far-field coherent combined light intensity as the evaluation function of the SPGD algorithm. Through closed-loop iterative optimization, the driving voltage of each channel is optimized, ultimately achieving phase locking and coherent combining of multiple laser channels.
[0003] The implementation process of the existing technology is as follows: In the initialization stage, the FPGA configures the parameters such as the gain coefficient, perturbation amplitude, and extreme value of the evaluation function of the SPGD algorithm. The digital-to-analog converter (DA) module outputs the initial voltage, and the phase modulator of each channel is in the initial phase state. In the iterative optimization stage, the SPGD module of the FPGA applies random parallel perturbation to the voltage of each channel to generate positive and negative perturbation voltage vectors. After being output to the phase modulator by the DA module, the photodetector collects the corresponding far-field light intensity, calculates the change in the evaluation function, and then updates the voltage of each channel.
[0004] However, existing technologies have significant drawbacks: On the one hand, the output voltage range of the DA module is limited to a fixed value by hardware and needs to be matched with the half-wave voltage of the phase modulator to achieve 0~2π phase control. However, the voltage iteration of the SPGD algorithm has no range constraint guidance and the disturbance vector is randomly generated. When the number of channels increases or the phase noise is large, the voltage is prone to shift towards the boundary of the DA range, and the probability of exceeding the range is high. On the other hand, when the channel voltage exceeds the range, the existing technology uses the half-wave voltage compensation method, which causes the channel voltage to jump significantly. Because the phase-voltage characteristics of the phase modulator have a slight nonlinearity, the drastic voltage jump will cause instantaneous phase fluctuations in a single channel, resulting in glitches in the far-field coherent synthesized light intensity. Moreover, the asynchronous voltage jumps of multiple channels will further aggravate the light intensity fluctuations and even cause short-term phase lock-up, which seriously affects the stability of the synthesized energy. Summary of the Invention
[0005] In view of this, the present invention proposes a voltage optimization method for the laser coherent synthesis SPGD algorithm based on FPGA to solve the above problems.
[0006] Includes the following steps: S1: Construct a hyperplane H, which is positively complementary to the vector space with equal voltage increments for each channel, and the hyperplane H passes through the origin of the coordinate system. n is the number of channels, and n≥1. S2: Construct the rotation matrix W; S3: Based on the rotation matrix W, the initial voltage vector Projecting onto the hyperplane H, we obtain the voltage vector U' within the hyperplane; S4: Apply random parallel perturbation to the voltage vector U' within the hyperplane H to generate a positive perturbation voltage vector U'. + and negative disturbance voltage vector U' - , Among them U' + =U'+ΔU',U' - =U'-ΔU', where ΔU' is the perturbation vector; S5: The positive disturbance voltage vector U' + and the negative disturbance voltage vector U' - Restored to the initial voltage vector space, the positive output voltage vector U is obtained. + and negative output voltage vector U - ; S6: Calculate the change in the evaluation function based on the far-field light intensity corresponding to the output voltage vector, and update the voltage vector in the hyperplane based on the change in the evaluation function; S7: Repeat steps S3-S6 until the multichannel laser coherent synthesis converges.
[0007] Furthermore, in step S1, the construction process of the hyperplane H includes: S11: Define the vector with equal voltage increments in each channel as the first vector a. The hyperplane H is perpendicular to the first vector a. It is an n-dimensional real vector space; S12: Definition ,in For any point on the hyperplane H, expand the dot product. The hyperplane H perpendicular to a and passing through the origin is denoted as .
[0008] Furthermore, in step S2, constructing the rotation matrix W includes: Construct an n×n rotation matrix W, wherein the column vectors of the rotation matrix W are... constitute A set of orthonormal bases.
[0009] Furthermore, the column vectors of the rotation matrix W satisfy: The first column vector w1 is a preset unit uniform vector. , the remaining column vectors are unit vectors that are orthogonal to both u and each other; For any 1 ≤ i < j ≤ n, orthogonality is satisfied, ; For any 1 ≤ k ≤ n, unitarity is satisfied, ; .
[0010] Furthermore, the construction process of the i-th column vector w i (i ≥ 2) in the rotation matrix W includes: S21: Randomly sample a vector from an n-dimensional standard normal distribution ; S22: Subtract all projection components of on the constructed basis vectors to obtain an orthogonal residual vector, ensuring is orthogonal to all previous basis vectors; S23: Normalize the orthogonal residual vector to obtain the i-th orthonormal basis vector.
