Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology Improvements of Petzval Field Curvature of HDTV Projector Lens Optics 1 Cheng-Mu Tsai and 2 Yi-Chin Fang 1 Dept. of Computer and Communication, Kun Shan University, No.949, Da Wan Rd., Yung-Kang Dist., Tainan City 710, Taiwan. E-mail: [email protected]2 Institute 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
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Improvements of Petzval Field Curvature of HDTV Projector Lens Optics
Improvements of Petzval Field Curvature of HDTV Projector Lens Optics. 1 Cheng-Mu Tsai and 2 Yi-Chin Fang 1 Dept. of Computer and Communication, Kun Shan University, No.949, Da Wan Rd., Yung-Kang Dist., Tainan City 710, Taiwan. E-mail: [email protected] - PowerPoint PPT Presentation
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Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology
Improvements of Petzval Field Curvature of HDTV Projector Lens
Optics1Cheng-Mu Tsai and 2Yi-Chin Fang
1Dept. 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.
Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology
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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
Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology
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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
Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology
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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;
Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology
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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
Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology
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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
Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology
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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
Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology
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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
Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology
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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
Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology
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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
Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology
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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
Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology
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Preliminary design of a projector lens
09:43:54
Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology
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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
Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology
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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
Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology
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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
Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology
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The gene parameters of the radius of curvature of lenses.
Simulation Results (1)Gens Best Worst Average STDev |STDev/Average| %
Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology
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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.
Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology