A Flat-Top Beam Shaping Method Based on Last-Place Elimination GSGA Algorithm

Abstract

This invention belongs to the field of flat-top beam shaping technology and discloses a flat-top beam shaping method based on the last-place elimination GSGA algorithm. The fundamental mode beam output from a semiconductor laser is connected to a phase-type liquid crystal spatial light modulator (LCSSM) via an optical signal input interface. A computer is connected to the LCSSM via USB and HDMI interfaces. The computer transmits phase distribution information to the modulator via the USB interface, and the modulator feeds back the shaped flat-top beam amplitude distribution to the computer via the HDMI interface. The LCSSM outputs the shaped flat-top beam spatial light through an optical output coupler. In this invention, the computer uses a novel algorithm to calculate the phase distribution and shapes the input Gaussian beam using the LCSSM, resulting in a flat-top beam with high energy utilization and high top uniformity.

Description

Technical Field

[0001] This invention belongs to the field of flat-top beam shaping technology, specifically relating to a method for adjusting a phase-type liquid crystal spatial light modulator using computer algorithms to achieve flat-top beam shaping. Background Technology

[0002] With the continuous development and improvement of laser theory and the increasing maturity of laser technology, lasers have shown broad application prospects in many fields. For example, in medicine, thulium-doped lasers can achieve shallow penetration into biological tissues and good thermal coagulation hemostasis; in biology, lasers can induce mutagenesis in *Pseudomonas aeruginosa* to cultivate highly efficient petroleum hydrocarbon-degrading bacteria; in the military field, they are used in reconnaissance imaging lidar, homing guidance lidar, and helicopter obstacle avoidance lidar; in materials science, laser flash heating can be used to measure thermal diffusivity, and so on. However, with the widespread application of lasers, the disadvantages of the Gaussian distribution of laser intensity have gradually become apparent: non-uniform energy distribution can lead to excessively high local temperatures, damaging material properties. Therefore, beam shaping technology is needed to shape the Gaussian beam into a flat-top beam with uniform energy distribution.

[0003] Beam shaping is essentially the process of transforming an input beam through an optical system to obtain the desired beam distribution on the output plane. In 1965, foreign scholar Frieden proposed using aspherical lenses or a pair of selective aberration lenses to shape a TEM. 00 After shaping the multimode beam, Dickey et al. used a microlens array optical focusing system to achieve multimode beam shaping. Other methods include Dammann gratings, birefringent lens groups, and liquid crystal spatial modulators. Among these, liquid crystal spatial modulators are widely used in various optical fields due to their controllable transmittance function, good flexibility, and real-time performance. Shaping the laser beam using a liquid crystal spatial modulator mainly utilizes the characteristic of liquid crystal molecules to change the phase of the incident beam.

[0004] Currently, the main phase distribution function algorithms include the GS algorithm, GAA algorithm, YG algorithm, and MRAF algorithm. Global optimization algorithms mainly include simulated annealing and genetic (GA) algorithms. The GS algorithm is a local optimization algorithm with fast convergence speed, but it is sensitive to the initial phase value and easily gets trapped in local extrema. The GAA algorithm is an optimization of the GS algorithm, which treats the ideal amplitude as a weighted result of the input light intensity and the ideal light intensity. The YG algorithm improves diffraction efficiency. The MRAF algorithm uses the signal region and noise region to divide the output surface to obtain extremely high top uniformity, but sacrifices energy utilization.

[0005] None of the aforementioned phase distribution algorithms can simultaneously achieve both high top inhomogeneity and high energy utilization, which requires further research. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a flat-top beam shaping method based on the last-place elimination GSGA algorithm. This method optimizes the phase distribution function algorithm in beam shaping using a liquid crystal spatial light modulator, and uses computer-controlled liquid crystal spatial light modulator to shape a Gaussian beam into a flat-top beam. This solves the problem that the shaped flat-top beam cannot simultaneously satisfy high top uniformity and high energy utilization, thus achieving efficient and highly uniform beam shaping.

