CN102313989A - A kind of method of single non-spherical lens aberration correction - Google Patents

A kind of method of single non-spherical lens aberration correction Download PDF

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CN102313989A
CN102313989A CN201110268994A CN201110268994A CN102313989A CN 102313989 A CN102313989 A CN 102313989A CN 201110268994 A CN201110268994 A CN 201110268994A CN 201110268994 A CN201110268994 A CN 201110268994A CN 102313989 A CN102313989 A CN 102313989A
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秦华
张伟元
孙存志
宋延松
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Shandong University of Technology
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Abstract

The invention discloses a kind of non-spherical lens design and aberration correcting method, at first designed vertex curvature radius about the aspheric surface equation of higher degree r, equation of higher degree each item coefficient
Figure 2011102689941100004DEST_PATH_IMAGE001
,
Figure 125573DEST_PATH_IMAGE002
Figure DEST_PATH_IMAGE003
, the distance between the lens face dAs the optical system structure parameter; Position and speed by these structural parameters structure population; Position calculation by population goes out fitness function, finds out the historical optimum position Gbest that historical optimum position Pbest that each particle experiences and colony are experienced with this function as evaluation function; Utilize Pbest and Gbest that population is carried out position and Velocity Updating; Calculate particle once more at this locational fitness function, upgrade the historical optimum position Gbest that historical optimum position Pbest that each particle experiences and colony are experienced; So move in circles, till finding satisfied fitness value or being recycled to maximum iterations, output Gbest is the optical system structure parameter.

Description

A kind of method of single non-spherical lens aberration correction
Technical field
The present invention relates to a kind of aberration correcting method, especially a kind of method of utilizing particle cluster algorithm to carry out single non-spherical lens aberration correction.。
Background technology
Damped least square method is as the widespread use in the overwhelming majority's optical design software of most popular optimized Algorithm.The ultimate principle of this optimized Algorithm, the firstth, linear-apporximation promptly replaces actual non-linear aberration equations group with the aberration system of linear equations, replaces difference quotient with difference coefficient; The secondth, progressive one by one.Linear-apporximation can only be just meaningful in the less on every side independent variable space of primal system, therefore can only use one by one progressive way, and system is progressively improved.Another important feature of this method is at first to provide a primal system; Just possibly the method with numerical evaluation set up approximate aberration system of linear equations, do like this and in fact can only near primal system, find one and separate preferably at the original starting point place in independent variable space.And this separates to differ and meets the demands surely, and is not preferably separating of system probably.In order to overcome these problems that damped least square method exists, people constantly seek the new method that optical system is optimized.
For the design and the optimization of aspheric surface system, can participate in correction optimization with other structure variable of system the high-order term coefficient of aspheric surface equation as the optical system structure variable.But the result who does like this increases sharply the structure variable of optical system, and the aberration system of linear equations increases rapidly, and calculated amount is multiplied.
The method of existing solution damped least square method local minimum problem comprises global search, simulated annealing, escape function algorithm and genetic algorithm etc. global search and simulated annealing have solved the local minimum problem in the optimizing process; But these algorithms have and consume that optimization time is exponential growth with the increase of variable quantity and because random sampling and obtain shortcoming such as some systems that can't realize (marginal as occurring, negative center thickness etc.) easily can only be used for the analysis of single system.The escape function algorithm that Isshiki proposes has been realized jumping out automatically local minimum and has been continued to seek other better optical texture through evaluation function being added the method for an escape function, and this algorithm has overcome the shortcoming of global search and simulated annealing.The optical design optimized Algorithm of more than mentioning all is on the basis of having selected the initial optical structure, just the optical texture parameter is optimized selection, and the intelligent degree of its design of Optical System also is not very high.
Summary of the invention
For solving the problems of the technologies described above, the present invention has adopted following technical scheme:
Regard each optimised aspheric optical system structural parameters as a particle (Particle), particle position vector dimension and velocity dimension D are determined by the system structure parameter variable.System structure parameter comprises C, a in the aspheric surface equation of higher degree (1) 2, a 4, a 6, a 8, a 10, a 12, a 14, a 16And between the minute surface apart from d etc.
Figure 168606DEST_PATH_IMAGE001
(1)
In the formula (1) xBe the amount of bow of curved surface, Be the height of incidence of light, C is the curvature on aspheric surface summit,
Figure 359733DEST_PATH_IMAGE003
Be the high order aspheric surface coefficient,
Figure 242239DEST_PATH_IMAGE004
Be the constant relevant with quadric eccentricity.
