CN107544140B - Free-form surface lens design method based on genetic algorithm - Google Patents
Free-form surface lens design method based on genetic algorithm Download PDFInfo
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- CN107544140B CN107544140B CN201710954836.9A CN201710954836A CN107544140B CN 107544140 B CN107544140 B CN 107544140B CN 201710954836 A CN201710954836 A CN 201710954836A CN 107544140 B CN107544140 B CN 107544140B
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Abstract
The present invention provides a kind of free-form surface lens design method based on Gene hepatitis B vaccine, for designing free-form surface lens, the shaping to light intensity spatial distribution is realized, to meet such as the needs of laser peening, Uniform Illumination etc..The algorithmic statement is stablized, and the free-curved-surface-type being calculated is smooth continuous, is conducive to processing, and the transmission-type free-form curved mirror that the present invention obtains has very high optical damage threshold.
Description
Technical field
The present invention relates to optical technical fields, more particularly to a kind of free-form surface lens design side based on genetic algorithm
Method.
Background technique
Beam shaping is the regulation to the spatial intensity distribution of light beam, is had in Uniform Illumination, field of laser processing extensive
Application space.The design method of optical shaping element is broadly divided into two classes: first is that carrying out algorithm design using Fourier Optics
Diffraction element is to optical shaping；Second is that according to primary energy distribution and target beam Energy distribution, according to Si Nieerding
Rule and law of conservation of energy calculate the curved surface face type of transmission or reflection type optical element required for beam shaping.
It is studied in large quantities using the optical design thinking of iteration optimization algorithms and for designing diffractive-optical element progress
The shaping of laser pulse homogenizes, such as the optimization of input-output algorithm, genetic algorithm, GS algorithm and these algorithms
Version.The diffraction element that these algorithms are designed is well positioned to meet the needs of optical shaping, but its requirement on machining accuracy is high,
It is limited by diffraction limit, and damage threshold is low that (power is greater than damage threshold, then diffraction element is easy to be damaged, therefore, theoretical
On, damage threshold is the bigger the better), it may not apply to the shaping of high energy pulse laser, the industry for limiting this shaping element is answered
With.And the method for using snell law and law of conservation of energy to calculate curved surface face type, the optical element of design generally reflect
The smooth surface of type or transmission-type is able to bear higher pulsed laser energy.But due to needing analytically to obtain in calculating
The energy space distribution of output beam and output beam is obtained, institute cannot be advantageously applied in actual production irregular in this way
, the incident beam shaping for not having analytical form.
Therefore, the optical damage threshold of optical shaping element how is improved, simplifies processing technology and has become art technology
One of personnel's urgent problem to be solved.
Summary of the invention
In view of the foregoing deficiencies of prior art, the purpose of the present invention is to provide a kind of freedom based on genetic algorithm
Toroidal lens design method, the optical damage threshold for solving optical shaping element in the prior art is low, and processing technology is complicated
The problems such as.
In order to achieve the above objects and other related objects, the present invention provides a kind of free-form surface lens based on genetic algorithm
Design method, the incident beam of the free-form surface lens design method based on any intensity distribution based on genetic algorithm, until
Less the following steps are included:
Step S1: providing former generation's disaggregation of free-form surface lens position phase, and former generation's disaggregation includes one group of random focal length mark
The quantity of the equivalent phase of quasi- lens, the former generation Xie Jizhong individual is set as A；
Step S2: two individuals are arbitrarily chosen from the former generation Xie Jizhong and carry out crossover operation, generate population of new generation, institute
It states quantity individual in population of new generation and is set as B, wherein B > A；
Step S3: laser beam is calculated by the output of the corresponding free-form surface lens of individual each in the population of new generation
Light distribution；
Step S4: it is calculated separately based on the distribution of each output intensity and target laser intensity distribution each in the population of new generation
The fitness of individual, obtains the fitness function of each generation population；
Step S5: if getting a promotion after the fitness superposition of each individual in a new generation population, described new one is chosen
For A best individual of fitness in population as former generation's disaggregation of new generation, and return step S2 is recycled next time；If institute
It is no longer promoted after stating the fitness superposition of each individual in population of new generation, then end loop；
Step S6: after circulation terminates, free-form surface lens position phase is determined with latest generation former generation's disaggregation.