[0007] To achieve the above objectives, the present invention is implemented through the following technical means:

[0008] This invention is a flat-top beam shaping method based on the last-place elimination GSGA algorithm, comprising a computer, a phase-type liquid crystal spatial light modulator, a semiconductor laser LD, and an optical output coupler. The computer calculates the phase distribution function using the last-place elimination GSGA algorithm and outputs the phase distribution data to the phase-type liquid crystal spatial light modulator. The semiconductor laser outputs a Gaussian beam intensity distribution. The optical output coupler outputs the flat-top beam shaped by the phase-type liquid crystal spatial light modulator in the form of spatial light. The phase-type liquid crystal spatial light modulator can automatically change the long axis direction of the liquid crystal based on the phase distribution data input from the computer, thereby adjusting the beam phase distribution. It statistically analyzes the beam amplitude distribution after the phase change and outputs the distribution value to the computer in the form of spatial light.

[0009] This method utilizes a computer-controlled phase-type liquid crystal spatial light modulator to achieve flat-top beam shaping. The computer has a built-in phase distribution algorithm and is connected to the liquid crystal spatial light modulator via an HDMI and a USB interface. A semiconductor laser is connected to the spatial liquid crystal light modulator via an optical fiber and an optical input interface. The shaped beam is output through an optical output coupler. The phase distribution result obtained by the phase distribution algorithm is transmitted to the phase-type liquid crystal spatial light modulator via the USB interface. The laser generated by the semiconductor laser enters the spatial liquid crystal light modulator through the optical input port. The spatial liquid crystal light modulator automatically adjusts the direction of the liquid crystal main axis according to the phase information input by the computer to shape the input beam. The shaping result is statistically analyzed by the spatial liquid crystal light modulator, and then displayed on the computer via the HDMI interface or output as spatial light through the optical output coupler.

[0010] The computer incorporates a last-place elimination (GSGA) algorithm. The phase distribution result obtained by this algorithm is transmitted to a phase-type liquid crystal spatial light modulator via a USB interface. The laser generated by the semiconductor laser enters the modulator through the optical input port. The modulator automatically adjusts the direction of the liquid crystal main axis according to the phase information input from the computer, thereby shaping the input beam. The modulator then calculates the light intensity values ​​at each point based on the shaping result, and finally outputs the spatial light to the computer display via an HDMI interface or through an optical output coupler. The algorithm is explained in detail below.

[0011] Let the amplitude distribution of the input beam be U in (x,y), the reference beam amplitude distribution is U ref (x,y), initial phase The subscript indicates the m-th (m = 1, 2, ..., num) phase, and num represents the total number of individuals in each offspring population. Here, N initial phases are generated, and the two-dimensional phase points in each phase are randomly generated within the range [-π, π]. The algorithm flow can be described as follows:

[0012] Step 1: Solve for local extrema using the GS algorithm

[0013] Perform the following 5 steps for each phase of the num terms. The initial number of times step one is performed is 100, and then the number of times is increased by 50 for each subsequent iteration.

[0014] 1) Combine the input beam amplitude with the initial phase:

[0015]

[0016] Where i is the imaginary unit, G m (x,y) represents the complex amplitude of the m-th phase individual;

[0017] 2) The complex amplitude G m Perform a Fourier transform on (x,y) and extract the phase:

[0018]

[0019] Here, angle() represents extracting the phase function, and FFT2() represents a two-dimensional Fourier transform;

[0020] 3) Combined with a reference amplitude distribution:

[0021]

[0022] 4) The complex amplitude G 1,m Perform inverse Fourier transform on (x,y) and extract the phase:

[0023]

[0024] Where iFFT2() represents the two-dimensional inverse Fourier transform;

[0025] 5) Combined with the input beam amplitude, the amplitude is extracted after performing a Fourier transform:

[0026]

[0027] Here, abs() represents extracting the amplitude function;

[0028] 6) Regarding the amplitude U 1,m Calculate the mean squared error SSE and the fitting coefficient η for (x,y), and simultaneously calculate the Q1 index. (Q index table)

[0029] It is described as follows:

[0030] Q = η - SSE (1)

[0031] The larger the Q index, the higher the quality of the shaped beam. The purpose is to reduce the two indices for evaluating flat-top beams to one, making it easier to perform single-objective optimization using GS and GA algorithms.

[0032] Step 2: Perform a global search and eliminate the last-place candidate using the improved GA algorithm.

[0033] 1) Sort all the Q1 indices obtained above from largest to smallest, select the phases corresponding to the top 25% of Q1 values ​​to directly enter the next generation of phase groups, that is, directly proceed to step 5), and proceed to step 2) for the bottom 75% of phases.

