CN106168712A - A kind of Gaussian Beam Transformation is the population method for designing of flat top beam shaping lens - Google Patents
A kind of Gaussian Beam Transformation is the population method for designing of flat top beam shaping lens Download PDFInfo
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Abstract
The invention discloses the method for designing particle swarm optimization algorithm of the single aspheric surface shaping lens that a kind of Gaussian Beam Transformation is flat top beam.Obtain the theoretical value of shaping lens emergent ray and output face intersecting point coordinate according to preservation of energy before and after optical beam transformation, and using this theoretical value as desired value, obtain the actual value of shaping lens emergent ray and output face intersecting point coordinate according to the law of refraction.The actual value of many light constitutes the evaluation function of beam shaping system with the absolute value of target value difference, using this evaluation function as the fitness function in particle swarm optimization algorithm, the structural parameters making shaping lens couple together with fitness function in particle cluster algorithm, propose the method by particle cluster algorithm design beam shaping system, this method for designing of programming realization, the design sequencing making orthopedic systems is intelligent.The invention also discloses a kind of based on said method for the single non-spherical lens of laser beam shaping.
Description
Technical Field
The invention belongs to the technical field of non-imaging optics and laser beam shaping, and particularly relates to a novel design method of an aspheric lens for laser beam shaping.
Background
The flat-top light beam with uniformly distributed light intensity has wide application, such as the fields of laser cleaning, laser holography, laser medical treatment, laser shock peening, inertial confinement fusion and the like. The current methods for obtaining a flat-top beam mainly include: the method utilizes a special resonant cavity, a laser medium gain saturation effect method, a beam combining and beam shaping technology and the like, wherein the simplest and most common method is a beam shaping method.
Shaping techniques that shape gaussian beams into flat-topped beams require the assistance of a beam shaping system. Shaping methods that rely on shaping systems to obtain a flat-topped beam are for example: the filter method whose transmittance is inverse gaussian distribution absorption, the birefringence lens group, the microlens array shaping method, the diffractive optical element method, the liquid crystal spatial light modulator method, the holographic filter method, the amplitude modulation grating method, the aspherical lens group method, the laser beam uniformizing intracavity shaping laser method, and the like, which are proposed by IH and Klingsporn et al.
Among the shaping methods, the aspheric lens shaping technology has the advantages of simple structure, high shaping efficiency, high damage threshold, easiness in implementation and the like, and has important engineering application value. The traditional aspheric surface shaping system is complex in design process, a large amount of numerical calculation is needed, or a complex differential equation needs to be solved, and the design effect is not easy to verify. Compared with the traditional design method, the optimization algorithm can obtain the structural parameters of the beam shaping system without solving differential equations or carrying out a large amount of numerical calculation, and the structural parameters of the system are determined by an optimization program, so that the research of the method suitable for the automatic optimization design of computer software has practical significance on the popularization of the shaping optical system. The genetic algorithm has been used in optical design as a global optimization algorithm, and the global optimization algorithm in the commercial software ZEMAX for optical design analysis is the genetic algorithm.
In recent years, another intelligent optimization algorithm, Particle Swarm Optimization (PSO), has received attention from scholars. The algorithm has high convergence speed, few set parameters and easy realization, can effectively solve the problem of complex optimization, and is widely applied to the fields of function optimization, neural network training, graphic processing, pattern recognition and some engineering. However, no particle swarm optimization has been introduced into the design of the beam shaping system so far, and therefore, combining the design of the beam shaping system with the particle swarm optimization has important practical significance in making the design of the beam shaping system more intelligent and programmable.
Disclosure of Invention
The invention theoretically establishes an evaluation function of the beam shaping lens, takes the evaluation function as a fitness function in a particle swarm optimization algorithm, connects the structural parameters of the shaping lens with the fitness function in the particle swarm optimization algorithm, provides a new method for designing a beam shaping system by using the particle swarm optimization algorithm, realizes the design method by programming, and enables the design programming of the shaping system to be intelligent.
The technical scheme adopted by the invention for solving the technical problem is that the method comprises the following steps:
1. the shaping system is a single aspheric lens with an aspheric front surface and a planar back surface, and the aspheric equation is
In the above formulaIs the height of any point of the aspheric surface from the axis,Cis the curvature of the vertex of the aspheric surface,is the coefficient of the quadratic surface,is an aspheric surface deformation coefficient.
