A method for precise control of the optical path of a water-guided laser.

By using a water-guided laser optical path control method with real-time monitoring and feedback, the problems of insufficient accuracy and stability in traditional methods have been solved, achieving high-precision and high-efficiency laser processing that can adapt to the processing needs of different materials and shapes.

CN119772363BActive Publication Date: 2025-10-31SHAANXI WOTE RADIUM CESIUM MASCH MFG CO LTD
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Patent Information

Application Number
CN202510231388.4
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2025-02-28
Publication Date
2025-10-31
Estimated Expiration
2045-02-28

AI Technical Summary

Technical Problem

Existing laser optical path control methods have shortcomings in terms of accuracy, stability, and adjustment range, especially in complex environments where effective control is difficult to achieve, which limits the application of water-guided lasers in high-precision processing.

Method used

A precise control method for the optical path of a water-guided laser is adopted. Through real-time monitoring and information feedback of the optical focusing system, combined with adaptive optics technology, motor drive system, parameter adjustment of the water-guided system, high-precision optical detection and advanced control algorithms, the precise control of the optical path is achieved.

Benefits of technology

It improves machining accuracy and quality, expands the machining range, reduces the heat-affected zone, lowers costs, and increases machining efficiency and effectiveness.

✦ Generated by Eureka AI based on patent content.

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Abstract

This invention belongs to the field of water-guided laser processing technology and relates to a precise control method for the optical path of a water-guided laser. The method includes: a laser generator, an optical focusing system, a water-guided system, an optical detection system, and a control system. The steps of this method include: 1. Control of the optical focusing system; 2. Control of the water-guided system; 3. Control of the optical detection system; 4. Design of the control system; 5. After the water-guided laser debugging process is completed, product processing is performed. This invention, by precisely controlling the optical path of the water-guided laser, can focus the laser beam to a smaller area, improving processing accuracy. This invention can improve processing accuracy to the sub-micron level. Therefore, this invention has higher control accuracy for the optical path of the water-guided laser, and it can also reduce processing time, improve processing efficiency, and reduce thermal damage during processing.
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Description

Technical Field

[0001] This invention belongs to the field of water-guided laser processing technology and relates to a method for precise control of the optical path of a water-guided laser. Background Technology

[0002] Water-guided laser technology is a novel laser processing technology that uses water as a transmission medium to deliver laser light to the processing area. It offers advantages such as high processing precision, a small heat-affected zone, and no dust pollution, making it a promising technology for applications in micromachining and medical fields. In specific applications, such as micromachining and high-precision cutting, precise control of the laser's optical path is required to improve processing accuracy and quality. Traditional laser optical path control methods primarily employ optical components such as mirrors and lenses for adjustment.

[0003] However, existing laser optical path control methods suffer from low accuracy, poor stability, and limited adjustment range. Furthermore, existing methods struggle to achieve effective optical path control in complex processing environments, such as underwater, high-temperature, and high-pressure conditions. This limits the application of water-guided lasers in high-precision machining.

[0004] Therefore, a precise control method for the optical path of water-guided lasers is needed to solve the above-mentioned technical problems. Summary of the Invention

[0005] This invention employs a precise control method for the optical path of a water-guided laser. It involves real-time monitoring of the optical focusing system and feedback of this information to the control system for adjustment. By adjusting the parameters of both the optical focusing system and the water-guided system based on the feedback information, precise control of the optical path is achieved. This overcomes the limitation of optical focusing systems being unable to adapt to changes in processing requirements during practical applications.

[0006] The technical solution adopted by this invention to solve the technical problem is: a method for precise control of the optical path of a water-guided laser, comprising: a laser generator for generating a laser beam; an optical focusing system for focusing the laser beam onto a water-guided laser processing area; a water-guided system for transmitting the laser beam and cooling the processing area, the water-guided system including a water nozzle and a water cavity; an optical detection system for detecting the optical path of the laser beam and the state of the processing area; and a control system for controlling the optical focusing system and the water-guided system based on feedback information from the optical detection system, thereby achieving precise control of the optical path; the method for precise control of the optical path of a water-guided laser includes the following steps:

[0007] Step S1: Control of the optical focusing system;

[0008] Adaptive optics technology is employed to adjust the position and angle of the lens and mirror in the optical focusing system in real time according to the wavefront distortion of the laser beam, thereby eliminating wavefront distortion and improving the focusing accuracy of the laser beam. A high-precision motor drive system is used to achieve fine-tuning of the lens and mirror, improving adjustment accuracy and stability. A mathematical model of the optical focusing system is established, and the parameters of the optical focusing system are optimized through numerical calculation and simulation analysis to improve the focusing effect.

