Method for shaping Gaussian light into linear beam based on analytical method

Abstract

The invention relates to the technical field of optical application, and discloses a method for shaping Gaussian light into a linear light beam based on an analytical method, which comprises the following steps: S1, establishing a mathematical model of an input Gaussian light beam and an output linear light beam, and determining a relationship between a shape parameter of the output linear light beam and Uout (x, y), S2, deducing a phase compensation function, the method comprises the following steps: S1, deducing a phase compensation function which needs to be loaded by an SLM by means of an analytical method, S3, loading the phase function to the SLM, and checking the accuracy of phase modulation by using the characteristic that the SLM modulates a light beam phase, and S4, shaping and verifying the light beam. According to the method, the phase pattern can be accurately calculated according to the specific light beam parameters and the target shape, and the method has better universality. Corresponding phase patterns can be calculated through an analytical method for Gaussian beams with different wavelengths and waist radiuses or linear beams with different widths, lengths and light intensity distribution requirements, and the phase patterns are loaded to the SLM, so that efficient and accurate beam shaping is realized.

Description

Technical Field

[0001] The present invention relates to the field of optical application technology, and in particular to a method for shaping Gaussian light into a linear light beam based on an analytical method. Background Art

[0002] In the wide application scenarios of modern optical technology, the shape and distribution characteristics of the beam play a vital role in the system performance. As a common output form of laser source, Gaussian beam has a specific Gaussian curve characteristic in its light intensity distribution. However, in many practical applications, such as laser cutting of metal sheets, a line beam is required to ensure that the energy is evenly distributed on the cutting line, thereby improving the cutting quality and efficiency. In the field of laser projection display, the line beam is used to generate precise scanning lines to draw clear images. Therefore, shaping the Gaussian beam into a line beam has become a key link in the development of optical technology.

[0003] Current beam shaping technologies mainly include the following methods:

[0004] Global optimization method: The phase pattern on the SLM is iteratively adjusted through a numerical optimization algorithm until the target beam shape is obtained. This method is usually computationally intensive and has a slow convergence speed.

[0005] Iterative method: Iteratively design the phase pattern of SLM based on iteration and simulation results, but this method often requires multiple iterative adjustments and is prone to falling into local optimality.

[0006] Machine learning method: Generates phase patterns by learning the phase maps corresponding to different target light beams. It has high hardware requirements and poor flexibility.

[0007] The disadvantages of these methods are complex design, large amount of calculation, lack of flexibility and limited implementation accuracy, which make it difficult to meet the needs of efficient and accurate beam shaping. In view of this, we propose a method to shape Gaussian light into a line beam based on analytical method. Summary of the invention

[0008] In view of the shortcomings of the prior art, the present invention provides a method for shaping Gaussian light into a linear beam based on an analytical method, which solves the problems in the prior art that the beam shaping technology is complex in design, has a large amount of calculation, lacks flexibility and has limited implementation accuracy, making it difficult to meet the needs of efficient and accurate beam shaping.

[0009] To achieve the above objectives, the present invention is implemented by the following technical solutions: A method for shaping Gaussian light into a linear beam based on an analytical method, comprising the following steps:

[0010] S1: Establish mathematical models of input Gaussian beam and output line beam

[0011] By setting different output light field complex amplitudes U in the formulaout( x,y ) , solve the corresponding modulation phase φ ( x,y ) , clarify the shape parameters of the output line beam and U out( x,y ) the relationship between;

[0012] S2: Derivation of phase compensation function

[0013] Based on the specific requirements of the target line beam, the phase compensation function that needs to be loaded on the SLM is derived using an analytical method;

[0014] S3: Loading the phase function into the SLM

[0015] The derived analytical phase function is loaded onto the SLM, and the accuracy of the phase modulation is checked using the SLM's characteristic of modulating the beam phase;

[0016] S4: Beam shaping and verification

[0017] After the phase function is loaded, the beam is shaped and then tested by the detection system to verify whether its shape meets the expected linear beam requirements.