[0034] 2) Perform selection, crossover, and mutation in the GA algorithm. The selection method uses roulette wheel selection, with each individual having a probability of being selected; the crossover probability is 0.6, and the phase is two-dimensional data. The crossover method involves two dimensions...

[0035] Multi-point crossover is used for all degrees; the mutation probability is 0.2, and mutation is performed on each two-dimensional phase point. 3) The phase group after GA algorithm is combined with the amplitude distribution of the input beam, and Fourier transform is performed.

[0036] And take the amplitude.

[0037] 4) Calculate SSE and η for the amplitude obtained in step 4), and calculate the Q2 value. Sort the Q2 values ​​from largest to smallest, and select the phases corresponding to the top 50% of the Q2 values ​​to enter the next generation phase group.

[0038] 5) Assign the next generation of phase groups to the initial phase. Then restart from step 1).

[0039] The beneficial effects of this invention are:

[0040] Compared with traditional methods, the flat-top beam shaping method provided by this invention yields beam performance superior by the LPE-GSGA algorithm. Compared with the GS algorithm, LPE-GSGA reduces the SSE index by 10.1% and increases the η index by 0.85%, and can improve the problem of traditional algorithms relying on initial values ​​to a certain extent.

[0041] By comparing the top pattern of the output beam, this invention shows that the LPE-GSGA algorithm outputs fewer intensity abrupt changes at the top of the beam, fewer side lobes, and lower amplitude.

[0042] Since the algorithm only involves phase transformation, a flat-top beam can be obtained by connecting a computer with a phase-type spatial light modulator, which demonstrates the effectiveness of the algorithm. It can effectively improve the quality of the output flat-top beam and obtain a flat-top beam with high energy utilization and high beam top uniformity. Attached Figure Description

[0043] Figure 1 This is a schematic diagram of the structure of the present invention.

[0044] Figure 2 This is a flowchart of the algorithm structure of the present invention.

[0045] Figure 3 This is the amplitude distribution diagram of the output beam through the modulator in this invention. Detailed Implementation

[0046] The embodiments of the present invention will be disclosed below with reference to the drawings. For clarity, many practical details will be described in the following description. However, it should be understood that these practical details are not intended to limit the invention. That is, in some embodiments of the invention, these practical details are not essential.

[0047] like Figure 1As shown, this invention is a flat-top beam shaping method based on the last-place elimination GSGA algorithm. This method utilizes a computer 3 to control a phase-type liquid crystal spatial light modulator 4 to achieve flat-top beam shaping. The computer has a built-in phase distribution algorithm. The computer 3 is connected to the liquid crystal spatial light modulator 4 via an HDMI interface and a USB interface. A semiconductor laser 2 is connected to the spatial liquid crystal light modulator 4 via an optical fiber and an optical input interface. The shaped beam is output through an optical output coupler 1. The phase distribution result obtained through the phase distribution algorithm is transmitted to the phase-type liquid crystal spatial light modulator 4 via the USB interface. The laser generated by the semiconductor laser 2 enters the spatial liquid crystal light modulator 4 through the optical input port. The spatial liquid crystal light modulator 4 automatically adjusts the liquid crystal main axis direction according to the phase information input by the computer to achieve beam shaping. The shaping result is statistically analyzed by the spatial liquid crystal light modulator 4, and then displayed on the computer 3 via the HDMI interface or output as spatial light through the optical output coupler 1.

[0048] like Figure 2 As shown, the phase distribution algorithm built into the computer 3 is the last-place elimination GSGA algorithm, which calculates the phase distribution function and outputs phase distribution data to the phase-type liquid crystal spatial light modulator 4.

[0049] The last-place elimination GSGA algorithm is as follows: Let the amplitude distribution of the input beam be U. in (x,y), the reference beam amplitude distribution is U ref (x,y), initial phase The subscript indicates the m-th (m = 1, 2, ..., num) phase, and num represents the total number of individuals in each offspring population. A total of N initial phases are generated, and the two-dimensional phase points in each phase are randomly generated in the range [-π, π]. The process includes the following steps:

[0050] Step 1: Solve for local extrema using the GS algorithm, specifically as follows:

[0051] For each num item phase, the following steps 1-1 to 1-5 are performed respectively. The initial number of times step 1 is performed is 100, and then the number of times is increased by 50 for each subsequent iteration. The specific steps include the following:

[0052] Step 1-1: Combine the input beam amplitude with the initial phase:

[0053]

[0054] Where i is the imaginary unit, G m (x,y) represents the complex amplitude of the m-th phase individual;

[0055] Step 1-2, convert the complex amplitude G m Perform a Fourier transform on (x,y) and extract the phase:

[0056]

[0057] Here, angle() represents extracting the phase function, and FFT2() represents a two-dimensional Fourier transform;

[0058] Steps 1-3, Combined with a reference amplitude distribution:

[0059]

[0060] Steps 1-4: The complex amplitude G 1,m Perform inverse Fourier transform on (x,y) and extract the phase:

[0061]

[0062] Where iFFT2() represents the two-dimensional inverse Fourier transform;

[0063] Steps 1-5, Combined with the input beam amplitude, the amplitude is extracted after performing a Fourier transform:

[0064]

[0065] Where abs() represents the extraction amplitude function;

[0066] Steps 1-6: Adjust the amplitude U 1,m Calculate the mean squared error SSE and the fitting coefficient η for (x,y), and simultaneously calculate the Q1 index, which is expressed as:

[0067] Q = η - SSE (1)

[0068] The larger the Q index, the higher the quality of the shaped beam. The purpose is to reduce the two indices for evaluating flat-top beams to one, making it easier to perform single-objective optimization using GS and GA algorithms.

[0069] Step 2: Perform a global search and eliminate the last-placed candidate using the improved GA algorithm. This includes the following steps:

[0070] Step 2-1: Sort all Q1 indices obtained in Step 1-6 from largest to smallest, select the phases corresponding to the top 25% of Q1 values ​​to directly enter the next generation of phase groups, i.e. directly proceed to Step 2-5, and proceed to Step 2-2 for the bottom 75% of phases.

[0071] Step 2-2: Perform selection, crossover, and mutation in the GA algorithm. The selection method uses roulette wheel selection, with each individual having a probability of being selected. The crossover probability is 0.6. The phase is two-dimensional data. The crossover method uses multi-point crossover in both dimensions. The mutation probability is 0.2. Mutation is performed on each two-dimensional phase point.

[0072] Steps 2-3: Combine the phase group after GA algorithm with the amplitude distribution of the input beam, and perform Fourier transform and amplitude extraction;

[0073] Steps 2-4: Calculate SSE and η for the amplitude obtained in Step 2-3, and calculate Q2 value. Sort the Q2 values ​​from largest to smallest, and take the phases corresponding to the top 50% of Q2 values ​​to enter the next generation phase group.

[0074] Steps 2-5: Assign the next generation phase group to the initial phase. Then start over from step 1-1.

[0075] Figure 2 In the diagram, R represents the number of times the GS algorithm is executed, k is the descendant index, m is the phase individual index in the descendant population, and num is the total number of individuals in the descendant population. The flowchart illustrates the basic process of steps 1 and 2 of the algorithm. It can be seen that the LEP-GSGA algorithm first converges quickly using the GS algorithm to reach a local extremum, then uses the GA algorithm to escape the local extremum and search for a global extremum. Finally, it uses a last-place elimination method to remove phase individuals with poor evaluation metrics, reassigns values ​​to the initial phase population, and iterates until the phase individual with the best performance is selected.

[0076] To verify the shaping method of the present invention, the algorithm of the present invention was compared with the output beam index of other algorithms, and the results are shown in Table 1.

[0077] Table 1

[0078]

[0079] This invention connects a phase-type liquid crystal spatial light modulator to a power source, and the fundamental mode Gaussian beam output from a semiconductor laser is input to the phase-type liquid crystal spatial light modulator through an optical input interface. A last-place elimination (GSGA) algorithm is executed on a computer, which yields the phase distribution of the target beam. This phase distribution is then output from the computer to the phase-type liquid crystal spatial light modulator via a USB interface.

[0080] A phase-type liquid crystal spatial light modulator automatically adjusts the long axis direction and orientation of the liquid crystal molecules after receiving phase distribution information, ensuring that the polarization direction of the incident beam is the same as the long axis direction. It utilizes the principle of electrically controlled birefringence of liquid crystals to adjust the phase of the incident beam.