[0009] Step S2: Control of the water conduction system;

[0010] The shape and size of the water nozzle are controlled to optimize the transmission efficiency and stability of the laser beam in water; the water flow speed and pressure in the water cavity are adjusted to control the transmission direction and focusing position of the laser beam; ultrasonic technology is used to stir and vibrate the water in the water cavity to improve the uniformity and stability of the water, thereby improving the transmission accuracy of the laser beam.

[0011] Step S3: Control of the optical detection system;

[0012] High-precision optical sensors, such as interferometers and photodetectors, are used to detect the optical path of the laser beam and the state of the processing area in real time. A mathematical model of the optical detection system is established, and the parameters of the optical sensors are optimized through numerical calculation and simulation analysis to improve detection accuracy and stability. Data fusion technology is used to fuse the detection information from multiple optical sensors to improve the accuracy and reliability of the detection results.

[0013] Step S4: Design of the control system;

[0014] Advanced control algorithms, such as fuzzy control and neural network control, are employed to achieve precise control of the optical focusing system and the water guiding system. A mathematical model of the control system is established, and the parameters of the control algorithm are optimized through numerical calculation and simulation analysis to improve the control effect. Real-time monitoring and fault diagnosis technologies are used to monitor and diagnose faults in the control system in real time, thereby improving the reliability and stability of the system.

[0015] Step S5, after the water-guided laser debugging process is completed, product processing will begin.

[0016] Preferably, in step S1, the focusing formula of the laser beam in the mathematical model is:

[0017]

[0018] In equation (1), f represents the focal length, r represents the radius of curvature of the lens, and θ represents the incident angle of the laser beam;

[0019] The control equation for the adaptive optics system is:

[0020]

[0021] In equation (2), μ represents the control signal, and a i The coefficients represent the adaptive optics system. This represents the wavefront distortion function of the laser beam.

[0022] Preferably, in step S2, the mathematical model for the transmission of the laser beam in water is as follows:

[0023] n1sinθ1=n2sinθ2 (3)

[0024] In equation (3), n1 and n2 represent the refractive indices of air and water, respectively, and θ1 and θ2 represent the incident angles of the laser beam in air and water, respectively.

[0025] The formula for calculating the shape and size of the water nozzle is:

[0026]

[0027] In equation (4), Q represents the water flow rate, and d represents the diameter of the water nozzle. It indicates the speed of water flow.

[0028] Preferably, in step S3, the detection formula for the interferometer in the mathematical model is:

[0029]

[0030] In equation (5), λ represents the phase difference of the interference fringes, λ represents the wavelength of the laser, and Δl represents the displacement of the object being measured.

[0031] The detection formula for the photodetector is:

[0032] Ⅰ=KP (6)

[0033] In equation (6), I represents the output current of the photodetector, K represents the sensitivity of the photodetector, and P represents the power of the laser.

[0034] Preferably, in step S4, the calculation formula for the fuzzy control algorithm in the mathematical model is:

[0035]

[0036] In equation (7), u represents the control output, and w i x represents the weight of the fuzzy rule. i Indicates input variables;

[0037] The calculation formula for the neural network control algorithm is:

[0038] y = f(wx + b) (8)

[0039] In equation (8), y represents the control output, f represents the activation function, w represents the weight matrix, x represents the input vector, and b represents the bias vector.

[0040] The beneficial effects of this invention are:

[0041] 1. Improved processing accuracy: This invention improves processing accuracy by precisely controlling the optical path of the water-guided laser, which allows the laser beam to be focused into a smaller area. Experimental results show that the method of this invention can improve processing accuracy to the sub-micron level.

[0042] 2. Improved processing quality: This invention reduces laser beam scattering and reflection by precisely controlling the optical path, thereby improving the energy utilization rate of the laser beam and thus enhancing processing quality. Furthermore, the water-guided system can cool the processing area, reducing the heat-affected zone and further improving processing quality.