[0018] Preferably, in the step of establishing a mathematical model of the input Gaussian beam and the output linear beam, the modulation phase φ is calculated. ( x,y ) During the process, U is set according to different target line beam shape parameters. out( x,y ) .

[0019] Preferably, in the step of deriving the phase compensation function, when deriving the shape formula of the prism with a curved vertex, the relationship between the refraction and reflection of the light beam on different propagation paths is considered in combination with the principle of geometric optics to determine the phase compensation function and the prism parameters c, Q and the beam waist a. 1 、a 2 The precise relationship between them.

[0020] Preferably, in the step of loading the phase function into the spatial light modulator, before loading the phase function, the analytical phase function is discretized according to the pixel resolution and operating wavelength of the spatial light modulator to ensure the compatibility of the phase function with the spatial light modulator.

[0021] Preferably, in the beam shaping and verification step, a beam analyzer is used as a detection system to accurately measure the shape, width, and light intensity distribution of the shaped beam, and the phase function of the spatial light modulator or the lens parameters in the optical system are adjusted according to the measurement results.

[0022] Preferably, in the analytically based Gaussian beam shaping method, when deriving the phase compensation function, the refractive index inhomogeneity of the beam propagation medium is also taken into account. By establishing a refractive index distribution model, the phase compensation function is corrected, and the compensation function is used to compensate for the beam distortion caused by the change in the refractive index of the medium.

[0023] A Gaussian beam shaping device based on analytical method, comprising the following devices:

[0024] Gaussian beam source: used to generate the Gaussian beam to be shaped;

[0025] Spatial light modulator: used to load the analytical phase function derived according to the method of claim 1 to perform phase modulation on the Gaussian beam;

[0026] Lens group: including a Fourier lens, used to focus and convert the light beam modulated by the spatial light modulator to achieve conversion from angular intensity distribution to spatial intensity distribution;

[0027] Detection system: used to detect the shape, width and intensity distribution of the shaped light beam. The detection system includes a beam analyzer, which adjusts the phase function of the spatial light modulator or the lens group parameters according to the detection result feedback.

[0028] Preferably, the output parameters of the Gaussian beam source include a wavelength and a beam waist radius that can be adjusted according to the input parameters, and the pixel resolution and operating wavelength of the spatial light modulator match the derived analytical phase function.

[0029] Preferably, the focal length of the Fourier lens in the lens group is selected according to the parameters of the target line beam and the parameters of the Gaussian beam source.

[0030] Preferably, the detection system further comprises a data processing unit for receiving measurement data from the beam analyzer, analyzing the data and generating adjustment instructions to be sent to the adjustment device of the spatial light modulator or the lens group.

[0031] The present invention provides a method for shaping Gaussian light into a linear beam based on an analytical method.

[0032] Beneficial effects:

[0033] 1. In the present invention, the phase pattern can be accurately calculated according to the specific beam parameters and target shape, which has better universality. Whether it is a Gaussian beam with different wavelengths and waist radii, or a line beam with different widths, lengths and light intensity distribution requirements, the corresponding phase pattern can be calculated by analytical methods and loaded onto the SLM, thereby achieving efficient and accurate beam shaping.

[0034] 2. In the present invention, the phase pattern loaded by the SLM is directly calculated based on the analytical method, which is one of the significant differences from the prior art. In the prior art, the phase pattern of the SLM is often generated by empirical formulas, numerical simulation adjustments or machine learning models. The analytical method of the present invention can accurately calculate the phase pattern according to the specific beam parameters and target shape, and has better universality. Whether it is a Gaussian beam with different wavelengths and waist radii, or a line beam with different widths, lengths and light intensity distribution requirements, the corresponding phase pattern can be calculated by the analytical method and loaded onto the SLM, thereby achieving efficient and accurate beam shaping.

[0035] 3. The present invention can quickly achieve efficient beam shaping. In practical applications, such as online beam adjustment in laser processing or real-time image generation in laser display, there are high requirements for the speed and efficiency of beam shaping. The method of the present invention does not require long-term iterative calculations or complex model training processes. It can calculate the phase pattern and complete beam shaping according to needs in a short time. It is suitable for a variety of different laser systems and application scenarios, greatly improving the application value of beam shaping technology in practical engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 A flow chart of a method for shaping Gaussian light into a line beam based on an analytical method;

[0037] Figure 2 Schematic diagram of the initial amplitude of the incident Gaussian beam of the present invention;

[0038] Figure 3 It is a phase compensation function diagram derived by the present invention based on the analytical method;

[0039] Figure 4 This is the far-field line beam distribution diagram after the SLM of the present invention is loaded with phase;

[0040] Figure 5 It is a schematic diagram of the experimental device of the present invention, including a schematic diagram of the layout of the laser, SLM and detection system. DETAILED DESCRIPTION

[0041] The following will be combined with the drawings in the specification of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0042] Example:

[0043] Please refer to the attached Figure 1 -Attached Figure 4 The embodiment of the present invention provides a method for shaping Gaussian light into a linear beam based on an analytical method, comprising the following steps:

[0044] S1: Establish mathematical models of input Gaussian beam and output line beam

[0045] At the spatial light modulator (front focal plane of the lens), let the coordinates be ( x,y ) , and the image plane coordinates of the rear focal plane of the lens are (u, v), the wavelength of the incident Gaussian beam is λ, the corresponding wave number k = 2π / λ, and the complex amplitude of the incident light field U is known in( x,y ) ,according to Figure 1 The formula for calculating U out( u,v ) ;

[0046] By setting different output light field complex amplitudes U in the formula out( x,y ) , solve the corresponding modulation phase φ ( x,y ) , in the present invention, the linear beam expression is set as:

[0047]

[0048] where w 0 is the beam waist radius. Through this expression, the shape parameters of the output line beam and U out( x,y ) The relationship between them lays the foundation for the subsequent derivation of the phase function;

[0049] S2: Derivation of phase compensation function

[0050] Based on the specific requirements of the target line beam, the phase compensation function that the SLM needs to load is derived by analytical method. This function can be directly expressed in the form of optical path difference. There is a commonly used refraction device that can expand a Gaussian laser beam into a line with uniform intensity distribution. In 1987, its inventor Ian Powell described it as "a prism with a small radius at its vertex". In the present invention, through simple consideration of geometric optics, the following is derived: Figure 2 The prism shape formula with curved vertices Q, c, x shown in;

[0051] Where c describes the curvature of the vertex, Q is the conic constant, which is a variable of the slope of the prism and is (-1-Q)^-0.5. a1 and a2 are the waists of the beam (the latter in the Fourier plane), while Q and c are variables that affect the opening angle of the uniformly expanded beam. The Weil lens results in a uniform angular intensity distribution, and the conversion to a spatial intensity distribution must be accomplished by an additional focusing lens, which in the present example is Figure 2 The Fourier lens shown in , through the comprehensive application of these optical element characteristics and geometric optical relationships, can accurately derive the relationship between the phase compensation function and these parameters, thereby determining the phase pattern that should be loaded on the SLM;

[0052] S3: Loading the phase function into the SLM

[0053] Accurately load the derived analytical phase function onto the SLM, making full use of the SLM's ability to modulate the light beam phase. As an optical element that can dynamically control the phase of the light field, after receiving the loaded phase function, the SLM will phase modulate the incident Gaussian light beam according to the phase distribution specified by the function. During the loading process, it is necessary to ensure that the phase function matches the SLM's pixel resolution, operating wavelength and other parameters to ensure the accuracy and effectiveness of the phase modulation;

[0054] S4: Beam shaping and verification

[0055] After the phase function is loaded, the beam is shaped. The shaped beam is detected by a specific detection system to verify whether its shape meets the expected linear beam requirements. The detection system can use high-precision optical detection equipment such as beam analyzers to accurately measure key parameters such as the shape, width, and light intensity distribution of the beam. If the measurement results deviate from the expected results, the phase function or other parameters in the optical system (such as lens position, focal length, etc.) are fine-tuned according to the deviation to optimize the shaping effect until a linear beam that meets the requirements is obtained.

[0056] In the step of establishing the mathematical model of the input Gaussian beam and the output linear beam, the modulation phase φ is calculated. ( x,y ) During the process, U is set according to different target line beam shape parameters. out( x,y ) .

[0057] In the step of deriving the phase compensation function, when deriving the shape formula of the prism with a curved vertex, the relationship between the refraction and reflection of the light beam on different propagation paths is considered in combination with the principle of geometric optics to determine the phase compensation function and the prism parameters c, Q and the beam waist a. 1 、a 2 The precise relationship between them.

[0058] In the step of loading the phase function into the spatial light modulator, before loading the phase function, the analytical phase function is discretized according to the pixel resolution and working wavelength of the spatial light modulator to ensure the compatibility of the phase function with the spatial light modulator.

[0059] In the beam shaping and verification steps, a beam analyzer is used as a detection system to accurately measure the shape, width, and light intensity distribution of the shaped beam, and the phase function of the spatial light modulator or the lens parameters in the optical system are adjusted according to the measurement results.

[0060] The Gaussian beam shaping method based on analytical method, in which the refractive index inhomogeneity of the beam propagation medium is also taken into account when deriving the phase compensation function, and the phase compensation function is corrected by establishing a refractive index distribution model, and the beam distortion caused by the change of the medium refractive index is compensated by the compensation function.

[0061] Please refer to the attached Figure 5 , a Gaussian beam shaping device based on analytical method, comprising the following devices:

[0062] Gaussian beam source: used to generate the Gaussian beam to be shaped;

[0063] Spatial light modulator: used to load the analytical phase function derived according to the method of claim 1 to perform phase modulation on the Gaussian beam;

[0064] Lens group: including a Fourier lens, used to focus and convert the light beam modulated by the spatial light modulator to achieve conversion from angular intensity distribution to spatial intensity distribution;

[0065] Detection system: used to detect the shape, width and intensity distribution of the shaped light beam. The detection system includes a beam analyzer, which adjusts the phase function of the spatial light modulator or the lens group parameters according to the detection result feedback.

[0066] In the present invention, the output parameters of the Gaussian beam source include wavelength and beam waist radius, which can be adjusted according to the input parameters. Specifically, the wavelength can be adjusted as needed to meet the needs of different application scenarios. The beam waist radius can also be adjusted according to the input parameters to achieve the best beam focusing effect. In addition, the pixel resolution and operating wavelength of the spatial light modulator are matched with the derived analytical phase function to ensure accurate modulation and control of the beam.

[0067] In the lens set, the focal length of the Fourier lens is selected according to the parameters of the target line beam and the parameters of the Gaussian beam source. This selection ensures that the lens set can effectively convert the Gaussian beam into the target line beam to meet specific application requirements. By accurately selecting the focal length of the Fourier lens, the best beam conversion effect can be achieved and the overall performance of the system can be improved.

[0068] The detection system also includes a data processing unit. The unit is responsible for receiving the measurement data from the beam analyzer and analyzing the data. By analyzing the data, the data processing unit can generate corresponding adjustment instructions. These instructions will be sent to the adjustment device of the spatial light modulator or the lens group to achieve real-time adjustment of the beam parameters. In this way, the detection system can ensure that the output of the beam always meets the predetermined performance standards, thereby improving the stability and reliability of the entire system.

[0069] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for shaping Gaussian light into a linear beam based on an analytical method, characterized in that: The following steps are involved: S1: Establish mathematical models of input Gaussian beam and output line beam By setting different output light field complex amplitudes U in the formula out (x, y), solve the corresponding modulation phase φ(x, y), and clarify the shape parameters of the output line beam and U out The relationship between (x,y); S2: Derivation of phase compensation function Based on the specific requirements of the target line beam, the phase compensation function that needs to be loaded on the SLM is derived using an analytical method; S3: Loading the phase function into the SLM The derived analytical phase function is loaded onto the SLM, and the accuracy of the phase modulation is checked using the SLM's characteristic of modulating the beam phase; S4: Beam shaping and verification After the phase function is loaded, the beam is shaped and then tested by the detection system to verify whether its shape meets the expected linear beam requirements.

2. The method for shaping Gaussian light into a linear beam based on an analytical method according to claim 1, characterized in that: In the step of establishing the mathematical model of the input Gaussian beam and the output line beam, during the process of calculating the modulation phase φ(x, y), U is set according to different target line beam shape parameters. out (x,y).

3. The method for shaping Gaussian light into a linear beam based on an analytical method according to claim 1, characterized in that: In the step of deriving the phase compensation function, when deriving the shape formula of the prism with a curved vertex, the refraction and reflection relationship of the light beam on different propagation paths is considered in combination with the principle of geometric optics to determine the precise relationship between the phase compensation function and the prism parameters c, Q and the beam waists a1, a2.

4. The method for shaping Gaussian light into a linear beam based on an analytical method according to claim 1, characterized in that: In the step of loading the phase function into the spatial light modulator, before loading the phase function, the analytical phase function is discretized according to the pixel resolution and working wavelength of the spatial light modulator to ensure the compatibility of the phase function with the spatial light modulator.

5. The method for shaping Gaussian light into a linear beam based on an analytical method according to claim 1, characterized in that: In the beam shaping and verification steps, a beam analyzer is used as a detection system to accurately measure the shape, width, and light intensity distribution of the shaped beam, and the phase function of the spatial light modulator or the lens parameters in the optical system are adjusted according to the measurement results.

6. The method for shaping Gaussian light into a linear beam based on an analytical method according to claim 1, characterized in that: The Gaussian beam shaping method based on analytical method, in which the refractive index inhomogeneity of the beam propagation medium is also taken into account when deriving the phase compensation function, and the phase compensation function is corrected by establishing a refractive index distribution model, and the beam distortion caused by the change of the medium refractive index is compensated by the compensation function.

7. A Gaussian beam shaping device based on analytical method according to any one of claims 1 to 6, characterized in that: Includes the following devices: Gaussian beam source: used to generate the Gaussian beam to be shaped; Spatial light modulator: used to load the analytical phase function derived according to the method of claim 1 to perform phase modulation on the Gaussian beam; Lens group: including a Fourier lens, used to focus and convert the light beam modulated by the spatial light modulator to achieve conversion from angular intensity distribution to spatial intensity distribution; Detection system: used to detect the shape, width and intensity distribution of the shaped light beam. The detection system includes a beam analyzer, which adjusts the phase function of the spatial light modulator or the lens group parameters according to the detection result feedback.

8. The Gaussian beam shaping device based on analytical method according to claim 7, characterized in that: The output parameters of the Gaussian beam source include a wavelength and a beam waist radius that can be adjusted according to input parameters, and the pixel resolution and operating wavelength of the spatial light modulator match the derived analytical phase function.

9. The Gaussian beam shaping device based on analytical method according to claim 7, characterized in that: The focal length of the Fourier lens in the lens group is selected according to the parameters of the target line beam and the parameters of the Gaussian beam source.

10. The Gaussian beam shaping device based on analytical method according to claim 7, characterized in that: The detection system also includes a data processing unit, which is used to receive measurement data from the beam analyzer, analyze the data and generate adjustment instructions to send to the adjustment device of the spatial light modulator or the lens group.

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