[0011] Furthermore, in step S3, multiply the initial voltage vector U by the rotation matrix W to obtain an intermediate vector, and set the first-dimensional component of the intermediate vector to 0 to obtain the voltage vector within the hyperplane.
[0012] Furthermore, in step S4, the perturbation amplitude of the random parallel perturbation is a preset perturbation amplitude, the vector size of the perturbation vector ΔU' is the same as that of U', and the first-dimensional component is 0.
[0013] Furthermore, in step S5, multiply the positive perturbation voltage vector U' + and the negative perturbation voltage vector U' - by the transpose matrix W T of the rotation matrix W respectively to obtain the positive output voltage vector U + and the negative output voltage vector U - .
[0014] Furthermore, step S6 includes collecting the positive far-field light intensity J + corresponding to the positive output voltage vector U + and the negative far-field light intensity J - corresponding to the negative output voltage vector U - , calculating the change in the evaluation function δJ = J + - J - , and updating the voltage vector U' within the hyperplane based on the change in the evaluation function δJ.
[0015] Accordingly, this invention also discloses a voltage optimization system for the laser coherent synthesis SPGD algorithm based on FPGA, used to implement the above method, including: A hyperplane and rotation matrix construction module is used to construct a hyperplane and a rotation matrix, wherein the hyperplane is positively complementary to the vector space with equal voltage increments for each channel, and the hyperplane passes through the origin of the coordinate system. The projection module is used to project the initial voltage vector onto the hyperplane based on the rotation matrix to obtain the voltage vector in the hyperplane; The perturbation module is used to apply random parallel perturbations to the voltage vector in the hyperplane, generating positive perturbation voltage vectors and negative perturbation voltage vectors. The restoration module is used to restore the positive disturbance voltage vector and the negative disturbance voltage vector to the initial voltage vector space to obtain the output voltage vector; The light intensity acquisition and calculation module is used to acquire the far-field light intensity corresponding to the output voltage vector and calculate the change in the evaluation function. The update module is used to update the voltage vector in the hyperplane based on the change in the evaluation function; The iterative control module is used to control the projection module, disturbance module, restoration module, light intensity acquisition and calculation module, and update module to work repeatedly until the multi-channel laser coherent synthesis converges.
[0016] The hyperplane H constructed in this invention serves as the orthogonal complement space for the synchronous phase offset components of each channel. Projecting the initial voltage vector onto the hyperplane eliminates the synchronous phase offset components that cause voltage shifts towards the DA range boundary, retaining only the voltage changes corresponding to the relative phase differences between channels. Simultaneously, the perturbation and update processes of the SPGD algorithm are performed within the hyperplane, avoiding invalid voltage vector shifts and fundamentally reducing the probability of voltage exceeding the fixed output range of the DA module. This is particularly suitable for scenarios with a large number of channels or high phase noise. Furthermore, the perturbation vector within the hyperplane more closely aligns with the phase optimization direction, making the iterative updates of the SPGD algorithm more targeted and improving convergence stability. It also avoids multi-channel phase mismatch caused by frequent compensation, thereby improving the overall operational stability of the multi-beam coherent combining system. Attached Figure Description
[0017] Figure 1 This is a flowchart of a voltage optimization method for a laser coherent synthesis SPGD algorithm based on FPGA according to the present invention; Figure 2 This is a diagram of the voltage optimization system for laser coherent synthesis SPGD algorithm based on FPGA according to the present invention. Detailed Implementation
[0018] In the field of fiber laser coherent combining, active phase control technology is the core for achieving efficient coherent combining of multiple beams. Among them, the multi-channel phase control technology based on the Stochastic Parallel Gradient Descent (SPGD) algorithm using a Field Programmable Gate Array (FPGA) is widely used. This technology uses an FPGA as the hardware carrier of the SPGD algorithm. The FPGA outputs an analog voltage to drive the phase modulator, changing the phase of each laser channel. Simultaneously, a photodetector is used to collect the far-field coherent combined light intensity as the evaluation function of the SPGD algorithm. Through closed-loop iterative optimization, the driving voltage of each channel is optimized, ultimately achieving phase locking and coherent combining of multiple laser channels.
