CN115113390B - Beam shaping method based on improved particle swarm optimization - Google Patents
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- G—PHYSICS
- G02—OPTICS
- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
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- G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
- G02B27/09—Beam shaping, e.g. changing the cross-sectional area, not otherwise provided for
- G02B27/0927—Systems for changing the beam intensity distribution, e.g. Gaussian to top-hat
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- G02B27/09—Beam shaping, e.g. changing the cross-sectional area, not otherwise provided for
- G02B27/0938—Using specific optical elements
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- G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
- G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
- G02F1/01—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour
- G02F1/13—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour based on liquid crystals, e.g. single liquid crystal display cells
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Abstract
The invention discloses a beam shaping method based on an improved particle swarm algorithm, and belongs to the technical field of laser beam shaping. The method comprises the following steps: and taking the Zernike coefficient as a particle position vector of the particle swarm algorithm, designing an adaptability function of the particle swarm algorithm based on the root mean square error of the light intensity distribution of the output light beam and the target light beam, and obtaining the near-field phase distribution corresponding to the far-field target light beam through iterative solution of the particle swarm algorithm. The method is based on an improved particle swarm algorithm, can optimally obtain a pure phase hologram of near-field phase distribution required by target beam shaping, is conveniently realized by using phase modulation elements such as a liquid crystal spatial light modulator and the like, and completes the shaping of amplitude beams with specific shapes, such as ring shape, square shape and the like; the shaping algorithm has the advantages of high convergence speed, novel method, simplicity, practicality and good shaping effect.
Description
Technical Field
The invention relates to the field of laser beam shaping, in particular to a beam shaping method based on an improved particle swarm algorithm.
Background
The beam shaping technology can adjust the spatial distribution of the laser beam to obtain a target beam with specific light intensity distribution, and has important application value in the fields of laser processing, atomic capturing, inertial confinement nuclear fusion, optical imaging systems and the like. Currently, beam shaping techniques are mainly based on fixed optical elements and adaptive wavefront correction devices. The former includes aspheric lens group, diffraction optical element and long focal depth shaping element, and shaping parameter is fixed, only can output specific light intensity distribution, and the flexibility is relatively poor, is difficult to realize dynamic shaping. The latter includes double refraction lens group, liquid crystal spatial light modulator, deformation reflector, taking deformation reflector as example, its mirror surface is flexible and adjustable, it can construct wave front phase required by beam shaping, and can implement real-time beam shaping. The near field modulation phase corresponding to the light intensity distribution of the target light beam is obtained as a key of the pure phase modulation laser beam shaping technology. Compared with the traditional method, the optimization algorithm can obtain structural parameters required by beam shaping, such as the GS algorithm, without solving a large number of numerical calculations such as differential equations. But the GS algorithm is very sensitive to initial values and is prone to being trapped in local extreme points. The particle swarm Optimization, also called particle swarm Optimization (PARTICLE SWARM Optimization), abbreviated as PSO, is a new evolutionary algorithm (Evolutionary Algorithm-EA) developed in recent years. The PSO algorithm belongs to one of evolutionary algorithms, and is characterized in that from a random solution, an optimal solution is searched for through iteration, the quality of the solution is evaluated through fitness, and the global optimal is searched for through following the currently searched optimal value. The algorithm attracts great importance in academia due to the advantages of easiness, high precision, rapid convergence and the like, and the algorithm shows superiority in solving the practical problems.
Therefore, we use the superiority of the particle swarm algorithm to propose a beam shaping method based on an improved particle swarm algorithm, which uses Zernike coefficients as particle position vectors of the particle swarm algorithm, designs an adaptability function of the particle swarm algorithm based on root mean square error of light intensity distribution of an output beam and a target beam, and obtains near-field phase distribution corresponding to a far-field target beam through iterative solution of the particle swarm algorithm.
The method is based on an improved particle swarm algorithm, can optimally obtain a pure phase hologram of near-field phase distribution required by beam shaping, is conveniently realized by using phase modulation elements such as a liquid crystal spatial light modulator and the like, and completes the beam shaping of amplitude beams with specific shapes, such as ring shape, square shape and the like; the shaping algorithm has the advantages of high convergence speed, novel method, simplicity, practicality and good shaping effect.