Preferably, in step sl, former generation's disaggregation is the continuous function of multinomial distribution.
Preferably, in step S2, two individuals of the former generation Xie Jizhong are operated using linear crossing or Nonlinear and crossing behaviour
Obtain the population of new generation.
It is highly preferred that the crossover operation meets following relational expression:
Wherein,For the n-th generation population；AndTo be selected at random from the former generation Xie Jizhong
Two individuals；fn(x, y) is the continuous function of the codomain that generates at random to individual each in the n-th generation population from 0 to 1.
It is highly preferred that the continuous function fn(x, y) meets following relational expression:
fn(x, y)=(q1+q2·x2+q3·x4+q4·x6)(q1+q2·y2+q3·y4+q4·y6) wherein, q1,q2,q3,q4
For the floating number generated at random.
Preferably, in step S3, output intensity distribution meets following relational expression:
Wherein, (x, y) is the coordinate of incoming position；(u, v) is the coordinate of target position；A (x, y) is light beam in incident position
The COMPLEX AMPLITUDE set；a'n(u, v) is the COMPLEX AMPLITUDE of Exit positions corresponding to each individual in the n-th generation population；For the corresponding free-form surface lens position phase of the n-th generation population；K is laser wave vector；Z is the propagation distance of laser.
Preferably, in step S4, respectively meet following relationship for the fitness function of population:
Wherein, F (n) is the n-th generation fitness function, a 'n(u, v) is Exit positions corresponding to each individual in the n-th generation population
COMPLEX AMPLITUDE；T is the target laser intensity distribution.
Preferably, the size of former generation's disaggregation and the convergence effect of genetic algorithm are directly proportional.
Preferably, it is defeated using discrete data that hot spot is inputted in the free-form surface lens design method based on genetic algorithm
Enter or parse data input.
As described above, the free-form surface lens design method of the invention based on genetic algorithm, has the advantages that
Free-form surface lens design method based on genetic algorithm of the invention uses Gene hepatitis B vaccine, by constantly changing
Generation and the free form surface for preferentially obtaining optimization, to realize the uniform shaping being distributed to any given incident beam, this method is received
Holding back property is stablized, and the free form surface being calculated can be ensured to be smooth continuous, and the transmission-type for being conducive to processing, and obtaining is freely bent
Face mirror has very high optical damage threshold.
Detailed description of the invention
Fig. 1 is shown as the intensity distribution schematic diagram of the incident field for the incident beam that the present invention uses.
Fig. 2 is shown as the flow diagram of the free-form surface lens design method of the invention based on genetic algorithm.
Fig. 3 is shown with oneself of the lens of the free-form surface lens design method design of the invention based on genetic algorithm
By curved surface profile schematic diagram.
Fig. 4 is shown as shoot laser intensity distribution schematic diagram of the present invention on objective plane.
Fig. 5 is shown as verifying system schematic of the invention.
Fig. 6 is shown as the spatial distribution schematic diagram of input light beam of the invention.
Fig. 7 is shown as the spatial distribution schematic diagram of outgoing beam of the invention.
Component label instructions
1 laser
2 free-form surface lens
3 charge coupling device imaging sensors
S1~S6 step
Specific embodiment
Illustrate embodiments of the present invention below by way of specific specific example, those skilled in the art can be by this specification
Other advantages and efficacy of the present invention can be easily understood for disclosed content.The present invention can also pass through in addition different specific realities
The mode of applying is embodied or practiced, the various details in this specification can also based on different viewpoints and application, without departing from
Various modifications or alterations are carried out under spirit of the invention.
Please refer to FIG. 1 to FIG. 7.It should be noted that diagram provided in the present embodiment only illustrates this in a schematic way
The basic conception of invention, only shown in schema then with related component in the present invention rather than package count when according to actual implementation
Mesh, shape and size are drawn, when actual implementation kenel, quantity and the ratio of each component can arbitrarily change for one kind, and its
Assembly layout kenel may also be increasingly complex, is applicable in any incident intensity distribution that is irregular, not having analytical form.