[0019] The implementation process of the existing technology is as follows: In the initialization stage, the FPGA configures the parameters such as the gain coefficient, perturbation amplitude, and extreme value of the evaluation function of the SPGD algorithm. The digital-to-analog converter (DA) module outputs the initial voltage, and the phase modulator of each channel is in the initial phase state. In the iterative optimization stage, the SPGD module of the FPGA applies random parallel perturbation to the voltage of each channel to generate positive and negative perturbation voltage vectors. After being output to the phase modulator by the DA module, the photodetector collects the corresponding far-field light intensity, calculates the change in the evaluation function, and then updates the voltage of each channel.
[0020] However, existing technologies have significant drawbacks: On the one hand, the output voltage range of the DA module is limited to a fixed value by hardware and needs to be matched with the half-wave voltage of the phase modulator to achieve 0~2π phase control. However, the voltage iteration of the SPGD algorithm has no range constraint guidance and the disturbance vector is randomly generated. When the number of channels increases or the phase noise is large, the voltage is prone to shift towards the boundary of the DA range, and the probability of exceeding the range is high. On the other hand, when the channel voltage exceeds the range, the existing technology uses the half-wave voltage compensation method, which causes the channel voltage to jump significantly. Because the phase-voltage characteristics of the phase modulator have a slight nonlinearity, the drastic voltage jump will cause instantaneous phase fluctuations in a single channel, resulting in glitches in the far-field coherent synthesized light intensity. Moreover, the asynchronous voltage jumps of multiple channels will further aggravate the light intensity fluctuations and even cause short-term phase lock-up, which seriously affects the stability of the synthesized energy.
[0021] In view of this, the present invention proposes a voltage optimization method and system for laser coherent synthesis SPGD algorithm based on FPGA to solve the above problems.
[0022] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the various embodiments of this application will be described in detail below with reference to the accompanying drawings. However, those skilled in the art will understand that many technical details have been presented in the various embodiments of this application to enable the reader to better understand this application. However, the technical solutions claimed in this application can be implemented even without these technical details and various changes and modifications based on the following embodiments.
[0023] In the following description, certain specific details are set forth for the purpose of illustrating various disclosed embodiments in order to provide a thorough understanding of the various disclosed embodiments. However, those skilled in the art will recognize that embodiments may be practiced without one or more of these specific details. In other instances, well-known apparatuses, structures, and techniques associated with this application may not have been shown or described in detail to avoid unnecessarily obscuring the description of the embodiments.
[0024] Unless the context requires otherwise, throughout the specification and claims, the word “comprising” and its variations, such as “including” and “having”, shall be understood to have an open, inclusive meaning, that is, to be interpreted as “including, but not limited to”.
[0025] The embodiments of this application will be described in detail below with reference to the accompanying drawings to provide a clearer understanding of the purpose, features, and advantages of this application. It should be understood that the embodiments shown in the drawings are not intended to limit the scope of this application, but are merely for illustrating the essential spirit of the technical solution of this application.
[0026] Throughout this specification, references to "an embodiment" or "an embodiment" indicate that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment. Therefore, the appearance of "in an embodiment" or "an embodiment" in various places throughout the specification does not necessarily refer to the same embodiment. Furthermore, a particular feature, structure, or characteristic may be combined in any manner in one or more embodiments.
[0027] like Figure 1 As shown, a voltage optimization method for the laser coherent synthesis SPGD algorithm based on FPGA includes the following steps: S1: Construct a hyperplane H, which is positively complementary to the vector space with equal voltage increments for each channel, and the hyperplane H passes through the origin of the coordinate system. n is the number of channels, and n≥1. S2: Construct the rotation matrix W; S3: Project the initial voltage vector U onto the hyperplane H based on the rotation matrix W to obtain the voltage vector U' in the hyperplane; S4: Apply random parallel perturbation to the voltage vector U' within the hyperplane H to generate a positive perturbation voltage vector U'. + and negative disturbance voltage vector U' - , Among them U' + =U'+ΔU',U' - =U'-ΔU', where ΔU' is the perturbation vector; S5: The positive disturbance voltage vector U' + and the negative disturbance voltage vector U' -Restored to the initial voltage vector space, the positive output voltage vector U is obtained. + and negative output voltage vector U - ; S6: Calculate the change in the evaluation function based on the far-field light intensity corresponding to the output voltage vector, and update the voltage vector in the hyperplane based on the change in the evaluation function; S7: Repeat steps S3-S6 until the multichannel laser coherent synthesis converges.