By adjusting the aspheric parameters of the front surface of the lensAnd distance between vertex of front and back surfaces of lensd 1Distance from the vertex of the rear surface to the output surfaced 2As a component of each particle position vector in the particle swarm algorithm; the value range of each component of the position vector is determined according to the radius of the incident Gaussian beam, so that the aspheric surfaceThe maximum off-axis height is larger than the radius of the incident Gaussian beam;
2. dispersing the incident Gaussian beam into light rays, and making N light rays incident on the beam shaping lens, wherein the incident height of the ith incident light ray is ξiLet us order
Anda maximum and a minimum of incident high, respectively, N being greater than 100;
3. assuming that the light intensity distribution of the input light beam on the two-dimensional plane is，I0Is the light intensity at the center of the beam, y is the distance from any point in the beam to the center of the beam, I (y) is the light intensity at y, y0For the intensity of the light falling to 1/e of the central value2The spot radius defined. The constant H is the light intensity distribution value of the output light beam which is a flat-top light beam, and the energy enclosed by the input light beam and the optical axis on the input surface and the energy enclosed by the output light beam and the optical axis on the output surface are conserved to obtain the intersection point coordinate of the emergent light beam and the output surfaceR itTheoretical value of (2):
wherein erf is an erf function in matlab
4. The coordinate value of the actual intersection point of the ith ray and the output surface after passing through the beam shaping lens is assumed to beR iaAnd the point of intersection of the Gaussian beam converted into the flat-topped beamThe target theoretical value isR itThe evaluation function F of the beam-shaping lens is then written as
Wherein,is the weighting factor of the ith ray.
5. Evaluation function and lens structure parametersThe method is an invisible function relationship, takes an evaluation function as a fitness function in a particle swarm algorithm, and performs minimum operation on the function to obtain a structural parameter which enables the fitness function to be minimumThis is the shaping lens parameter for transforming the designed gaussian beam into a flat-topped beam.
The step 3 comprises the following steps:
(1) energy enclosed by the ith incident ray and the optical axis:by definition in matlabTo obtain；
(2) The output light beam is a flat-top light beam with uniformly distributed light intensity H, and the energy enclosed by the ith output light beam and the optical axis is as follows: b = HRit
(3) From conservation of energy A = B, we obtain。
The step 4 comprises the following steps:
(1) let the shaping lens relate toxAxial rotational symmetry, again assuming that the incident ray of the Gaussian beam is parallel toxAxis of unit vector ofThe coordinate of a point on the incident light ray isP i1 (x i1,y i10), from known quantities according to the law of refraction and the equation of the surface form of the front and back two refraction surfacesAndP i1can calculate the coordinate of the actual intersection point of the emergent ray and the output surfaceP i3 (x i3,y i3,0)，P i3Is a parameter of the lens structureA function of (a);
（2）P i1 (x i1,y i11) of (0)y i1I.e. the incident height ξ of the ith incident rayiFrom ξiDetermining R in the evaluation function Fit；
（3）P i3 (x i3,y i30) iny i3Is to evaluate R in the function Fia；
(4) ByR iaAnd RitAn evaluation function F was obtained.
The invention has the advantages of
Compared with the traditional design method of the aspheric surface shaping system, the method can obtain the structural parameters of the beam shaping system without solving a differential equation or carrying out a large amount of numerical calculation, determines the structural parameters of the system by an optimization program, is suitable for carrying out automatic optimization design by utilizing computer software, and has important practical significance for the design of the shaping optical system.
The method is realized by computer programming, and can completely and automatically find out the aspheric surface parameter with the optimal combinationThe method has the advantages of quickness, convenience and the like, and has certain application prospect in the technical field of laser beam shaping, particularly in the field of shaping lens system design for shaping by using a geometric method. The design result of the method can be processed into a die by a numerical control machine according to a specific aspheric equation, flow line production is realized, and the processing technology is simple.
The invention is further illustrated by the following examples in conjunction with the accompanying drawings
Description of the drawings:
FIG. 1: a schematic diagram of transforming a Gaussian beam into a flat-topped beam;
FIG. 2: the energy transformation principle of the Gaussian beam in a one-dimensional space is schematically shown;
FIG. 3: the ray tracing process schematic diagram;
FIG. 4: the two-dimensional cross section of the designed beam shaping lens and a light transmission process simulation diagram;
FIG. 5: the relative light intensity distribution of the designed aspheric beam shaping lens on the output surface thereof;
in the figure: 1. beam shaping lens 2. beam exit surface
The specific implementation mode is as follows:
example 1:
let the input Gaussian beam have one-dimensional light intensity distribution ofLet us orderI 0=1, gaussian spot radius y0=7mm, the irradiation light intensity H =0.1 of the outgoing light beam, and the material used for the lens is SK2 glass with a refractive index of 1.601681 for red light.
