CN106168712B - Particle swarm design method for shaping lens for converting Gaussian beam into flat-topped beam - Google Patents

Particle swarm design method for shaping lens for converting Gaussian beam into flat-topped beam Download PDF

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CN106168712B
CN106168712B CN201610802909.8A CN201610802909A CN106168712B CN 106168712 B CN106168712 B CN 106168712B CN 201610802909 A CN201610802909 A CN 201610802909A CN 106168712 B CN106168712 B CN 106168712B
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CN106168712A (en
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秦华
张爽
杨开
刘珍
李文瑞
韩克祯
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Shandong University of Technology
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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
    • 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
    • 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
    • G02B27/0012—Optical design, e.g. procedures, algorithms, optimisation routines
    • 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
    • G02B27/09—Beam shaping, e.g. changing the cross-sectional area, not otherwise provided for
    • G02B27/0938—Using specific optical elements
    • G02B27/095—Refractive optical elements
    • G02B27/0955—Lenses

Abstract

The invention discloses a method for designing a single aspheric shaping lens for converting a Gaussian beam into a flat-topped beam, namely a particle swarm optimization algorithm. And obtaining a theoretical value of the intersection point coordinate of the emergent ray of the shaping lens and the output surface according to the energy conservation before and after the light beam transformation, taking the theoretical value as a target value, and obtaining an actual value of the intersection point coordinate of the emergent ray of the shaping lens and the output surface according to the law of refraction. The absolute value of the difference between the actual value and the target value of a plurality of rays forms an evaluation function of the beam shaping system, the evaluation function is used as a fitness function in a particle swarm optimization algorithm, the structural parameters of the shaping lens are connected with the fitness function in the particle swarm optimization algorithm, a method for designing the beam shaping system by the particle swarm optimization algorithm is provided, the design method is realized by programming, and the design programming of the shaping system is intelligentized. The invention also discloses a single aspheric lens for laser beam shaping based on the method.