[0028] In the above, FPGA: Field Programmable Gate Array, a hardware platform with high-speed parallel processing capabilities, which can be used to implement algorithm logic and data processing.
[0029] SPGD algorithm: Stochastic Parallel Gradient Descent algorithm, an iterative algorithm for multi-channel optimization control, which achieves target optimization by applying random perturbations and updating the control quantity based on feedback from the evaluation function.
[0030] Coherent combining: refers to the technique of achieving phase consistency of multiple laser beams through phase control, thereby forming a high-intensity combined light field in the far field.
[0031] The hyperplane H constructed in this invention serves as the orthogonal complement space for the synchronous phase offset components of each channel. Projecting the initial voltage vector onto the hyperplane eliminates the synchronous phase offset components that cause voltage shifts towards the DA range boundary, retaining only the voltage changes corresponding to the relative phase differences between channels. Simultaneously, the perturbation and update processes of the SPGD algorithm are performed within the hyperplane, avoiding invalid voltage vector shifts and fundamentally reducing the probability of voltage exceeding the fixed output range of the DA module. This is particularly suitable for scenarios with a large number of channels or high phase noise. Furthermore, the perturbation vector within the hyperplane more closely aligns with the phase optimization direction, making the iterative updates of the SPGD algorithm more targeted and improving convergence stability. It also avoids multi-channel phase mismatch caused by frequent compensation, thereby improving the overall operational stability of the multi-beam coherent combining system.
[0032] In step S1, the construction process of the hyperplane H includes: S11: Define the vector with equal voltage increments in each channel as the first vector a. The hyperplane H is perpendicular to the first vector a. It is an n-dimensional real vector space; S12: Definition ,in For any point on the hyperplane H, expand the dot product. The hyperplane H perpendicular to a and passing through the origin is denoted as .
[0033] In step S2, constructing the rotation matrix W includes: Construct an \(n\times n\) rotation matrix \(W\), where the column vectors of the rotation matrix \(W\) form an orthonormal basis.
[0034] Furthermore, the column vectors of the rotation matrix \(W\) satisfy: The first column vector \(w_1\) is a preset unit uniform vector , and the remaining column vectors are unit vectors that are orthogonal to \(u\) and to each other; For any \(1\leq i < j\leq n\), orthogonality is satisfied, ; For any \(1\leq k\leq n\), unity is satisfied, ; .
[0035] During the conversion of the voltage vector between the hyperplane space and the initial space, only the synchronous phase offset component is eliminated, and the numerical relationship of the relative phase difference between channels is not changed; meanwhile, the characteristics of the standardized column vectors facilitate the implementation of efficient matrix operation logic in the FPGA.
[0036] Furthermore, the construction process of the \(i\)-th column vector \(w\) i (\(i\geq2\)) in the rotation matrix \(W\) includes: S21: Randomly sample a vector from an \(n -\)dimensional standard normal distribution; S22: Subtract all projection components of on the already constructed basis vectors to obtain an orthogonal residual vector, ensuring that is orthogonal to all previous basis vectors; S23: Normalize the orthogonal residual vector to obtain the \(i\)-th orthonormal basis vector.
[0037] By means of the process of random sampling - orthogonalization - normalization, basis vectors satisfying orthogonality and unity are generated, which are suitable for scenarios with different numbers of channels; and by sampling the initial vector based on the standard normal distribution, the randomness and uniformity of the basis vectors are ensured, avoiding the problem of unbalanced hyperplane constraints caused by the deviation of the basis vector distribution, and improving the generality and reliability of the rotation matrix. ]
[0038] Furthermore, in step S3, it includes multiplying the initial voltage vector \(U\) by the rotation matrix \(W\) to obtain an intermediate vector, and setting the first - dimension component of the intermediate vector to 0 to obtain the voltage vector within the hyperplane .
[0039] Furthermore, in step S4, the perturbation amplitude of the random parallel perturbation is a preset perturbation amplitude, the vector magnitude of the perturbation vector ΔU' is the same as that of U', and the first dimension component is 0.