[0081] The output beam is a complex amplitude resulting from the combination of the input beam amplitude and the phase provided by the computer. A phase-type liquid crystal spatial light modulator senses the output beam and feeds back its amplitude distribution to the computer via an HDMI interface. Figure 3 As shown, the shaped flat-top beam can be output simultaneously through output coupler 1.

[0082] The above description is merely an embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principle of the present invention should be included within the scope of the claims of the present invention.

Claims

1. A method for flattop beam shaping based on last-elimination GSGA algorithm, characterized in that: This method uses a computer (3) to control a phase-type liquid crystal spatial light modulator (4) to achieve flat-top beam shaping. The computer has a built-in phase distribution algorithm, which is the last-place elimination GSGA algorithm. The computer (3) is connected to the liquid crystal spatial light modulator (4) through an HDMI interface and a USB interface. The semiconductor laser (2) is connected to the liquid crystal spatial light modulator (4) through an optical input interface using an optical fiber. The shaped beam is output through an optical output coupler (1). The phase distribution result obtained by the phase distribution algorithm is transmitted to the liquid crystal spatial light modulator (4) through the USB interface. The laser generated by the semiconductor laser (2) enters the liquid crystal spatial light modulator (4) through the optical input interface. The liquid crystal spatial light modulator (4) automatically adjusts the direction of the liquid crystal main axis according to the phase information input by the computer to achieve shaping of the input beam. The shaping result is statistically analyzed by the liquid crystal spatial light modulator (4) for light intensity values ​​at each point, and then transmitted to the computer (3) for display through the HDMI interface or output through the optical output coupler (1) for spatial light. The last-place elimination GSGA algorithm is as follows: Let the input beam amplitude distribution be... The amplitude distribution of the reference beam is initial phase The subscript indicates the first... Phase of the item, This represents the total number of individuals in each offspring population. The initial phase generates N terms, and the two-dimensional phase point in each term is... Random generation includes the following process: Step 1: Use the GS algorithm to solve for local extrema, for all The phase term is processed through steps 1-1 to 1-5, with step 1 initially performed 100 times and then increased by 50 times for each subsequent iteration. The specific steps include: Step 1-1: Combine the input beam amplitude with the initial phase: in, The imaginary unit, Indicates the first The complex amplitude of the phase individual; Steps 1-2: The complex amplitude Perform Fourier transform and extract phase: in, This indicates the extraction of the phase function. Represents a two-dimensional Fourier transform; Steps 1-3, Combined with a reference amplitude distribution: Steps 1-4: The complex amplitude Perform inverse Fourier transform and extract phase: in, This represents the two-dimensional inverse Fourier transform. Steps 1-5, Combined with the input beam amplitude, the amplitude is extracted after performing a Fourier transform: in, This indicates the extraction of the amplitude function; Steps 1-6: Amplitude Calculate the mean square error (SSE) and the fitting coefficient. Simultaneous calculation index, The indicator is described as follows: (1) The larger the index, the higher the quality of the shaped beam. The purpose is to reduce the two indices for evaluating flat-top beams to one, making it easier to perform single-objective optimization using GS and GA algorithms. Step 2: Perform a global search and eliminate the last-placed candidate using the improved GA algorithm, specifically including the following steps: Step 2-1: For all the results obtained in Steps 1-6 Sort the indicators from largest to smallest, and select the top 25%. The phase corresponding to the value directly enters the next generation of phase group, that is, directly proceeds to step 2-5, and the last 75% of the phases proceed to step 2-2; Step 2-2: Perform selection, crossover, and mutation in the GA algorithm. The selection method uses roulette wheel selection, with each individual having a probability of being selected. The crossover probability is 0.

6. The phase is two-dimensional data. The crossover method uses multi-point crossover in both dimensions. The mutation probability is 0.

2. Mutation is performed on each two-dimensional phase point. Steps 2-3: Combine the phase group after GA algorithm with the amplitude distribution of the input beam, and perform Fourier transform and amplitude extraction; Step 2-4: Calculate the mean square error (SSE) and fitting coefficients for the amplitudes obtained in Step 2-3. and calculate Value, based on Sort the values ​​from largest to smallest and take the top 50%. The phase corresponding to the value enters the next phase group; Steps 2-5: Assign the next generation phase group to the initial phase. Then start over in step 1-1.

2. The flat-top beam shaping method based on the last-place elimination GSGA algorithm according to claim 1, characterized in that: The output beam of the semiconductor laser (2) is the fundamental mode output.

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