Concrete steps are:
1. with the population initialization.Use DDimensional vector Xi=( x I1 , x I2 ..., x ID ) represent iThe position of individual particulate is used V i=( υ i1 , υ i1 , υ ID ) represent iThe speed of individual particulate.Provide the initial position X of each particle with random fashion iWith speed V iInitial position is relevant with the hunting zone, and this hunting zone can be set according to system structure parameter.
2. calculate fitness function Φ (fitness function).Fitness function Φ, promptly optimised function provides each particle and each mechanism for population estimated.The evaluation function (MF:merit function) that we get in the optical design is a fitness function, promptly
Figure 594722DEST_PATH_IMAGE005
, in the formula
Figure 6112DEST_PATH_IMAGE006
Be poor, the promptly actual residual amount of aberration of system's actual aberration and desired value, q iIt is a weight coefficient.Evaluation function
Figure 444047DEST_PATH_IMAGE007
the residual amount of more little aberration is more little, more near our requirement. Be the residual amount of a sensu lato aberration, comprise the various geometrical aberrations or the wave aberration of representative system image quality, also comprise the characterisitic parameter of some paraxial optics, like focal length f', an axle magnification hangs down β, conjugate distance L Conj(distance between principal plane), image distance l', system's length overall OL(first face is the distance of one side to the end), lens barrel is long TL(first distance), glass gross thickness maximal value to image planes GL Max , emergent pupil is apart from projection height on the emergent pupil face of, full visual field chief ray, maximum defocus amount etc.; That participates in correction actually in these ten parameters; Must select according to concrete designing requirement by the deviser, in addition, also must provide the desired value that they require each parameter of participating in correction; And being different from the aberration that kind, desired value is zero forever.
3. seek Pbest and Gbest.Fitness function value according to each particle
Figure 806075DEST_PATH_IMAGE005
, find out the optimum position that it is experienced self in each particle search process up to the present P i=( p i1 , p i2 , p ID ), be also referred to as Pbest, the optimum position Gbest that all particulates live through.
4. according to speed and the position of formula (2) with formula (3) Refreshing Every particle.Return step 2, till obtaining a gratifying result or meeting the termination condition
Figure 919525DEST_PATH_IMAGE008
(2)
Figure 313597DEST_PATH_IMAGE009
(3)
Wherein , i=1,2 ..., M, MIt is the sum of particle in this colony;
Figure 537905DEST_PATH_IMAGE010
Be inertia weight (inertia weight); Be kInferior iteration particle iOf flight velocity vector nThe dimension component;
Figure 352594DEST_PATH_IMAGE012
Be kInferior iteration particle iOf position vector nThe dimension component;
Figure 765121DEST_PATH_IMAGE013
For iThe of the individual desired positions Pbest of particle nThe dimension component;
Figure 261961DEST_PATH_IMAGE014
Be of the desired positions Gbest of colony nThe dimension component;
Figure 443544DEST_PATH_IMAGE015
,
Figure 633217DEST_PATH_IMAGE016
Be weight factor, also claim the study factor; Rand () produces the uniform random number between [0,1].
Said step 1 comprises following steps:
A. designing the employed particle position vector of single non-spherical lens dimension is 10 dimensions, promptly Xi=( x i1 , x i2 ..., x ID )=( C, d 1,
Figure 500416DEST_PATH_IMAGE017
), D=10.
B. C =1/ r(r is the radius-of-curvature on aspheric surface summit) selected r> h Max ( h Max Maximum incident height for incident ray); Select to be not less than 0 apart from d to guarantee the positive lens edge thickness between the minute surface, the hunting zone apart from d between the single non-spherical lens minute surface generally is set in 1/3* h Max With 4/3* h Max Between; Choose
Figure 535368DEST_PATH_IMAGE018
,
Figure 837037DEST_PATH_IMAGE019
Extremely
Figure 197611DEST_PATH_IMAGE020
Value exist
Figure 53572DEST_PATH_IMAGE021
Extremely
Figure 423373DEST_PATH_IMAGE022
Near.
C. occur in the system iterative dispersing in order to prevent, need be to the maximal rate υ of particle MaxLimit.Get υ Max=X Max-X Min, υ Min=-υ MaxInitial velocity V iAt υ MaxAnd υ MinBetween generate at random.