In the present embodiment, laser wavelength 1064nm, hot spot 9mm with a tight waist, circular Gaussian being distributed using genetic algorithm
Light beam design shaping lens (as shown in Figure 1) make emergent light spot form rectangular uniform light spots, lens at 1000mm after the lens
Material is PMMA.Each parameter of optical system can be set as needed in actual use, meanwhile, it is of the invention to be calculated based on gene
The free-form surface lens design method of method be suitable for any incident intensity distribution incident beam, Gaussian Profile can be met also with
It is unsatisfactory for Gaussian Profile, is not limited to this embodiment.
In the present embodiment, input hot spot is inputted using discrete data, and it is irregular quasi- high can be suitable for various distributions
This light beam does not need the analytical function of input beam spatial distribution, and it is defeated that parsing data can be used in input hot spot in practical applications
Enter, is not limited to this embodiment.Correspondingly, in the present embodiment, lens are divided into 256*256 lattice point, incident field and go out
The distribution of light intensity also discrete 256*256 data point for corresponding position is penetrated, the quantity of data point can be carried out according to the size of hot spot
It divides, is not limited to this embodiment.
As shown in Fig. 2, the free-form surface lens design method based on genetic algorithm the following steps are included:
Step S1: providing former generation's disaggregation of free-form surface lens position phase, and former generation's disaggregation includes one group of random focal length mark
The quantity of the equivalent phase of quasi- lens, the former generation Xie Jizhong individual is set as A.
Specifically, the size for setting former generation's disaggregation can ensure that and iterate to calculate by setting suitable disaggregation size
Optimal solution is converged in the process, and the bigger convergence effect of former generation's disaggregation is better, can set according to actual needs, not with this implementation
Example is limited.In the present embodiment, the quantity A of the former generation Xie Jizhong individual is set as 50.
Step S2: two individuals are arbitrarily chosen from the former generation Xie Jizhong and carry out crossover operation, generate population of new generation, institute
It states quantity individual in population of new generation and is set as B, wherein B > A.
Specifically, in the present embodiment, two individuals of the former generation Xie Jizhong operate to obtain described new using linear crossing
Generation population.In the present embodiment, quantity B individual in the population of new generation is set as 300.The crossover operation meets such as
Lower relational expression:
Wherein,For the n-th generation population；AndTo be selected at random from the former generation Xie Jizhong
Two individuals；fn(x, y) is the continuous function of the codomain that generates at random to individual each in the n-th generation population from 0 to 1.
To realize square focus spot shaping and homogenization, the continuous function fn(x, y) meets following relational expression:
fn(x, y)=(q1+q2·x2+q3·x4+q4·x6)(q1+q2·y2+q3·y4+q4·y6) wherein, q1,q2,q3,q4
For the floating number generated at random.
In the present embodiment, former generation's disaggregation is the continuous function of multinomial distribution, and is operated using linear crossing, really
Disaggregation is protected all and be the curved surface of continuous and derivable, has been conducive to process and improve damage threshold.
Step S3: laser beam is calculated by the output of the corresponding free-form surface lens of individual each in the population of new generation
Light distribution.
Specifically, output intensity distribution meets following relational expression:
Wherein, (x, y) is the coordinate of incoming position；(u, v) is the coordinate of target position；A (x, y) is light beam in incident position
The COMPLEX AMPLITUDE set；a'n(u, v) is the COMPLEX AMPLITUDE of Exit positions corresponding to each individual in the n-th generation population；For the corresponding free-form surface lens position phase of the n-th generation population；K is laser wave vector；Z is the propagation distance of laser.
Step S4: it is calculated separately based on the distribution of each output intensity and target laser intensity distribution each in the population of new generation
The fitness of individual, obtains the fitness function of each generation population.
Specifically, respectively meet following relationship for the fitness function of population:
Wherein, F (n) is the n-th generation fitness function, a 'n(u, v) is Exit positions corresponding to each individual in the n-th generation population
COMPLEX AMPLITUDE；T is the target laser intensity distribution.
