Advances in optical design and optimization of miniature zoom optics with liquid lens element

Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology

Advances in optical design and optimization of miniature zoom optics with liquid lens element

1Cheng-Mu Tsai and 2Yi-Chin Fang1Dept. of Computer and Communication, Kun Shan University,

No.949, Da Wan Rd., Yung-Kang Dist., Tainan City 710, Taiwan. E-mail: [email protected]

2Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology, No. 2, Jhuoyue Rd.,

Nanzih Dist., Kaohsiung City 811, Taiwan, R.O.C. E-mail: [email protected]

Reporter: Yi-Chin Fang


2

Outline

Introduction Discussion of the primary field curvature

aberration The optical design of a preliminary telecentric

projector lens Suppression of the Petzval field curvature

aberration based on a genetic algorithm Simulation result and discussion Conclusions


3

What Issues in Optical System Design

There are five primary monochromatic aberrations in optical system Spherical Coma Astigmatism Field Curvature Distortion

Two kinds of primary chromatic aberration in optical system Lateral Chromatic Aberration Axial Chromatic Aberration


4

Advance Technology

The task of optimization in optical systems is now undertaken efficiently, partly because advances in computing aspherical surfaces antireflection coatings new developments in optical glass

From the point of view of optics optimization, ray tracing based on geometrical optics is still more efficient than time-consuming wave aberration calculation based on physical optics;


5

where hp is the radius of the exit pupil, and hmax is the maximum height of the Gaussian image. The five terms on the right-hand side of Equation are called Seidel aberrations. In order of presentation, they are the spherical aberration, coma, astigmatism, field curvature and distortion.

Seidel aberrations

sorder termhigher and third

3max

3

2

12max

2

2)22(

)(4

1

2max

2

22

2

1

max3)22(

2

14

2)22(

8

1),,(

ph

yVS

ph

yxIVSIIIS

ph

yIIIS

ph

yxyIIS

ph

yxISyxW


6

Seidel Sum (1)

The correlation coefficients SI ~ SV are known as the Seidel Sum, which can be derived from paraxial optics theory as follows:

surfaces all

2n

uhAIS

surfaces all n

uAhAIIS

surfaces all

2

n

uhAIIIS

surfaces all

12n

cHIVS

surfaces all

123

ncH

A

A

n

uh

A

AVS


7

The ray tracing for each parameter

(n ) (n ')

u u 'h

uu '

h '

m arg in a lray

ch ie f rayp u p il


8

Discussion of Petzval aberration Observing the transverse aberration, it is easy

to see that the other Seidel Sum of the primary FCA, SIV, depends on the refractive index and the curvature of the lens system.

The transverse aberration can be derived from

where R is the radius of the reference sphere which passes through the center of the exit pupil.

y

W

n

Rx

W

n

R


9

Petzval curvature aberrations

P u p il

G au ss ianIm ag e P lan e

P e tz v a l C u rv a tu reS u rface

R efe ren ce S p h e re

R h p -u


10

Derivation of Petzval field curvature aberrations (1) Assuming that the ratio of the variation of ray

tracing from exit pupil to the transverse aberration of the Gaussian image plane is a constant, the distance between the real image and the Gaussian image plane is

2max

2

22

2max

2

2)22(

4

1

ph

xIVSn

R

ph

yxIVSxn

Rx

R

2max

2

22

2max

2

2)22(

4

1

ph

yIVSn

R

ph

yxIVSyn

Ry

R

2max

2

21

2

2

ph

IVSn

R


11

Derivation of Petzval field curvature aberrations (2)

According to the spherical wavefront approximation equation, is as follows:

Here CPetzval is the curvature of the Petzval field plane and is equal to nSIV/H2.

Since the Lagrange invariant H is a constant, H = nuh = n'u'h', it will not change as a ray tracing in a different plane.

The Petzval FCA is induced by the refractive index and curvature of the lens system only.