D. getting the population number is between 50 ~ 100.
E. according to particle position among b, the c and speed setting scope, generate the initial position of population at random Xi=( x i1 , x i2 ..., x ID )=( C, d 1,
Figure 313969DEST_PATH_IMAGE023
) and initial velocity V i=( υ i1 , υ i2 , υ ID ).
Said step 2 comprises following steps:
A. list the aberration that needs correction: comprise the broad sense aberration, like focal length f', an axle magnification hangs down β, conjugate distance L Conj(distance between principal plane), image distance l', system's length overall OL(first face is the distance of one side to the end), lens barrel is long TL(first distance), glass gross thickness maximal value to image planes GL Max , emergent pupil is apart from projection height on the emergent pupil face of, full visual field chief ray, maximum defocus amount etc.
B. according to particle position Xi=( x i1 , x i2 ..., x ID )=( C, d 1,
Figure 579865DEST_PATH_IMAGE023
) the listed aberration value of calculating
Figure 188701DEST_PATH_IMAGE006
C. obtain fitness function, i.e.
Figure 362193DEST_PATH_IMAGE024
to square rear weight summation of listed aberration value.
Said step 3 comprises following steps:
A. find out the historical desired positions that each particle is experienced self according to fitness function, and be stored in this desired positions among the Pbest (i).
B. find out the historical desired positions that whole population experiences according to fitness function, and this location storage in Gbest.
Said step 4 comprises following steps:
A. weighting function
Figure 841716DEST_PATH_IMAGE025
Confirm by following formula:
Figure 809672DEST_PATH_IMAGE026
(4)
Where,
Figure 374646DEST_PATH_IMAGE027
and
Figure 86250DEST_PATH_IMAGE028
are The maximum and minimum; ,
Figure 611406DEST_PATH_IMAGE031
, respectively, is the current iteration number and maximum number of iterations.Get ,
Figure 846395DEST_PATH_IMAGE033
b.? Select study factor
Figure 135249DEST_PATH_IMAGE034
=
Figure 205973DEST_PATH_IMAGE016
= 2.
C. according to the speed and the position of formula (2), (3) Refreshing Every particulate
D. return step 2 circulation after particle upgrades, till the condition that satisfies loop ends.
Beneficial effect of the present invention
(1) spherical aberration correction that utilizes particle cluster algorithm to carry out single non-spherical lens only need know lens focal length, entrance pupil diameter and the glass material that will use, be prone to understand, parameter is few, overcome the requirement of existing optical design software to initial configuration.
(2) utilize particle cluster algorithm to carry out the non-spherical lens design and can obtain a series of good results in overall solution space, intelligent degree is high.Select wherein a kind of according to actual needs as optimal selection.
(3) be different from the least square method that the contemporary optics design software mostly adopts, need do not calculate the difference coefficient matrix, calculated amount is few, has therefore saved a large amount of computing times.
Below in conjunction with accompanying drawing and embodiment the present invention is further specified
Description of drawings:
Fig. 1 is the process flow diagram that carries out the non-spherical lens design with particle cluster algorithm;
Fig. 2 is the detail operations process flow diagram of the embodiment of the invention 1;
The design optimization result of Fig. 3 embodiment of the invention 1, the index path corresponding with table 3 in the instructions;
The design optimization result of Fig. 4 embodiment of the invention 1, the index path corresponding with table 4 in the instructions;
The design optimization result of Fig. 5 embodiment of the invention 1, the index path corresponding with table 5 in the instructions;
Fig. 6. the embodiment of the invention 1 usefulness PSO algorithm obtains serial Optimization result (the corresponding evaluation function value of the numeric representation among the figure)
Embodiment:
Embodiment 1: seeing also Fig. 1 and Fig. 2, is example with the simple lens, and the front surface of lens is an aspheric surface, and the surface, back is the plane.Main spherical aberration corrector, optical property parameter is following: object distance l=∞; The entrance pupil diameter D Max=120 (maximum incident height on the pupil h Max =60); Objective focal length Entrance pupil exists l z=0.These length amount units all are millimeters.
It is following that the initialization of said step 1 population comprises step: the hunting zone of selective system structural parameters.A. select r h Max + 5 to h Max Between+100, promptly between 65 to 160; B. select d at 1/3* h Max With 4/3* h Max Between, promptly between 20 and 80; C. select
Figure 568002DEST_PATH_IMAGE036
, promptly-6.1111≤a 2≤6.1111; D. set
Figure 517503DEST_PATH_IMAGE037
,
Figure 809944DEST_PATH_IMAGE038
,
Figure 135883DEST_PATH_IMAGE039
,
Figure 830170DEST_PATH_IMAGE040
,
Figure 481731DEST_PATH_IMAGE041
,
Figure 995889DEST_PATH_IMAGE042
,
Figure 391098DEST_PATH_IMAGE043
C. iThe position of individual particulate Xi=( x i1 , x i2 ..., x ID )=( C, d 1,
Figure 408733DEST_PATH_IMAGE017
) in aspheric surface parameter search scope, produce at random, here D=10.The iThe speed of individual particulate V i=( υ i1 , υ i2 , υ ID ) υ iNmax With- υ iNmax Between produce at random, wherein υ iNmax = x INmax - x iNmin , N is an integer between 1 to D.
The single non-spherical lens aspheric surface parameters of choice scope (maximal value and minimum value separate with comma) of having listed that form 1 is neat.
Figure 496775DEST_PATH_IMAGE044
It is following that said step 2 confirms that fitness function Φ comprises step: we want six spherical aberrations of corrective system from
Figure 232649DEST_PATH_IMAGE045
six incidence points a., here
Figure 431550DEST_PATH_IMAGE046
.B. focal length is participated in the design correction as the aberration of broad sense with six spherical aberrations together, and such 7 aberrations get into correction in the lump.C. confirm in the system aberration desired value and the tolerance that will proofread and correct see table 2
Figure 562634DEST_PATH_IMAGE048
D. by particle position Xi=( x i1 , x i2 ..., x I10 ) calculate from
Figure 316963DEST_PATH_IMAGE049
Six spherical aberrations at six incidence point places,
Figure 21352DEST_PATH_IMAGE046
Figure 544737DEST_PATH_IMAGE047
E. by particle position Xi=( x i1 , x i2 ..., x ID ) the computing system focal length, the difference of calculating resultant focal length and target focal length is as the broad sense aberration.What f. d and e obtained is exactly , the weight of six kinds of spherical aberrations and focus difference all as 1, promptly q i=1, according to formula
Figure 419469DEST_PATH_IMAGE005
Calculate fitness function.
It is following that said step 3 comprises step: a. finds out the historical optimum position of each particle according to fitness function P i=( p i1 , p i2 , p ID ), P iBe stored in Pbest (i).B. find out the historical optimum position that whole population experiences and be stored in Gbest according to fitness function.
Said step 4 is following: a. gets
Figure 429013DEST_PATH_IMAGE032
;
Figure 72484DEST_PATH_IMAGE033
, the study factor =
Figure 605414DEST_PATH_IMAGE016
=2.Speed and position by formula (2), (3) and (4) Refreshing Every particulate.B. get back to step 2 and continue loop iteration, appoint and get iterations T Max=1000, till reaching cycling condition.
Table 3, table 4 and table 5 are to have write down the design optimization result three times, have obtained the numerical value of the parameters optimization of wanting, and have also write down the optimal value of wanting optimization aim, i.e. focal length and six axle spherical aberrations of hanging down.
  
The single aspheric lens structures parameter after table 3 design is accomplished and the axle spherical aberration of hanging down
Figure 684228DEST_PATH_IMAGE050
The single aspheric lens structures parameter after table 4 design is accomplished and the axle spherical aberration of hanging down
Figure 651047DEST_PATH_IMAGE051
The single aspheric lens structures parameter after table 5 design is accomplished and the axle spherical aberration of hanging down
Figure 157115DEST_PATH_IMAGE052

Claims (4)

1. the method for designing of a single non-spherical lens, especially a kind of method of utilizing particle cluster algorithm to carry out the non-spherical lens aberration correction is characterized in that comprising the steps:
(1) regard each optimised aspheric optical system structural parameters as a particle (Particle), particle position vector dimension and velocity dimension D are determined by the system structure parameter variable;
(2) confirm C, a in the aspheric surface equation of higher degree (1) 2, a 4, a 6, a 8, a 10, a 12, a 14, a 16And be system structure parameter apart from d between the minute surface;
Figure 460426DEST_PATH_IMAGE001
(1)
?