Step S5: if getting a promotion after the fitness superposition of each individual in a new generation population, described new one is chosen
For A best individual of fitness in population as former generation's disaggregation of new generation, and return step S2 is recycled next time；If institute
It is no longer promoted after stating the fitness superposition of each individual in population of new generation, then end loop；
Step S6: after circulation terminates, free-form surface lens position phase is determined with latest generation former generation's disaggregation.
It is illustrated in figure 3 the lens of the free-form surface lens design method design using of the invention based on genetic algorithm
Free-Form Surface Profile S (x, y), the position phase introduced by free-form surface lensIt may be expressed as:
Wherein, S (x, y) is apparent height of the free form surface at (x, y) coordinate, n0For the refractive index of lens.More than ten
After secondary iterative cycles, the mean square deviation of the simulation outgoing Laser beam energy distribution of the free form surface of generation drops to 0.05.
It is illustrated in figure 4 the shoot laser intensity distribution on objective plane, rectangular Laser beam energy distribution has obvious clear
Clear failing edge, about 98% energy have been fallen in specified region, and the rectangular self-energy uniformity is up to 92%.
After completing the optimization to free form surface, Machining Free-Form Surfaces, simple process.As shown in figure 5, processing is obtained
Free-form surface lens 2 be placed in laser 1 and CCD (charge coupled device, charge coupling device image sensing
Device) between 3, through being imaged after the free-form surface lens after laser transmitting laser, image is acquired by the CCD.Such as Fig. 6 institute
It is shown as the spatial distribution of input light beam, Fig. 7 show the spatial distribution of outgoing beam, by Fig. 6 and Fig. 7 it is found that laser is from lens
Plane it is incident, free form surface outgoing obtains uniform square focus spot at imaging position.
It is smooth curved surface based on the free-form surface lens surface that the present invention designs, it is easy to process, and swash by high energy
When light impacts, damage threshold is higher, is suitably applied in the beam shaping of laser peening.The laser shaping of this transmission-type is compared
In there is smaller energy loss using the method for diffraction optical element, can be protected on the basis of generating designated shape hot spot
Demonstrate,prove enough laser energy output.
Free-form surface lens design method based on genetic algorithm of the invention uses Gene hepatitis B vaccine, by constantly changing
Generation and the free form surface for preferentially obtaining optimization, to realize the uniform shaping being distributed to any given incident beam, this method is received
Holding back property is stablized, and the free form surface being calculated can be ensured to be smooth continuous, and the transmission-type for being conducive to processing, and obtaining is freely bent
Face mirror has very high optical damage threshold.
In conclusion the invention proposes a kind of free-form surface lens design method based on iteration optimization algorithms, is applicable in
In any incident intensity distribution incident beam, it can be achieved that light beam shaping and homogenization.In the design of free-form surface lens,
Using Gene hepatitis B vaccine, the free form surface of optimization by continuous iteration and is preferentially obtained, to realize to any given incidence
The uniform shaping of beam distribution, the Algorithm Convergence are stablized, and the free form surface being calculated can be ensured to be smooth continuous, are conducive to
Processing, and there is very high optical damage threshold as transmission-type free-form curved mirror.So the present invention effectively overcome it is existing
Various shortcoming in technology and have high industrial utilization value.
The above-described embodiments merely illustrate the principles and effects of the present invention, and is not intended to limit the present invention.It is any ripe
The personage for knowing this technology all without departing from the spirit and scope of the present invention, carries out modifications and changes to above-described embodiment.Cause
This, institute is complete without departing from the spirit and technical ideas disclosed in the present invention by those of ordinary skill in the art such as
At all equivalent modifications or change, should be covered by the claims of the present invention.