[0040] The first dimension component of the perturbation vector is zero, which avoids the reintroduction of synchronous phase shift during the perturbation process, ensures that the constraint effect of the hyperplane remains effective, and improves the perturbation iteration's targeting and stability.
[0041] Furthermore, in step S5, the positive disturbance voltage vector U' + and negative disturbance voltage vector U' - The transpose of the rotation matrix W is respectively... T Multiplying them together yields the positive output voltage vector U. + and negative output voltage vector U - .
[0042] This ensures that the restoration process is the inverse operation of the projection process, without losing or distorting the relative phase difference information; and that matrix multiplication operations can be quickly implemented in FPGA through hardware logic, meeting the real-time requirements of coherent synthesis systems and improving the engineering practicality of the method.
[0043] Furthermore, step S6 includes acquiring the positive output voltage vector U. + The corresponding positive far-field light intensity J + With the negative output voltage vector U - The corresponding negative far-field light intensity J - Calculate the change in the evaluation function δJ=J + -J - The voltage vector U' in the hyperplane is updated based on the change δJ of the evaluation function.
[0044] By collecting the far-field light intensity corresponding to the positive and negative output voltage vectors, the difference between the two is calculated as the change in the evaluation function, reflecting the impact of the disturbance on the coherent synthesis effect and providing a reliable basis for voltage updates. Based on this change, the voltage vector in the hyperplane is directly updated to ensure that the update direction is consistent with the optimization objective, avoid invalid updates, and improve the convergence speed and optimization accuracy of the SPGD algorithm.
[0045] Accordingly, this invention proposes a voltage optimization system for the laser coherent synthesis SPGD algorithm based on FPGA, such as... Figure 2 As shown, it includes: A hyperplane and rotation matrix construction module is used to construct a hyperplane and a rotation matrix, wherein the hyperplane is positively complementary to the vector space with equal voltage increments for each channel, and the hyperplane passes through the origin of the coordinate system. The projection module is used to project the initial voltage vector onto the hyperplane based on the rotation matrix to obtain the voltage vector in the hyperplane; The perturbation module is used to apply random parallel perturbations to the voltage vector in the hyperplane, generating positive perturbation voltage vectors and negative perturbation voltage vectors. The restoration module is used to restore the positive disturbance voltage vector and the negative disturbance voltage vector to the initial voltage vector space to obtain the output voltage vector; The light intensity acquisition and calculation module is used to acquire the far-field light intensity corresponding to the output voltage vector and calculate the change in the evaluation function. The update module is used to update the voltage vector in the hyperplane based on the change in the evaluation function; The iterative control module is used to control the projection module, disturbance module, restoration module, light intensity acquisition and calculation module, and update module to work repeatedly until the multi-channel laser coherent synthesis converges.
[0046] The solutions provided by the embodiments of this application have been described in detail above. The various embodiments in the specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to in the method section. It should be noted that those skilled in the art can make several improvements and modifications to this application without departing from the principles of this application, and these improvements and modifications also fall within the protection scope of the claims of this application.
[0047] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.
[0048] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein can be implemented directly by hardware, a software module executed by a processor, or a combination of both. The software module can be located in random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium known in the art.
Claims
1. A voltage optimization method for a laser coherent synthesis SPGD algorithm based on FPGA, characterized in that, Includes the following steps: S1: Construct a hyperplane H, which is positively complementary to the vector space with equal voltage increments for each channel, and the hyperplane H passes through the origin of the coordinate system. n is the number of channels, and n≥1. S2: Construct the rotation matrix W; S3: Based on the rotation matrix W, the initial voltage vector Projecting onto the hyperplane H, we obtain the voltage vector U' within the hyperplane; S4: Apply random parallel perturbation to the voltage vector U' within the hyperplane H to generate a positive perturbation voltage vector U'. + and negative disturbance voltage vector U' - , Among them U' + =U'+ΔU',U' - =U'-ΔU', where ΔU' is the perturbation vector; S5: The positive disturbance voltage vector U' + and the negative disturbance voltage vector U' - Restored to the initial voltage vector space, the positive output voltage vector U is obtained. + and negative output voltage vector U - ; S6: Calculate the change in the evaluation function based on the far-field light intensity corresponding to the output voltage vector, and update the voltage vector in the hyperplane based on the change in the evaluation function; S7: Repeat steps S3-S6 until the multichannel laser coherent synthesis converges.