Description

Particle swarm design method for shaping lens for converting Gaussian beam into flat-topped beam
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
Figure DEST_PATH_IMAGE001
In the above formula
Figure 303692DEST_PATH_IMAGE002
Is the height of any point of the aspheric surface from the axis,Cis the curvature of the apex and is,
Figure DEST_PATH_IMAGE003
is the coefficient of the quadratic surface,
Figure 391472DEST_PATH_IMAGE004
is an aspheric surface deformation coefficient.
By adjusting the aspheric parameters of the front surface of the lensC、
Figure DEST_PATH_IMAGE005
、
Figure 502034DEST_PATH_IMAGE004
And 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 the incident Gaussian beam into light rays, and taking N light rays from the light rays to be incident on the light beam shaperOn the shape lens, the incident height of the ith incident ray is
Figure 428402DEST_PATH_IMAGE006
Let us order
Figure DEST_PATH_IMAGE007
Figure 305091DEST_PATH_IMAGE008
And
Figure DEST_PATH_IMAGE009
are the maximum and minimum values of the incident height,
Figure 783346DEST_PATH_IMAGE010
greater than 100;
3. assuming that the light intensity distribution of the input light beam on the two-dimensional plane is
Figure DEST_PATH_IMAGE011
，
Figure 643855DEST_PATH_IMAGE012
Is 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,
Figure DEST_PATH_IMAGE013
is the 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 with flat top, 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 position coordinate of the emergent light beam on the output surfaceR itTheoretical value of (2):
Figure 496884DEST_PATH_IMAGE014
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
Figure DEST_PATH_IMAGE015
Wherein the content of the first and second substances,
Figure 228079DEST_PATH_IMAGE016
is the weighting factor of the ith ray.
5. Evaluation function and lens structure parametersC、
Figure 752602DEST_PATH_IMAGE005
、
Figure 38090DEST_PATH_IMAGE004
、d 1、d 2The 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 minimumC、
Figure 306260DEST_PATH_IMAGE005
、
Figure 360804DEST_PATH_IMAGE004
、d 1、d 2This 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:
Figure DEST_PATH_IMAGE017
by definition in matlab
Figure 852965DEST_PATH_IMAGE018
To obtain
Figure DEST_PATH_IMAGE019
；
(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:
Figure 159837DEST_PATH_IMAGE020
(3) from conservation of energy A = B, we obtain
Figure 966119DEST_PATH_IMAGE014
。
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 of
Figure DEST_PATH_IMAGE021
The 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 surfaces
Figure 671907DEST_PATH_IMAGE022
AndP i1can calculate the coordinate of the actual intersection point of the emergent ray and the output surfaceP i3 (x i3, y i3,0)，P i3 (x i3, y i30) is a lens construction parameterC、
Figure 538231DEST_PATH_IMAGE005
、
Figure 798312DEST_PATH_IMAGE004
、d 1、d 2A function of (a);
（2）P i1 (x i1, y i11) of (0)y i1Is thatIncident height of ith incident rayx iFromx iDetermining 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 combinationC、
Figure 408284DEST_PATH_IMAGE005
、
Figure DEST_PATH_IMAGE023
、
Figure 703000DEST_PATH_IMAGE024
、
Figure DEST_PATH_IMAGE025
、d 1、d 2The 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 of
Figure 333701DEST_PATH_IMAGE026
Let us orderI 0=1, gaussian spot radius
Figure DEST_PATH_IMAGE027
mm, the irradiation light intensity H =0.1 of the emergent beam, and the material used by the lens is SK2 glass with the 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
Figure 81077DEST_PATH_IMAGE001
In the above formula
Figure 294408DEST_PATH_IMAGE002
Is the height of any point of the aspheric surface from the axis,Cis the curvature of the apex and is,
Figure 912471DEST_PATH_IMAGE003
is the coefficient of the quadratic surface,
Figure 386178DEST_PATH_IMAGE004
is an aspheric surface deformation coefficient.
By adjusting the aspheric parameters of the front surface of the lensC、
Figure 152009DEST_PATH_IMAGE005
、
Figure 103784DEST_PATH_IMAGE023
、
Figure 841933DEST_PATH_IMAGE024
、
Figure 752120DEST_PATH_IMAGE025
、d 1、d 2As a component of each particle location vector in the particle swarm optimization algorithm, thus 7 variables in total, i.e., the dimension of each particle location vector in the particle swarm optimization algorithm is 7; the maximum off-axis height of the aspheric surface is larger than the radius of the incident Gaussian beam
Figure 208510DEST_PATH_IMAGE027
mm, the value range of each component of the position vector is shown in table 1:
Figure 963976DEST_PATH_IMAGE028
2. dispersing incident Gaussian beams into light rays, wherein N light rays are incident on a beam shaping lens, and the incident height of the ith incident light ray isx iLet us order
Figure DEST_PATH_IMAGE029
Figure 87790DEST_PATH_IMAGE030
And
Figure DEST_PATH_IMAGE031
respectively, the maximum and minimum of the incident height due to the Gaussian spot radius
Figure 434457DEST_PATH_IMAGE027
mm, therefore
Figure 378143DEST_PATH_IMAGE032
，
Figure DEST_PATH_IMAGE033
N is greater than 100, 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
Figure 471388DEST_PATH_IMAGE011
，I 0=1，y0For the intensity of the light falling to 1/e of the central value2The radius of the spot defined by (a),
Figure 184129DEST_PATH_IMAGE027
mm, y is the distance from any point in the beam to the center of the beam,
Figure 904961DEST_PATH_IMAGE013
the constant H is the intensity distribution value of the light beam with the flat-top output beam, H =0.1, for intensity at y from the center of the beam. 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). As can be seen from the figure 1, it is,
Figure 335942DEST_PATH_IMAGE034
and
Figure DEST_PATH_IMAGE035
inverse sign, therefore
Figure 964369DEST_PATH_IMAGE036
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
Figure DEST_PATH_IMAGE037
Wherein the content of the first and second substances,
Figure 328355DEST_PATH_IMAGE016
is the weight factor of the ith ray, in this example
Figure 220087DEST_PATH_IMAGE038
。
5. Evaluation function and lens structure parametersC、
Figure 138365DEST_PATH_IMAGE005
、
Figure 39325DEST_PATH_IMAGE023
、
Figure 461079DEST_PATH_IMAGE024
、
Figure 789292DEST_PATH_IMAGE025
、d 1、d 2The 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.
Figure DEST_PATH_IMAGE039
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:
Figure 460445DEST_PATH_IMAGE040
by definition in matlab
Figure 165095DEST_PATH_IMAGE018
To obtain
Figure DEST_PATH_IMAGE041
；
(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:
Figure 229304DEST_PATH_IMAGE042
(3) from the conservation of energy a = B, as can be seen again in fig. 1,
Figure 728419DEST_PATH_IMAGE034
and
Figure 355709DEST_PATH_IMAGE035
inverse sign, so as to obtain
Figure DEST_PATH_IMAGE043
。
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
Figure 51002DEST_PATH_IMAGE021
The 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 surfaces
Figure 978507DEST_PATH_IMAGE022
AndP i1can calculate the coordinate of the actual intersection point of the emergent ray and the output surfaceP i3 (x i3, y i3,0)；P i3 (x i3, y i30) is a lens construction parameterC、
Figure 179681DEST_PATH_IMAGE005
、
Figure 297197DEST_PATH_IMAGE004
、d 1、d 2A function of (a);
（2）P i1 (x i1, y i11) of (0)y i1That is, the incident height of the ith incident ray is highx iFromx iDetermining 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 (2)

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
Figure FDA0002761429240000011
In the above formula
Figure FDA0002761429240000012
Height of any point off axis of the aspheric surface, C being topPoint curvature, 1+ a2Is a coefficient of a quadratic surface2jThe method is characterized by comprising the following steps:
step 1 aspheric parameters C, a of the front lens surface2、a2jAnd distance d between the vertex of the front and rear surfaces of the lens1Distance d from the vertex of the rear surface to the output surface2As 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;
step 2, dispersing the 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 is xiiLet us order
Figure FDA0002761429240000013
ξmaxAnd ximinAre the maximum and minimum values of the incident height, N is greater than 100;
step 3 assumes that the light intensity distribution of the input light beam on the two-dimensional plane is
Figure FDA0002761429240000014
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 R of the emergent light beam and the output surfaceit：
Figure FDA0002761429240000015
Wherein erf is an erf function in matlab;
step 4, assuming that the coordinate value of the actual intersection point of the emergent ray and the output surface of the ith ray after the ith ray passes through the beam shaping lens is RiaAnd the theoretical value of the coordinates of the intersection point converted into the flat-topped beam according to the Gaussian beam is RitThe evaluation function F of the beam-shaping lens is then written as
Figure FDA0002761429240000021
Wherein, wiThe weighting factor of the ith ray;
step 5 evaluation of the function and lens configuration parameters C, a2、a2j、d1、d2The method is an invisible functional relation, the evaluation function is taken as a fitness function in the particle swarm optimization, minimum operation is carried out on the function, and the structural parameters C, a which enable the fitness function to be minimum can be obtained2、a2j、d1、d2The parameters of the shaping lens for converting the designed Gaussian beam into the flat-top beam;
the step 4 comprises the following steps:
step a, enabling the shaping lens to be rotationally symmetrical about an x axis, and assuming that incident rays of Gaussian beams are parallel to the x axis and unit vectors of the incident rays are
Figure FDA0002761429240000022
One point on the incident light ray has the coordinate of Pi1(xi1,yi10), from known quantities according to the law of refraction and the equation of the surface form of the front and back two refraction surfaces
Figure FDA0002761429240000023
And Pi1The actual intersection point coordinate P of the emergent ray and the output surface can be obtainedi3(xi3,yi3,0)；Pi3Is the lens configuration parameter C, a2、a2j、d1、d2A function of (a);
step b, Pi1(xi1,yi1Y in 0)i1I.e. the ith incident lightHigh xi of line incidenceiFrom xiiDetermining R in the evaluation function Fit；
Step c, Pi3(xi3,yi3Y in 0)i3Is to evaluate R in the function Fia；
Step d, from RiaAnd RitAn evaluation function F was obtained.
2. The method of claim 1, wherein the step 3 comprises the steps of:
step a, the energy enclosed by the ith incident ray and the optical axis:
Figure FDA0002761429240000031
get I0＝1，y07 mm; by definition in matlab
Figure FDA0002761429240000032
To obtain
Figure FDA0002761429240000033
Step b, the output light beam is a flat-top light beam with a light intensity distribution value of H and uniform distribution, and the energy surrounded by the ith output light beam and the optical axis is as follows: HR ═ Bit
Step c, obtaining the compound by taking the energy conservation A as B and H as 0.1
Figure FDA0002761429240000034
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