The particle swarm design method for transforming the Gaussian beam into the flat-topped beam shaping lens comprises the following steps:
1. the shaping system is a single aspheric lens with a convex aspheric front surface and a flat back surface, as shown in fig. 1. The aspheric equation is
In the above formulaIs the height of any point of the aspheric surface from the axis,Cis the curvature of the vertex of the aspheric surface,is the coefficient of the quadratic surface,is an aspheric surface deformation coefficient.
The aspheric surface parameter of the front surface of the lens is compared with two distance parameters in the lensAs a component of each particle position vector in the particle swarm optimization, thus 7 variables in total, i.e. particle swarm optimizationThe dimension of each particle location vector in the algorithm is 7; the maximum off-axis height of the aspheric surface is larger than the radius y of the incident Gaussian beam0=7 mm; the value ranges of each component of the position vector are shown in table 1:
2. dispersing the incident Gaussian beam into light rays, and making N light rays incident on the beam shaping lens, wherein the incident height of the ith incident light ray is ξiLet us order
Andrespectively, the maximum and minimum of the incident height due to the Gaussian spot radius y0=7mm, therefore ξmax=7，ξmin=0, N is greater than 100, taking N =401, i =1, …, 401.
3. Referring to FIGS. 1 and 2, the intensity distribution of the input beam in the two-dimensional plane is，I 0=1，y0For the intensity of the light falling to 1/e of the central value2At a defined spot radius, y0And (= 7 mm), y is the distance from any point in the light beam to the center of the light beam, i (y) is the light intensity at the position of the center of the light beam, a constant H is the light intensity distribution value of the output light beam which is a flat-top light beam, and H = 0.1. The energy enclosed by the input light and the optical axis on the input surface and the energy enclosed by the output light and the optical axis on the output surface are conserved to obtain the position coordinate of the emergent light on the output surfaceR itThe theoretical value of (1). ByAs can be seen in figure 1 of the drawings,R itand ξiInverse sign, therefore
Wherein erf is an erf function in matlab.
4. The coordinate value of the actual intersection point of the ith ray and the output surface after passing through the beam shaping lens is assumed to beR iaAnd the theoretical value of the conversion from a Gaussian beam to a flat-topped beam isR itThe evaluation function F of the beam-shaping lens is then written as
Wherein,weight factor for the ith ray, W in this examplei=1。
5. Evaluation function and lens structure parametersThe method is an invisible functional relation, the evaluation function is taken as a fitness function in a particle swarm algorithm, minimum operation is carried out on the function, and structural parameters which enable the fitness function to be minimum can be obtained and are shown in a table 2, namely parameters of a shaping lens for converting a designed Gaussian beam into a flat-top beam.
The two-dimensional cross-section and ray distribution of the beam-shaping lens obtained from the data in Table 2 are shown in FIG. 4, and the light intensity distribution at its output face is shown in FIG. 5.
The step 3 comprises the following steps:
(1) energy enclosed by the ith incident ray and the optical axis:by definition in matlabTo obtain；
(2) The output beam is a flat-topped beam with uniformly distributed light intensity H =0.1, and the energy enclosed by the ith output ray and the optical axis: b = HR it=0.1R it
(3) From the conservation of energy a = B, as can be seen again in fig. 1,R itand ξiInverse sign, so as to obtain
。
The step 4 comprises the following steps:
please refer to fig. 3
(1) Let the shaping lens relate toxAxial rotational symmetry, again assuming that the incident ray of the Gaussian beam is parallel toxAxis of unit vector of，αi1=1, one point coordinate on the incident ray isP i1 (x i1,y i10), from known quantities according to the law of refraction and the equation of the surface form of the front and back two refraction surfacesAndP i1the coordinates of the actual intersection point of the emergent ray and the output surface can be obtained by ray tracingP i3 (x i3,y i3,0)，P i3Is a parameter of the lens structureA function of (a);
（2）P i1 (x i1,y i11) of (0)y i1I.e. the incident height ξ of the ith incident rayiFrom ξiDetermining R in the evaluation function Fit；
（3）P i3 (x i3,y i30) iny i3Is to evaluate R in the function Fia；
(4) ByR iaAnd RitAn evaluation function F was obtained.