[0043] 3. Expanded processing range: This invention can adapt to different processing needs and expand the processing range. By adjusting the parameters of the optical focusing system and the water guiding system, it is possible to process workpieces of different materials and shapes.

[0044] 4. Improved processing efficiency: This invention can reduce processing time and improve processing efficiency. Furthermore, the water-guided system can cool the processing area, reducing thermal damage during processing and further improving efficiency.

[0045] 5. Reduced processing costs: This invention can improve processing accuracy and quality, reduce scrap rate, and lower processing costs. Furthermore, the water-guided system can cool the processing area, reducing tool wear and further reducing processing costs. Detailed Implementation

[0046] The relevant technologies of this invention will be clearly and completely described below with reference to the embodiments of this invention. Obviously, the described embodiments are only some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0047] The precise control method for the optical path of a water-guided laser in this embodiment mainly includes the following parts:

[0048] 1. Laser generator: generates a laser beam.

[0049] 2. Optical focusing system: focuses the laser beam onto the water-guided laser processing area.

[0050] 3. Water guiding system: including water nozzles, water chambers, etc., used to transmit the laser beam and cool the processing area.

[0051] 4. Optical inspection system: used to detect the optical path of the laser beam and the state of the processing area.

[0052] 5. Control system: Based on feedback information from the optical detection system, the optical focusing system and water guiding system are controlled to achieve precise control of the optical path.

[0053] Its working principle is as follows: the laser beam generated by the laser generator is focused by the optical focusing system and then enters the water guiding system. Water nozzles in the water guiding system transmit the laser beam to the processing area, while water in the water chamber cools the processing area. The optical detection system monitors the optical path of the laser beam and the state of the processing area in real time and feeds the detection information back to the control system. Based on the feedback information, the control system adjusts the parameters of the optical focusing system and the water guiding system to achieve precise control of the optical path.

[0054] The following details the methods for implementing the present invention. The following embodiments are merely descriptions of elements conceived to achieve the intended purpose and are not intended to limit the essential elements of the invention. Various omissions, substitutions, or modifications to the structure are possible without departing from the spirit of the invention. The invention will be further described in detail with reference to embodiments of a novel method for precise control of water-guided laser optical paths.

[0055] S1: Control of the optical focusing system

[0056] - Adaptive optics technology is employed to adjust the position and angle of the lenses and mirrors in the optical focusing system in real time based on the wavefront distortion of the laser beam, thereby eliminating wavefront distortion and improving the focusing accuracy of the laser beam. - A high-precision motor drive system is used to achieve fine-tuning of the lenses and mirrors, improving adjustment accuracy and stability.

[0057] - Establish a mathematical model of the optical focusing system, and optimize the parameters of the optical focusing system through numerical calculation and simulation analysis to improve the focusing effect.

[0058] The formula for focusing a laser beam: Where f is the focal length, r is the radius of curvature of the lens, and θ is the incident angle of the laser beam.

[0059] - Control formula for adaptive optics system: Where μ is the control signal, a i For the coefficients of the adaptive optics system, Let be the wavefront distortion function of the laser beam.

[0060] S2: Control of the water guiding system

[0061] - Control the shape and size of the water nozzle to optimize the transmission efficiency and stability of the laser beam in the water.

[0062] - Adjust the water flow speed and pressure in the water cavity to control the transmission direction and focusing position of the laser beam.

[0063] -Using ultrasonic technology, the water in the water cavity is stirred and vibrated to improve the uniformity and stability of the water, thereby improving the transmission accuracy of the laser beam.

[0064] The formula for laser beam propagation in water is: n1sinθ1=n2sinθ2, where n1 and n2 are the refractive indices of air and water, respectively, and θ1 and θ2 are the incident angles of the laser beam in air and water, respectively.

[0065] - Formula for calculating the shape and size of water nozzles: Where Q is the water flow rate and d is the diameter of the water nozzle. The velocity of the water.

[0066] S3: Control of the optical inspection system

[0067] - High-precision optical sensors, such as interferometers and photodetectors, are used to detect the optical path of the laser beam and the state of the processing area in real time.

[0068] - Establish a mathematical model of the optical detection system, and optimize the parameters of the optical sensor through numerical calculation and simulation analysis to improve detection accuracy and stability.

[0069] - Data fusion technology is used to fuse detection information from multiple optical sensors, thereby improving the accuracy and reliability of detection results.

[0070] - Interferometer detection formula: in λ is the phase difference of the interference fringes, λ is the wavelength of the laser, and ΔL is the displacement of the object being measured.

[0071] - The detection formula for a photodetector is: I = KP, where I is the output current of the photodetector, K is the sensitivity of the photodetector, and P is the power of the laser.

[0072] S4: Control System Design

[0073] -Advanced control algorithms, such as fuzzy control and neural network control, are employed to achieve precise control of the optical focusing system and the water guiding system.

[0074] - Establish a mathematical model of the control system, and optimize the parameters of the control algorithm through numerical calculation and simulation analysis to improve the control effect.

[0075] - By employing real-time monitoring and fault diagnosis technologies, the control system is monitored and faults are diagnosed in real time, thereby improving the system's reliability and stability.

[0076] - Calculation formula for fuzzy control algorithm: Where u is the control output, w i x represents the weight of the fuzzy rule. i For input variables.

[0077] - The calculation formula for the neural network control algorithm is: y = f(wx + b), where y is the control output, f is the activation function, w is the weight matrix, x is the input vector, and b is the bias vector.

[0078] S5: Therefore, the entire water-light commissioning process is complete, and product processing can proceed.

[0079] Example

[0080] First, the laser beam is shaped into parallel light by a beam shaping system (beam expander and collimator). After passing through a quarter-wave plate, the polarized light emitted by the laser beam is converted into a circularly polarized beam, providing uniform and high-quality light spots in various states for subsequent laser processing.

[0081] The beam is then deflected by the first 45° beam splitter and enters the lens. The lens focuses the beam into a diffraction-free beam with a smaller diameter than the nozzle of the water jet coupling cavity, a longer collimation range, and a smaller central spot, and then it propagates through total internal reflection inside the water column.

[0082] When the laser beam reaches the optical focusing system, the optical detection system checks the beam's state (perpendicularity, roundness, centering), etc. If the laser beam does not meet the technical specifications, the control system will be activated. Based on this information, the control system will activate the high-precision motor drive system to fine-tune the lenses and mirrors in the optical focusing system. By precisely adjusting the angle of the 45° beam splitter, the mirror reflects the laser beam to subsequent optical components at a more accurate angle. Simultaneously, using the established coordinate system transformation mathematical model, numerical calculations and simulation analyses of the angle adjustment are performed. Substituting the angle generated by the 45° mirror adjustment into (x′=xcosθ+ysinθ, y′=ycosθ-xsinθ), the optimal adjustment amount of the lens position can be determined to minimize the elimination of unmet technical specifications. The collimation, polarization state, and spot roundness of the laser beam are improved, enhancing the focusing accuracy of the laser beam and ensuring that it is accurately focused on the water-guided laser processing area to meet the actual state required for water-optical coupling.

[0083] Secondly, during the assembly and manufacturing of the water jet coupling cavity and nozzle, the center of the nozzle and the center of the laser beam are not concentric. This positional deviation prevents the laser beam from achieving total internal reflection within the water column of the water jet coupling cavity, thus hindering beam propagation and potentially damaging the nozzle by impact or ablation. This necessitates replacing the nozzle and recalibrating the beam center and nozzle. Therefore, a position detection system was employed for calibration and adjustment. This system includes a detection light source and a CCD camera. The beam emitted by the detection light source passes through a 45° second beam splitter and a 45° first beam splitter, then through a lens to directly illuminate the upper surface of the nozzle in the water jet coupling cavity. Based on the reversibility of the optical path, the CCD camera captures an image of the nozzle's center position and calculates its coordinates (x1, y1).

[0084] Third, the control system activates the micro-motion module to move the focusing module to a position far from the center of the nozzle, while simultaneously controlling the laser beam to process marking points on the focusing plate.

[0085] Fourth, the control system activates the CCD camera in the detection system to take pictures of the marked points and obtain their coordinates, while simultaneously calculating the position coordinates (x2, y2) of the marked points.

[0086] Fifth, the deviation values ​​(δx, δy) of the laser beam relative to the nozzle center position were obtained by detecting and calculating the position of the nozzle center position and the position of the laser beam in the water jet coupling cavity.