2max

2

22max

2

22

PetzvalC

nu

IVS22)( H

IVnS

nu

IVnSPetzvalC


12

Preliminary design of a projector lens

09:43:54


13

Parameters for the preliminary design

U L T R A N 3 0 _ S C H O T T

S u rface#

O b jec t123

S u rfaceT yp e

456789

1 0111 21 31 41 5

s to p1 71 81 92 02 12 22 32 42 52 62 72 82 93 03 13 23 3

Im ag e

S p h e reS p h e reS p h e reS p h e reS p h e reS p h e reS p h e reS p h e reS p h e reS p h e reS p h e reS p h e reS p h e reS p h e reS p h e reS p h e reS p h e reS p h e reS p h e reS p h e reS p h e reS p h e reS p h e reS p h e reS p h e reS p h e reS p h e reS p h e reS p h e reS p h e reS p h e reS p h e reS p h e reS p h e reS p h e re

YC u rv a tu re

0 .0 0 0 00 .0 0 8 40 .0 0 0 00 .0 2 2 20 .0 3 4 2

-0 .0 0 3 50 .0 3 5 10 .0 0 0 40 .0 0 7 40 .0 0 0 00 .0 1 3 9

-0 .0 0 3 00 .0 3 6 00 .0 0 1 90 .0 3 9 50 .0 6 7 80 .0 0 0 0

-0 .0 7 0 20 .0 1 6 1

-0 .0 4 4 60 .0 0 7 1

-0 .0 3 0 70 .0 0 9 1

-0 .0 0 5 6-0 .0 2 5 8-0 .0 0 8 30 .0 0 6 3

-0 .0 0 4 80 .0 1 5 90 .0 0 0 00 .0 0 0 0

Z o o m6 .3 8 0 21 .0 0 0 06 .9 9 3 48 .7 1 3 41 .6 0 0 05 .7 2 5 81 .6 0 0 0Z o o mZ o o m

3 .4 2 6 10 .1 0 0 05 .11 5 50 .6 8 4 67 .0 0 0 0Z o o m

1 0 .1 8 1 01 .6 0 0 06 .7 4 9 40 .1 0 0 05 .2 6 3 40 .1 0 0 02 .9 2 7 2Z o o m

1 .3 0 0 00 .1 0 0 02 .6 2 2 30 .1 0 0 03 .2 1 3 13 .6 2 3 2

1 9 .2 5 0 0

T h ick n ess G lass

6 2 3 5 6 9 _ C H A N C E

C 1 6 4 4 _ C O R N F R

B 1 8 6 5 _ C O R N F R

N P S K 5 7 _ S C H O T T

6 5 2 5 8 5 _ C H A N C E

B 2 9 7 7 _ C O R N F R

8 0 5 2 5 4 _ C H A N C E7 3 4 5 1 7 _ C H A N C E

S B A H 2 7 _ O H A R A

Z F 3 _ C H IN A

F F 8 _ H O Y A

6 5 8 5 0 9 _ C H A N C E

B 1 8 6 5 _ C O R N F R

B K 7 _ S C H O T T1 .5 0 0 03 .0 0 0 00 .4 4 5 00 .0 0 0 0

0 .0 0 0 00 .0 0 0 00 .0 0 0 00 .0 0 0 0

Z K N 7 _ S C H O T T

S u rface#

O b jec t

Z o o m 1 1 5 0 0 .0 0Z o o m 2 1 5 0 0 .0 0

9 1 5 2 38

Z o o m 3Z o o m 4Z o o m 5Z o o m 6Z o o m 7Z o o m 8Z o o m 9

Z o o m 1 0Z o o m 1 1Z o o m 1 2

1 5 0 0 .0 02 0 0 0 .0 02 0 0 0 .0 02 0 0 0 .0 03 5 0 0 .0 03 5 0 0 .0 03 5 0 0 .0 0In fin ityIn fin ityIn fin ity