Wherein xBe the amount of bow of curved surface,
Figure 402974DEST_PATH_IMAGE002
Be the height of incidence of light, C is the curvature on aspheric surface summit, Be the high order aspheric surface coefficient,
Figure 963323DEST_PATH_IMAGE004
Be the constant relevant with quadric eccentricity;
(3) initial position of particle Xi=( x I1 , x I2 ..., x i10 ) and initial velocity V i=( υ i1 , υ i2 , υ I10) generation;
(4) fitness function
Figure 170314DEST_PATH_IMAGE005
, the confirming of promptly optimised function;
(5) seek the historical optimum position that up to the present each particle self experiences P i=( p i1 , p i2 , p ID ), be also referred to as Pbest; Seek the historical optimum position Gbest of all particulate experience;
(6) speed of each particle and position renewal mode confirms;
(7) program loop iteration stopping condition is set at iterations 1000 ~ 5000 times or fitness function less than 0.001;
Table 1
Figure 221446DEST_PATH_IMAGE006
Table 2
Figure 146677DEST_PATH_IMAGE007
Table 3
(8) the single aspheric lens structures supplemental characteristic that uses the inventive method to obtain, it is included in table 1, table 2 and the table 3.
2. according to the method for designing of a kind of single non-spherical lens of claim 1, it is characterized in that said step (3) comprises the steps:
(a) radius-of-curvature on selection aspheric surface summit r> h Max ( h Max Maximum incident height for incident ray), C =1/ r, be set in 1/3* apart from d between the minute surface h Max With 4/3* h Max Between, choose ,
Figure 654516DEST_PATH_IMAGE010
Extremely
Figure 67043DEST_PATH_IMAGE011
Value exist
Figure 32725DEST_PATH_IMAGE012
Extremely Near;
(b) Xi=( x i1 , x i2 ..., x i10 )=( C, d 1, ), XiHunting zone such as claims 2 in (a) said, XiInitial position be the equally distributed random number in its hunting zone;
(c) get υ iNmax = x INmax - x iNmin , N is an integer between 1 to 10, υ iNmin =-υ iNmax , initial velocity V i=( υ i1 , υ i2 , υ i10 ) υ iNmax With- υ INmax Between generate at random.
3. according to the method for designing of a kind of single non-spherical lens of claim 1, it is characterized in that said step (4) comprises the steps:
(a) list spherical aberration and the focal length that need proofread and correct as the broad sense aberration design on six different incident height proofreading and correct;
(b) by particle position Xi=( x i1 , x i2 ..., x i10 ) the listed aberration value of calculating , the difference of focal length that current particle position calculates and target focal length is as the broad sense aberration;
(c) obtain fitness function, i.e. to square rear weight summation of listed aberration value.
4. according to the method for designing of a kind of single non-spherical lens of claim 1, it is characterized in that said step (6) comprises the steps:
(a) according to the speed and the position of formula (2), (3) Refreshing Every particulate
Figure 613660DEST_PATH_IMAGE017
(2)
Figure 177496DEST_PATH_IMAGE018
(3)
Wherein , i=1,2 ..., M, MIt is the sum of particle in this colony;
Figure 299036DEST_PATH_IMAGE019
Be inertia weight;
Figure 668837DEST_PATH_IMAGE020
Be kInferior iteration particle iOf flight velocity vector nThe dimension component; Be kInferior iteration particle iOf position vector nThe dimension component;
Figure 559750DEST_PATH_IMAGE022
For iThe of the individual desired positions Pbest of particle nThe dimension component;
Figure 168586DEST_PATH_IMAGE023
Be of the desired positions Gbest of colony nThe dimension component;
Figure 14182DEST_PATH_IMAGE024
,
Figure 24863DEST_PATH_IMAGE025
Be weight factor, also claim the study factor; Rand () produces the uniform random number between [0,1];
(b) weighting function
Figure 992819DEST_PATH_IMAGE026
is confirmed by formula (4):
Figure 525170DEST_PATH_IMAGE027
(4)
Figure 236774DEST_PATH_IMAGE028
and
Figure 101962DEST_PATH_IMAGE029
are
Figure 178502DEST_PATH_IMAGE030
The maximum and minimum;
Figure 761930DEST_PATH_IMAGE031
,
Figure 277225DEST_PATH_IMAGE032
, respectively, is the current iteration number and maximum number of iterations, whichever
Figure 934602DEST_PATH_IMAGE033
, ;
(C) the learning factor
Figure 315085DEST_PATH_IMAGE035
=
Figure 306175DEST_PATH_IMAGE025
= 2.
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CN112033645A (en) * 2020-08-07 2020-12-04 深圳市速腾聚创科技有限公司 Waveguide grating structure parameter determination method and device, storage medium and laser radar
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CN113960108A (en) * 2021-09-24 2022-01-21 株洲国创轨道科技有限公司 Method and system for simultaneously measuring heat conductivity coefficient and specific heat capacity of carbon fiber composite material
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