[0087] Sixth, the control system activates the micro-motion module to move the focusing module (δx,δy) on the plane (x2,y2) so that the center of its focused beam overlaps with the center of the nozzle, thus completing the position calibration.

[0088] Seventh, the control system under the power meter adjusts the height of the micro-motion module to adjust the focal point position of the focusing module, so as to maximize the water-light coupling rate and make fuller use of laser power in processing.

[0089] Eighth, once the above steps are completed, the optical detection system begins to correct and adjust the verticality of the waterline. First, it generates a three-dimensional water column diagram based on the waterline's coordinates at different heights on the sensor. Then, it compares and calculates the theoretically generated water column diagram with the actual one, accurately determining the angle and position. This calculation is then sent to the control system, which will adjust the water-optical coupling module and repeat the above steps.

[0090] Ninth, after the verticality of the water column is adjusted, the optical detection system installed below the coupling cavity will monitor the state of the water column in real time. When changes occur such as the water column shortening or stratification, the monitoring status will be fed back to the control system, which will then adjust the water pressure to maintain the state required during debugging.

[0091] Tenth, finally, when all factors reach the optimal settings during debugging, the control system controls the laser, water supply system, etc., to process the corresponding parts according to the drawings.

[0092] Traditional water-guided laser technology has significant limitations in operation, lacking effective adjustment mechanisms. Specifically, it employs a one-stop debugging mode, fixing the settings after initial debugging without performing focus testing or subsequent control adjustments on the optical focusing system. This means that no feedback mechanism is established for key parameters of the laser spot, such as position, perpendicularity, spot size, and roundness, throughout the entire processing flow. The laser is simply focused and coupled into a water-guided fiber, mechanically moved to the designated position on the workpiece, and the processing task begins immediately.

[0093] This traditional approach inevitably leads to numerous problems. Due to the lack of dynamic adjustment to the focusing system, it is difficult to maintain optimal performance. For example, during processing, factors such as equipment vibration, ambient temperature changes, or slight aging of optical components can cause the laser's focusing effect to gradually deviate from the ideal state, but the system cannot automatically detect and correct this. This not only results in low processing efficiency but also unstable processing quality, easily leading to defects such as substandard hole machining accuracy and increased edge roughness, severely limiting the application effectiveness of traditional water-guided laser technology in high-precision machining.

[0094] To overcome the drawbacks of traditional methods, a precise control method for the optical path of water-guided lasers has been adopted. The core of this innovative method lies in real-time monitoring of the optical focusing system. Utilizing high-resolution optical sensors and advanced image processing technology, the actual focused spot state can be accurately captured, and this information is transmitted online to the control system in real time. Based on the received spot state data, the control system uses sophisticated algorithms to dynamically adjust the roundness, position, and perpendicularity of the spot. This effectively solves the problem of visualizing and clarifying the laser beam during transmission, allowing operators to intuitively understand the beam's transmission characteristics and ensuring that the optical system maintains optimal performance in key stages such as focusing, alignment, and coupling.

[0095] During operation, the control system coordinates the parameters of the optical focusing system and the water guiding system based on feedback information. For example, when a deviation in the roundness of the light spot is detected, the control system automatically fine-tunes the lens position or curvature in the optical focusing system, while simultaneously optimizing the water flow pressure and velocity in the water guiding system to achieve precise control and parameter matching of water-light coupling. This refined adjustment strategy successfully overcomes a series of technical bottlenecks in traditional technologies, such as difficulties in focusing, coupling, and adjusting light.

[0096] The practical application results are significant. The water-optical coupling efficiency is improved by more than 30% compared to traditional methods. This means that more laser energy can be effectively transmitted to the processing area, thereby improving processing speed and quality. In terms of setup time, it saves more than 50% of operation time compared to traditional methods, significantly shortening the equipment preparation cycle and improving production efficiency. More importantly, throughout the entire processing flow, the optical focusing system can dynamically adjust in real time according to different processing requirements, always maintaining optimal working conditions. This results in processing quality and precision that are more than 1.2 times higher than traditional technologies, providing strong technical support for precision machining in high-end manufacturing and promoting the widespread application and development of water-guided laser technology in related fields.

[0097] In summary, by precisely controlling the optical path of the water-guided laser, this invention can focus the laser beam to a smaller area, thereby improving processing accuracy. This invention can improve processing accuracy to the sub-micron level; therefore, the control accuracy of the optical path of the water-guided laser in this invention is higher.