11 .3 1 8 65 .8 9 2 41 .3 3 3 4

11 .3 1 8 65 .8 9 2 41 .3 3 3 4

11 .3 1 8 65 .8 9 2 41 .3 3 3 4

11 .3 1 8 65 .8 9 2 41 .3 3 3 4

1 3 .1 2 5 5

1 2 .8 4 9 8

1 2 .8 4 9 8

1 2 .4 6 4 3

1 3 .1 2 5 5

1 2 .8 4 9 8

1 2 .8 4 9 8

1 2 .4 6 4 3

1 3 .1 2 5 5

1 2 .8 4 9 8

1 2 .8 4 9 8

1 2 .4 6 4 3

2 .5 0 0 03 .0 5 8 93 .8 7 8 72 .5 0 0 03 .0 5 8 93 .8 7 8 72 .5 0 0 03 .0 5 8 93 .8 7 8 72 .5 0 0 03 .0 5 8 93 .8 7 8 7

2 .5 4 1 54 .2 9 5 16 .0 2 7 82 .5 4 1 54 .2 9 5 16 .0 2 7 82 .5 4 1 54 .2 9 5 16 .0 2 7 82 .5 4 1 54 .2 9 5 16 .0 2 7 8

Basic parameters

Zoom parameters


14

Genetic Algorithm (GA) Concept

The concept of the Genetic Algorithm (GA) process is to evolve multiple groups of genes (e.g., factors) into adapting to an environment (that is, a specification)

Advantage

Search the global optimum The designer just needs less experience when

applying in optical system design Easy to assemble in optical system


15

Genetic Algorithm (GA) Operation

The function of the GA process are Initial population Selection Crossover Mutation

S T A R T

In itia liz a tio n

M e e t s to p p in g c rite r io n ?

G e n e tic a lg o rith m o p e ra to r(S e le c tio n , C ro sso v e r, a n d M u ta tio n )

T h e p o p u la tio n o f n e x t g e n e ra tio n a reg e n e ra te d a n d f itn e ss v a lu e s a re c a lc u la te d

fu n c tio n c a lls a n d fitn e ss D isp la y th e n u m b e ro f v a lu e

E N D

Y e s

N o


16

The gene parameters of the radius of curvature of lenses.

Simulation Results (1)Gens Best Worst Average STDev |STDev/Average| %

1 0.008200638 0.010745568 0.008150558 0.001104469 13.550836022 0 0 0 03 0.026172262 0.020537276 0.021350615 0.002022467 9.4726409114 0.034250016 0.034559981 0.033583391 0.003223503 9.5985029895 -0.00447862 -0.00338202 -0.00375611 0.000797156 21.222901866 0.033516105 0.039275143 0.03482914 0.004433354 12.728864647 0.000480362 0.00012328 0.000355602 0.00010314 29.004383878 0.006798957 0.007435932 0.006992664 0.001303493 18.640864419 0 0 0 0

10 0.01772096 0.012220861 0.014135493 0.002468046 17.4599207911 -0.00298807 -0.0033461 -0.00301753 0.000408348 13.5325123912 0.021758794 0.030991206 0.034327732 0.005395116 15.7164949813 0.00188702 0.002184809 0.002001932 0.00064071 32.0045770114 0.040774723 0.036235618 0.036888106 0.005181307 14.0460092515 0.071067256 0.059705787 0.071176197 0.007906087 11.1077677316 -0.08049826 -0.06713062 -0.07170608 0.006485533 9.04460600517 0.017062749 0.015506293 0.015825294 0.005840468 36.9059046718 -0.04816133 -0.05252434 -0.04447333 0.004449484 10.0048366219 0.007390185 0.00772777 0.007011149 0.001668949 23.8042117120 -0.03259481 -0.02252204 -0.0304851 0.003444737 11.2997391621 0.007977079 0.007802826 0.009298145 0.001638412 17.6208436122 -0.00722704 -0.00643404 -0.00532183 0.00128698 24.1830552923 -0.0282689 -0.02521884 -0.02520399 0.003732973 14.8110400724 -0.01322651 -0.00518074 -0.00857838 0.002352147 27.4194817425 0.005267741 0.006493884 0.006305752 0.00149207 23.662049326 -0.00474183 -0.00423029 -0.00402641 0.00106757 26.5141720627 0.017993524 0.011364362 0.015460673 0.001896264 12.26508329


17

The gene parameters of the thickness of a lens.