Disclosure of Invention
The invention aims to solve the technical problems that: the existing beam shaping technology has the problems that the shaping shape is limited and the shaping algorithm is complex, and the beam shaping method with the advantages of no limitation on the shaping shape, simple and novel shaping algorithm, high convergence speed and good shaping effect is needed.
The technical scheme adopted for solving the technical problems is as follows: a beam shaping method based on an improved particle swarm algorithm. And taking the Zernike coefficient as a particle position vector of the particle swarm algorithm, designing an adaptability function of the particle swarm algorithm based on the root mean square error of the light intensity distribution of the output light beam and the target light beam, and obtaining the near-field phase distribution corresponding to the far-field target light beam through iterative solution of the particle swarm algorithm. This phase distribution is loaded into the phase modulation device, completing the target beam shaping.
The specific implementation steps are as follows:
And (1) setting beam shaping parameters including the diameter, wavelength, phase and amplitude of the laser beam, determining the complex amplitude of the input beam, and determining the light intensity distribution of the target beam.
If the light intensity distribution of the target beam has perfect symmetry, then in the improved particle swarm algorithm, the specific term number of the Zernike polynomial with perfect symmetry can be selected as the particle position vector.
And (2) obtaining near-field phase distribution corresponding to the target beam based on an improved particle swarm algorithm according to a pure phase modulation laser beam shaping theory.
The improved particle swarm algorithm comprises the following specific processes:
Step (2.1), randomly initializing a population, initializing the speed and the position of each particle, and setting iteration times, population quantity, inertia weight and learning factors.
And (2.2) calculating the fitness value of each particle according to the fitness function.
Step (2.3), updating the optimal position Pbest of each particle and the optimal position Gbest of the population respectively.
Step (2.4), updating the speed and position of each particle according to the speed and position updating formula.
And (2.5) judging whether the iteration times are reached or whether the optimal adaptation value reaches a preset value, if not, returning to the step (2.2), otherwise, outputting a result and ending the operation.
The iterative process of the improved particle swarm algorithm comprises two variation strategies, namely the position speed of the selected particles to be reinitialized and the random disturbance of the selected particles to maintain the diversity of the particle swarm and improve the algorithm performance.
In the improved particle swarm algorithm, zernike polynomial coefficient is used as a particle position vector, and root mean square difference of the light intensity distribution of the output light beam and the target light beam is used as a fitness function.
And (3) taking the obtained phase distribution as a modulation phase required by beam shaping, and loading the modulation phase into a phase modulation device to finish the shaping of the target beam.
The phase modulation device includes a liquid crystal spatial light modulator and a deformable mirror.
The principle of the invention is as follows: according to the theory of shaping the pure phase modulation laser beam, the shaped focusing light spot can be obtained by focusing the input light beam through a lens after the input light beam passes through a phase modulation device. According to the theory of angular spectrum diffraction, the focusing of a beam by a lens mathematically behaves as a fourier transform, and the intensity distribution at the focal plane can be expressed as the square of its complex amplitude. Therefore, beam shaping can be achieved by changing the phase of the input beam to the near field modulation phase corresponding to the target beam. The near field modulation phase distribution required by the target beam can be obtained by fast iterative solution through the improved particle swarm algorithm, so that a novel beam shaping method can be realized based on the improved particle swarm algorithm.
Compared with the prior art, the invention has the following advantages: compared with the traditional beam shaping method, the method has the advantages of simplicity, novelty, high shaping convergence speed, good shaping effect, no limitation on shaping shape and the like, and particularly shapes some symmetrical target beams, the method takes Zernike coefficients as particle bit vectors of the particle swarm algorithm, can quickly obtain near-field phase distribution corresponding to the target beams, and realizes efficient shaping of the symmetrical target beams.