[0098] It should be emphasized that the above are merely preferred embodiments of the present invention and are not intended to limit the present invention in any way. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention shall still fall within the scope of the technical solution of the present invention.

Claims

1. A method for precise control of the optical path of a water-guided laser, characterized in that, include: A laser generator for generating a laser beam; An optical focusing system for focusing a laser beam onto a water-guided laser processing area; A water-conducting system, used to transmit the laser beam and cool the processing area, the water-conducting system including a water nozzle and a water cavity; An optical inspection system is used to detect the optical path of the laser beam and the state of the processing area; The control system controls the optical focusing system and the water guiding system based on feedback information from the optical detection system, thereby achieving precise control of the optical path. The precise control method for the water-guided laser optical path includes the following steps: Step S1: Control of the optical focusing system; Based on the wavefront distortion of the laser beam, the positions and angles of the lenses and mirrors in the optical focusing system are adjusted in real time to eliminate wavefront distortion and improve the focusing accuracy of the laser beam. A high-precision motor drive system is used to achieve fine-tuning of the lenses and mirrors, improving adjustment accuracy and stability. A mathematical model of the optical focusing system is established, and the parameters of the optical focusing system are optimized through numerical calculation and simulation analysis to improve the focusing effect. Step S2: Control of the water conduction system; Controlling the shape and size of the water nozzles optimizes the transmission efficiency and stability of the laser beam in water; Adjusting the water flow rate and pressure in the water cavity controls the transmission direction and focusing position of the laser beam; The water in the water cavity is stirred and vibrated to improve the uniformity and stability of the water, thereby improving the transmission accuracy of the laser beam; Step S3: Control of the optical detection system; Real-time detection of the optical path of the laser beam and the status of the processing area; A mathematical model of the optical detection system is established, and the parameters of the optical sensor are optimized through numerical calculation and simulation analysis to improve detection accuracy and stability. By fusing detection information from multiple optical sensors, the accuracy and reliability of detection results can be improved. Step S4: Design of the control system; A control algorithm is used to achieve precise control of the optical focusing system and the water guiding system; Establish a mathematical model of the control system, and optimize the parameters of the control algorithm through numerical calculation and simulation analysis to improve the control effect; Real-time monitoring and fault diagnosis of the control system improve the system's reliability and stability; Step S5, after the water-guided laser debugging process is completed, product processing will begin.

2. The method for precise control of the optical path of a water-guided laser according to claim 1, characterized in that, In step S1, the focusing method of the laser beam is as follows: In equation (1), f represents the focal length, r represents the radius of curvature of the lens, and θ represents the incident angle of the laser beam; The control equation for the adaptive optics system is: In equation (2), μ represents the control signal, and a i The coefficients represent the adaptive optics system. This represents the wavefront distortion function of the laser beam.

3. The method for precise control of the optical path of a water-guided laser according to claim 1, characterized in that, In step S2, the transmission formula of the laser beam in the water is as follows: n1sinθ1=n2sinθ2 (3) In equation (3), n1 and n2 represent the refractive indices of air and water, respectively, and θ1 and θ2 represent the incident angles of the laser beam in air and water, respectively. The formula for calculating the shape and size of the water nozzle is: In equation (4), Q represents the water flow rate, d represents the diameter of the water nozzle, and θ represents the water velocity.

4. The method for precise control of the optical path of a water-guided laser according to claim 1, characterized in that, In step S3, the detection formula of the interferometer is: In equation (5), λ represents the phase difference of the interference fringes, λ represents the wavelength of the laser, and Δl represents the displacement of the object being measured. The detection formula for the photodetector is: I = KP (6) In equation (6), I represents the output current of the photodetector, K represents the sensitivity of the photodetector, and P represents the power of the laser.

5. The method for precise control of the optical path of a water-guided laser according to claim 1, characterized in that, In step S4, the calculation formula for the fuzzy control algorithm is: In equation (7), u represents the control output, and w i x represents the weight of the fuzzy rule. i Indicates input variables; The calculation formula for the neural network control algorithm is: y = f(wx + b) (8) In equation (8), y represents the control output, f represents the activation function, w represents the weight matrix, x represents the input vector, and b represents the bias vector.

Citation Information

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