Claims (3)
1. A particle swarm design method for a shaping lens for transforming Gaussian beam into flat-topped beam, the shaping lens has aspheric front surface and planar back surface, and the aspheric equation is
In the above formulaIs an aspherical surfaceAny point is at a height from the axis,Cis the curvature of the vertex of the aspheric surface,is the coefficient of the quadratic surface,the method is characterized by comprising the following steps:
(1) aspheric parameters of the front surface of the lensAnd distance between vertex of front and back surfaces of lensd 1Distance from the vertex of the rear surface to the output surfaced 2As a component of each particle position vector in the particle swarm algorithm; the value range of each component of the position vector is determined according to the radius of the incident Gaussian beam, and the maximum off-axis height of the aspheric surface is required to be larger than the radius of the incident Gaussian beam;
(2) dispersing parallel incident Gaussian beams into light rays, taking N light rays to be incident on a beam shaping lens, wherein the incident height of the ith incident light ray isLet us order
Anda maximum and a minimum of incident high, respectively, N being greater than 100;
(3) assuming that the light intensity distribution of the input light beam on the two-dimensional plane is，I0Is the light intensity at the center of the beam, y is the distance from any point in the beam to the center of the beam, I (y) is the light intensity at y, y0For the intensity of the light falling to 1/e of the central value2A spot radius defined by (a); the constant H is the light intensity distribution value of the output light beam which is a flat-top light beam, and the energy enclosed by the input light beam and the optical axis on the input surface and the energy enclosed by the output light beam and the optical axis on the output surface are conserved to obtain the intersection point coordinate theoretical value of the emergent light beam and the output surfaceR it：
Wherein erf is an erf function in matlab;
(4) assuming that after the ith ray passes through the beam shaping lens, the coordinate value of the actual intersection point of the emergent ray and the output surface isR iaAnd the theoretical value of the coordinates of the intersection point of the Gaussian beam converted into the flat-top beam isR itThe evaluation function F of the beam-shaping lens is then written as
Wherein,the weighting factor of the ith ray;
(5) evaluation function and lens structure parametersThe method is an invisible function relationship, takes an evaluation function as a fitness function in a particle swarm algorithm, and performs minimum operation on the function to obtain a structural parameter which enables the fitness function to be minimumThis is the designed Gaussian beam transformThe parameters of the shaping lens are flat-topped beams.
2. A particle swarm design method for transforming gaussian beam into flat-top beam shaping lens according to claim 1, wherein said step (3) comprises the steps of:
(a) energy enclosed by the ith incident ray and the optical axis:by definition in matlabTo obtain；
(b) The output light beam is a flat-top light beam with uniformly distributed light intensity H, and the energy enclosed by the ith output light beam and the optical axis is as follows: b = HRit
(c) From conservation of energy A = B, we obtain。
3. A particle swarm design method for transforming gaussian beam into flat-top beam shaping lens according to claim 1, wherein said step (4) comprises the steps of:
(a) let the shaping lens relate toxAxial rotational symmetry, again assuming that the incident ray of the Gaussian beam is parallel toxAxis of unit vector ofA point on the incident light line isP i1 (x i1,y i10), from known quantities according to the law of refraction and the equation of the surface form of the front and back two refraction surfacesAndP i1can calculate the actual intersection point coordinate of the emergent ray and the output surfaceP i3 (x i3,y i3,0)，P i3Is a parameter of the lens structureA function of (a);
（b）P i1 (x i1,y i11) of (0)y i1I.e. the incident height ξ of the ith incident rayiFrom ξiDetermining R in the evaluation function Fit；
（c）P i3 (x i3,y i30) iny i3Is to evaluate R in the function Fia；
(d) ByR iaAnd RitAn evaluation function F was obtained.
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| CN106855657A (en) * | 2017-01-11 | 2017-06-16 | 浙江大学 | Beam shaping modulation piece and its method for focal beam spot Fast Convergent |
| CN110687680A (en) * | 2018-07-04 | 2020-01-14 | 中国科学院电子学研究所 | Method for optimizing lens |
| CN112558293A (en) * | 2020-11-26 | 2021-03-26 | 中国科学院上海微系统与信息技术研究所 | Compact common-path confocal infrared dual-waveband optical system and manufacturing method thereof |
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| CN113466976A (en) * | 2021-06-28 | 2021-10-01 | 中国人民解放军战略支援部队信息工程大学 | Single aspheric lens for converting Gaussian beam into flat-topped beam |
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| CN106855657A (en) * | 2017-01-11 | 2017-06-16 | 浙江大学 | Beam shaping modulation piece and its method for focal beam spot Fast Convergent |
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