Claims (7)
1. a kind of free-form surface lens design method based on genetic algorithm, which is characterized in that it is described based on genetic algorithm from
The incident beam being distributed by toroidal lens design method based on any incident intensity, is at least included the following steps:
Step S1: providing former generation's disaggregation of free-form surface lens position phase, and former generation's disaggregation includes that one group of random focal length standard is saturating
The quantity of the equivalent phase of mirror, the former generation Xie Jizhong individual is set as A；
Step S2: arbitrarily choosing two individuals from the former generation Xie Jizhong and carry out crossover operation, generates population of new generation, described new
Individual quantity is set as B in generation population, wherein B > A；The crossover operation meets following relational expression:
Wherein,For the corresponding free-form surface lens position phase of the n-th generation population,AndFor from institute
Two individuals that former generation Xie Jizhong is selected at random are stated,It is the codomain that is generated at random to individual each in the n-th generation population from 0
To 1 continuous function；
Step S3: laser beam is calculated by the output intensity of the corresponding free-form surface lens of individual each in the population of new generation
Distribution, output intensity distribution meet following relational expression:
Wherein,For the coordinate of incoming position,For the coordinate of target position,It is light beam in incoming position
COMPLEX AMPLITUDE,For in the n-th generation population it is each individual corresponding to Exit positions COMPLEX AMPLITUDE,
For the corresponding free-form surface lens position phase of the n-th generation population,For laser wave vector,For the propagation distance of laser；
Step S4: each individual in the population of new generation is calculated separately based on the distribution of each output intensity and target laser intensity distribution
Fitness, obtain the fitness function of each generation population；
Step S5: if getting a promotion after the fitness superposition of each individual in a new generation population, described a new generation kind is chosen
A best individual of fitness is as former generation's disaggregation of new generation in group, and return step S2 is recycled next time；If described new
It is no longer promoted after the fitness superposition of each individual in generation population, then end loop；
Step S6: after circulation terminates, determining free-form surface lens position phase with latest generation former generation's disaggregation, meets:, whereinFor laser wave vector,For the refractive index of lens,For freedom
Apparent height of the curved surface at (x, y) coordinate.
2. the free-form surface lens design method according to claim 1 based on genetic algorithm, it is characterised in that: in step
In S1, former generation's disaggregation is the continuous function of multinomial distribution.
3. the free-form surface lens design method according to claim 1 based on genetic algorithm, it is characterised in that: step S2
In, two individuals of the former generation Xie Jizhong are operated using linear crossing or Nonlinear and crossing operates to obtain the population of new generation.
4. the free-form surface lens design method according to claim 1 based on genetic algorithm, it is characterised in that: the company
Continuous functionMeet following relational expression:
Wherein,For the floating number generated at random.
5. the free-form surface lens design method according to claim 1 based on genetic algorithm, it is characterised in that: step S4
In, respectively meet following relationship for the fitness function of population:
Wherein,For the n-th generation fitness function,For the multiple vibration of Exit positions corresponding to individual each in the n-th generation population
Width distribution；T is the target laser intensity distribution.
6. the free-form surface lens design method according to claim 1 based on genetic algorithm, it is characterised in that: the father
The size of generation's disaggregation is directly proportional to the convergence effect of genetic algorithm.
7. the free-form surface lens design method according to claim 1 based on genetic algorithm, it is characterised in that: the base
Hot spot is inputted in the free-form surface lens design method of genetic algorithm inputs or parse data input using discrete data.
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| CN101477224A (en) * | 2009-01-20 | 2009-07-08 | 南京航空航天大学 | Bragg optical grating axial heterogeneous strain reconstruction method based on genetic planning |
| CN103246067A (en) * | 2013-05-23 | 2013-08-14 | 上海交通大学 | Method for shaping Gaussian laser beam into rectangular beam with uniformly distributed energy, and application of method |
| CN104836631A (en) * | 2015-03-04 | 2015-08-12 | 北京邮电大学 | Arbitrary-mode accurate conversion method based on genetic algorithm |
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| US5924788A (en) * | 1997-09-23 | 1999-07-20 | Teledyne Lighting And Display Products | Illuminating lens designed by extrinsic differential geometry |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN101477224A (en) * | 2009-01-20 | 2009-07-08 | 南京航空航天大学 | Bragg optical grating axial heterogeneous strain reconstruction method based on genetic planning |
| CN103246067A (en) * | 2013-05-23 | 2013-08-14 | 上海交通大学 | Method for shaping Gaussian laser beam into rectangular beam with uniformly distributed energy, and application of method |
| CN104836631A (en) * | 2015-03-04 | 2015-08-12 | 北京邮电大学 | Arbitrary-mode accurate conversion method based on genetic algorithm |
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