Simulation Results (2)Gens Best Worst Average STDev |STDev/Average| %

28 5.768374763 6.931686482 6.638592433 2.427022165 36.5592885829 0.7489143 0.920381407 1.036093005 0.285146152 27.5212891430 6.655969838 6.418745981 7.356645906 1.092639868 14.8524189231 4.827333593 9.862222329 7.973484916 3.647367524 45.7437063332 1.629027415 2.149008665 1.718677646 0.442812434 25.7647171133 3.151660916 4.815855593 5.347738799 1.230289405 23.0057871534 2.557382361 1.23631536 1.546670481 0.646936526 41.8276895235 11.55637623 11.91547831 11.89211527 1.298606897 10.9198983336 14.15182198 13.27871173 12.93231016 1.248514992 9.6542301937 5.440503086 1.668372481 3.809586362 1.168523477 30.6732376238 0.062249473 0.125152309 0.093807689 0.046634592 49.7129741739 8.047827802 4.961329824 5.032100595 1.776315835 35.299688540 0.715426519 0.598514237 0.643643777 0.215913568 33.5455069541 6.334986331 4.383819797 6.884714665 1.642931868 23.8634707242 0.807208596 3.68867751 2.282944661 0.669992456 29.3477309143 9.553424429 12.51000413 9.816803751 2.443837603 24.894432744 1.332030343 1.838867496 1.512688074 0.466065713 30.8104308745 6.925007043 6.615982524 7.041712404 1.110065259 15.7641379746 0.095567871 0.06992596 0.088165184 0.031547163 35.7818837547 3.236165205 5.8512294 5.2007384 1.803844065 34.6843837648 0.071026102 0.095006935 0.118857296 0.039265596 33.035915949 4.058028408 3.6498154 3.613160548 0.7546123 20.8851029650 1.869417854 3.271609906 2.396572433 0.870267105 36.3129898651 1.441570412 1.350271825 1.152751968 0.383321482 33.2527284852 0.13236769 0.16577513 0.096346934 0.027507964 28.5509493153 3.483556466 2.932199208 2.650120429 0.865332129 32.6525587154 0.122594553 0.113551611 0.096887669 0.03395393 35.0446355555 3.035402269 2.672729999 3.182126866 1.638788722 51.4997921656 5.889131463 6.442721796 6.112946234 1.378357512 22.5481700557 1.072134222 1.234352264 1.256353431 0.327663876 26.0805493258 13.73071396 12.94312908 12.97443717 1.029182636 7.93238753359 13.28067713 13.54179626 12.79759875 1.073936837 8.39170580560 12.59841862 14.51783846 13.17657307 4.647158533 35.2683395661 3.104315615 1.278735836 2.624749836 1.016446986 38.7254805162 2.845644408 2.871082711 3.422038915 0.974821254 28.4865624963 2.243932586 3.306582202 4.218486331 2.213185105 52.4639629264 5.241060233 6.936205775 6.114159767 2.086274153 34.12200911


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Conclusions

We proposed using the GA along with LSD simulations to extensively optimize lens parameters and then further eliminate the Petzval FCA.

Through this proposed optimization method, the crossover and mutation operations of the GA, the Petzval FCA has been comprehensively eliminated – up to 88.4%, according to our simulation results.


Thanks for your attentions

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Advances in optical design and optimization of miniature zoom optics with liquid lens element