2. The voltage optimization method for the FPGA-based laser coherent synthesis SPGD algorithm according to claim 1, characterized in that, In step S1, the construction process of the hyperplane H includes: S11: Define the vector with equal voltage increments in each channel as the first vector a. The hyperplane H is perpendicular to the first vector a. It is an n-dimensional real vector space; S12: Definition ,in For any point on the hyperplane H, expand the dot product. The hyperplane H perpendicular to a and passing through the origin is denoted as .
3. The voltage optimization method for the FPGA-based laser coherent synthesis SPGD algorithm according to claim 2, characterized in that, In step S2, constructing the rotation matrix W includes: Construct an n×n rotation matrix W, wherein the column vectors of the rotation matrix W are... constitute A set of orthonormal bases.
4. The voltage optimization method for the FPGA-based laser coherent synthesis SPGD algorithm according to claim 3, characterized in that, The column vectors of the rotation matrix W satisfy: The first column vector w1 is a preset unit uniform vector. The remaining column vectors are unit vectors that are orthogonal to u and to each other; For any 1 ≤ i < j ≤ n, orthogonality is satisfied, ; For any 1≤k≤n, the unit property is satisfied. ; 。 5. The voltage optimization method for the FPGA-based laser coherent synthesis SPGD algorithm according to claim 4, characterized in that, The i-th column vector w in the rotation matrix W i The construction process for (i≥2) includes: S21: Randomly sample a vector from an n-dimensional standard normal distribution. ; S22: From Subtract its value from the constructed basis vectors All projected components on the surface are used to obtain orthogonal residual vectors, ensuring Orthogonal to all previous basis vectors; S23: Normalize the orthogonal residual vector to obtain the i-th orthogonal basis vector.
6. The voltage optimization method for the FPGA-based laser coherent synthesis SPGD algorithm according to claim 1, characterized in that, Step S3 includes multiplying the initial voltage vector U by the rotation matrix W to obtain an intermediate vector, and setting the first dimension component of the intermediate vector to 0 to obtain the voltage vector in the hyperplane. .
7. The voltage optimization method for the FPGA-based laser coherent synthesis SPGD algorithm according to claim 1, characterized in that, In step S4, the perturbation amplitude of the random parallel perturbation is a preset perturbation amplitude, the vector magnitude of the perturbation vector ΔU' is the same as that of U', and the first dimension component is 0.
8. The voltage optimization method for the FPGA-based laser coherent synthesis SPGD algorithm according to claim 1, characterized in that, In step S5, the positive disturbance voltage vector U' + and negative disturbance voltage vector U' - The transpose of the rotation matrix W is respectively... T Multiplying them together yields the positive output voltage vector U. + and negative output voltage vector U - .
9. The voltage optimization method for the FPGA-based laser coherent synthesis SPGD algorithm according to claim 1, characterized in that, Step S6 includes acquiring the positive output voltage vector U. + The corresponding positive far-field light intensity J + With the negative output voltage vector U - The corresponding negative far-field light intensity J - Calculate the change in the evaluation function δJ=J + -J - The voltage vector U' in the hyperplane is updated based on the change δJ of the evaluation function.
10. A voltage tuning system for a laser coherent synthesis SPGD algorithm based on FPGA, characterized in that, include: A hyperplane and rotation matrix construction module is used to construct a hyperplane and a rotation matrix, wherein the hyperplane is positively complementary to the vector space with equal voltage increments for each channel, and the hyperplane passes through the origin of the coordinate system. The projection module is used to project the initial voltage vector onto the hyperplane based on the rotation matrix to obtain the voltage vector in the hyperplane; The perturbation module is used to apply random parallel perturbations to the voltage vector in the hyperplane, generating positive perturbation voltage vectors and negative perturbation voltage vectors. The restoration module is used to restore the positive disturbance voltage vector and the negative disturbance voltage vector to the initial voltage vector space to obtain the output voltage vector; The light intensity acquisition and calculation module is used to acquire the far-field light intensity corresponding to the output voltage vector and calculate the change in the evaluation function. The update module is used to update the voltage vector in the hyperplane based on the change in the evaluation function; The iterative control module is used to control the projection module, disturbance module, restoration module, light intensity acquisition and calculation module, and update module to work repeatedly until the multi-channel laser coherent synthesis converges.