Drawings
FIG. 1 is a flow chart of a beam shaping method based on an improved particle swarm algorithm according to the present invention;
FIG. 2 is an algorithm iteration process in a beam shaping method based on an improved particle swarm algorithm of the present invention;
FIG. 3 is a diagram showing a near field modulation phase obtained in a beam shaping method based on an improved particle swarm algorithm according to the present invention;
fig. 4 is a diagram showing a target ring beam and a shaped beam obtained in a beam shaping method based on an improved particle swarm algorithm according to the present invention, wherein fig. 4 (a) is a target ring beam and fig. 4 (b) is a shaped beam.
Detailed Description
The invention is further described below with reference to the drawings and detailed description.
The specific implementation method of the beam shaping method based on the improved particle swarm algorithm is as follows:
And (1) setting beam shaping parameters including the diameter, wavelength, phase and amplitude of the laser beam, determining the complex amplitude of the input beam, and determining the light intensity distribution of the target beam. In this embodiment, the laser beam is a gaussian beam, the diameter is 4mm, the wavelength is 635nm, the target beam is an annular beam, and the mathematical expression of the annular beam is:
Wherein the diameter D of the circular ring is 0.4mm, the width H of the circular ring is 0.08mm, I target (x, y) is the light intensity distribution of the target light beam at the focal plane, and (x, y) is far-field focal plane coordinates.
Since the annular light beam has perfect symmetry in light intensity distribution, coefficients of the 4 th term (defocus), the 12 th term (first order spherical aberration), the 24 th term (second order spherical aberration) and the 40 th term (third order spherical aberration) having perfect symmetry in the zernike polynomials are selected as particle position vectors in the improved particle swarm algorithm.
And (2) obtaining near-field phase distribution corresponding to the target beam based on an improved particle swarm algorithm according to a pure phase modulation laser beam shaping theory.
The improved particle swarm algorithm comprises the following specific processes:
Step (2.1), randomly initializing a population, initializing the speed and the position of each particle, and setting iteration times, population quantity, inertia weight and learning factors. As shown in fig. 1, a flow chart of a beam shaping method of the improved particle swarm algorithm of the present invention is shown. In this embodiment, the number of particle swarms is 40, the iteration number is 200, the initial value of the inertia weight is 1, the decreasing ratio of the inertia weight is 0.99, and the learning factor is 2.
And (2.2) calculating the fitness value of each particle according to the fitness function. The fitness function is root mean square difference of the light intensity distribution of the output light beam and the target light beam, and the formula of the fitness function is as follows:
Where I out (x, y) is the light intensity distribution of the output beam at the focal plane, and f reflects the deviation of the light intensity distribution of the actual output beam from the light intensity distribution of the target beam.
Step (2.3), updating the optimal position Pbest of each particle and the optimal position Gbest of the population respectively.
Step (2.4), updating the speed and position of each particle according to the speed and position updating formula.
And (2.5) judging whether the iteration times are reached or whether the optimal adaptation value reaches a preset value, if not, returning to the step (2.2), otherwise, outputting a result and ending the operation. As shown in fig. 2, for the adaptation value change curve in the improved particle swarm algorithm iteration process, the adaptation value at the 7 th iteration time can be reduced to a smaller value, and the adaptation value at the 48 th iteration time can be converged to the minimum adaptation value. As shown in fig. 3, is the near field modulation phase required for the target beam obtained by the shaping algorithm.
The iterative process of the improved particle swarm algorithm comprises two variation strategies, namely the position speed of the selected particles to be reinitialized and the random disturbance of the selected particles to maintain the diversity of the particle swarm and improve the algorithm performance.
In the improved particle swarm algorithm, zernike polynomial coefficient is used as a particle position vector, and root mean square difference of the light intensity distribution of the output light beam and the target light beam is used as a fitness function.
And (3) converting the obtained near field modulation phase into an 8-bit depth (256) gray scale image, and loading the 8-bit depth gray scale image into a liquid crystal spatial light modulator to finish shaping the target light beam. As shown in fig. 4, the theoretical light intensity distribution of the target ring beam and the light intensity distribution of the shaped beam are shown.
While the invention has been described with respect to specific embodiments thereof, it will be appreciated that the invention is not limited thereto, but rather encompasses modifications and substitutions within the scope of the present invention as will be appreciated by those skilled in the art.
Claims (1)
1. The beam shaping method based on the improved particle swarm optimization is characterized in that the beam shaping method is not limited in shaping shape, according to the pure phase modulation laser beam shaping theory, an input beam can be focused by a lens to obtain a shaped focusing light spot after passing through a phase modulation device, according to the angular spectrum diffraction theory, the focusing of the beam by the lens is mathematically represented as Fourier transform, the light intensity distribution at a focal plane can be represented as the square of complex amplitude of the light intensity distribution, the beam shaping can be realized by changing the phase of the input beam to be the near field modulation phase corresponding to the target beam, and the near field modulation phase distribution required by the target beam can be obtained by quick iterative solution through the improved particle swarm optimization, so that a new beam shaping method can be realized based on the improved particle swarm optimization, and the realization steps are as follows:
Setting beam shaping parameters including the diameter, wavelength, phase and amplitude of a laser beam, determining the complex amplitude of an input beam, and determining the light intensity distribution of a target beam; the laser beam is Gaussian beam, the diameter is 4mm, the wavelength is 635nm, the target beam is annular beam, and the mathematical expression of the annular beam is:
Wherein the diameter D of the circular ring is 0.4mm, the width H of the circular ring is 0.08mm, I tar get (x, y) is the light intensity distribution of the target light beam at the focal plane, and (x, y) is far-field focal plane coordinates;
The annular light beam has complete symmetry on light intensity distribution, so that coefficients of a 4 th item defocus, a 12 th item first order spherical aberration, a 24 th item second order spherical aberration and a 40 th item third order spherical aberration with complete symmetry in a Zernike polynomial are selected as particle position vectors in an improved particle swarm algorithm;
If the light intensity distribution of the target beam in the step (1) has perfect symmetry, in the improved particle swarm algorithm, a specific term number of the zernike polynomial with perfect symmetry can be selected as a particle position vector;
step (2), obtaining near-field phase distribution corresponding to the target beam based on an improved particle swarm algorithm according to a pure phase modulation laser beam shaping theory; the improved particle swarm algorithm comprises the following specific processes:
step (2.1), randomly initializing a population, initializing the speed and the position of each particle, and setting iteration times, population quantity, inertia weight and learning factors;
Step (2.2), calculating the fitness value of each particle according to the fitness function; the fitness function formula is:
Wherein I out (x, y) is the light intensity distribution of the output light beam at the focal plane, and f reflects the deviation of the light intensity distribution of the actual output light beam and the light intensity distribution of the target light beam;
step (2.3), respectively updating the optimal position Pbest of each particle and the optimal position Gbest of the population;
step (2.4), updating the speed and position of each particle according to a speed and position updating formula;
Step (2.5), judging whether the iteration times are reached or whether the optimal adaptation value reaches a preset value, if not, returning to the step (2.2), otherwise, outputting a result and ending the operation;
the iterative process of the improved particle swarm algorithm in the step (2) comprises two mutation strategies, namely, the speed of the reinitialized position of the selected particles and the random disturbance of the selected particles are increased, so that the diversity of the particle swarm is maintained and the performance of the algorithm is improved;
in the improved particle swarm algorithm described in the step (2), zernike polynomial coefficients are used as particle position vectors, and root mean square deviation of the light intensity distribution of the output light beam and the target light beam is used as a fitness function;
step (3), taking the obtained phase distribution as a modulation phase required by beam shaping, loading the modulation phase into a phase modulation device, and finishing the shaping of the target beam, wherein the phase modulation device comprises a liquid crystal spatial light modulator and a deformable reflector;
The method is based on an improved particle swarm algorithm for beam shaping, has the advantages of simplicity, novelty, high shaping convergence speed, good shaping effect and unlimited shaping shape, and can quickly obtain near-field phase distribution corresponding to a target beam by taking Zernike coefficients as particle bit sub-vectors of the particle swarm algorithm for shaping a plurality of symmetrical target beams, thereby realizing efficient shaping of symmetrical target beams.
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