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Optical Design with Zemax
Lecture 11: Correction I
2013-01-22
Herbert Gross
Summer term 2012
2 11 Correction I
Preliminary time schedule
1 16.10. Introduction
Introduction, Zemax interface, menues, file handling, preferences, Editors, updates, windows,
Coordinate systems and notations, System description, Component reversal, system insertion,
scaling, 3D geometry, aperture, field, wavelength
2 23.10. Properties of optical systems I Diameters, stop and pupil, vignetting, Layouts, Materials, Glass catalogs, Raytrace, Ray fans
and sampling, Footprints
3 30.10. Properties of optical systems II Types of surfaces, Aspheres, Gratings and diffractive surfaces, Gradient media, Cardinal
elements, Lens properties, Imaging, magnification, paraxial approximation and modelling
4 06.11. Aberrations I Representation of geometrical aberrations, Spot diagram, Transverse aberration diagrams,
Aberration expansions, Primary aberrations,
5 13.+27.11. Aberrations II Wave aberrations, Zernike polynomials, Point spread function, Optical transfer function
6 04.12. Advanced handling
Telecentricity, infinity object distance and afocal image, Local/global coordinates, Add fold
mirror, Vignetting, Diameter types, Ray aiming, Material index fit, Universal plot, Slider,IO of
data, Multiconfiguration, Macro language, Lens catalogs
7 11.12. Optimization I Principles of nonlinear optimization, Optimization in optical design, Global optimization
methods, Solves and pickups, variables, Sensitivity of variables in optical systems
8 18.12. Optimization II Systematic methods and optimization process, Starting points, Optimization in Zemax
9 08.01 Imaging Fundamentals of Fourier optics, Physical optical image formation, Imaging in Zemax
10 15.01. Illumination Introduction in illumination, Simple photometry of optical systems, Non-sequential raytrace,
Illumination in Zemax
11 22.01. Correction I
Symmetry principle, Lens bending, Correcting spherical aberration, Coma, stop position,
Astigmatism, Field flattening, Chromatical correction, Retrofocus and telephoto setup, Design
method
12 29.01. Correction II Field lenses, Stop position influence, Aspheres and higher orders, Principles of glass
selection, Sensitivity of a system correction, Microscopic objective lens, Zoom system
13 05.02. Physical optical modelling Gaussian beams, POP propagation, polarization raytrace, coatings
1. Symmetry principle
2. Lens bending
3. Correcting spherical aberration
4. Coma, stop position
5. Astigmatism
6. Field flattening
7. Chromatical correction
8. Retrofocus and telephoto setup
9. Design method
10. Starting points
11 Correction I
Contents
3
11 Correction I
Principle of Symmetry
Perfect symmetrical system: magnification m = -1
Stop in centre of symmetry
Symmetrical contributions of wave aberrations are doubled (spherical)
Asymmetrical contributions of wave aberration vanishes W(-x) = -W(x)
Easy correction of:
coma, distortion, chromatical change of magnification
front part rear part
2
1
3
4
11 Correction I
Symmetrical Systems
skew sphericalaberration
Ideal symmetrical systems:
Vanishing coma, distortion, lateral color aberration
Remaining residual aberrations:
1. spherical aberration
2. astigmatism
3. field curvature
4. axial chromatical aberration
5. skew spherical aberration
5
11 Correction I
Symmetry Principle
Triplet Double Gauss (6 elements)
Double Gauss (7 elements)Biogon
Ref : H. Zügge
Application of symmetry principle: photographic lenses
Especially field dominant aberrations can be corrected
Also approximate fulfillment
of symmetry condition helps
significantly:
quasi symmetry
Realization of quasi-
symmetric setups in nearly
all photographic systems
6
Effect of bending a lens on spherical aberration
Optimal bending:
Minimize spherical aberration
Dashed: thin lens theory
Solid : think real lenses
Vanishing SPH for n=1.5
only for virtual imaging
Correction of spherical aberration
possible for:
1. Larger values of the
magnification parameter |M|
2. Higher refractive indices
11 Correction I
Spherical Aberration: Lens Bending
20
40
60
X
M=-6 M=6M=-3 M=3
M=0
Spherical
Aberration
(a)
(b) (c)
(d)-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
Ref : H. Zügge
7
Correction of spherical aberration:
Splitting of lenses
Distribution of ray bending on several
surfaces:
- smaller incidence angles reduces the
effect of nonlinearity
- decreasing of contributions at every
surface, but same sign
Last example (e): one surface with
compensating effect
11 Correction I
Correcting Spherical Aberration: Lens Splitting
Transverse aberration
5 mm
5 mm
5 mm
(a)
(b)
(c)
(d)
Improvement
(a)à(b) : 1/4
(c)à(d) : 1/4
(b)à(c) : 1/2
Improvement
Improvement
(e)
0.005 mm
(d)à(e) : 1/75
Improvement
5 mm
Ref : H. Zügge
8
11 Correction I
Correcting Spherical Aberration: Cementing
0.25 mm0.25 mm
(d)
(a)
(c)
(b)
1.0 mm 0.25 mm
Crown
in front
Filnt
in front
Ref : H. Zügge
Correcting spherical aberration by cemented doublet:
Strong bended inner surface compensates
Solid state setups reduces problems of centering sensitivity
In total 4 possible configurations:
1. Flint in front / crown in front
2. bi-convex outer surfaces / meniscus shape
Residual zone error, spherical aberration corrected for outer marginal ray
9
Better correction
for higher index
Shape of lens / best
bending changes
from
1. nearly plane convex
for n= 1.5
2. meniscus shape
for n > 2
11 Correction I
Correcting Spherical Aberration: Refractive Index
-8
-6
-4
-2
0
1.4 1.5 1.6 1.7 1.8 1.9
Δs’
4.0
n
n = 1.5 n = 1.7 n = 1.9 n = 4.0
best shape
best shape
plano-convex
plano-convex
1.686
Ref : H. Zügge
10
Better correction
for high index also for meltiple
lens systems
Example: 3-lens setup with one
surface for compensation
Residual aberrations is quite better
for higher index
11 Correction I
Correcting Spherical Aberration: Refractive Index
-20
-10
0
10
20
30
40
1 2 3 4 5 6 sum
n = 1.5 n = 1.8
SI ()
Surface
n = 1.5
n = 1.8
0.0005 mm
0.5 mm
Ref : H. Zügge
11
Perfect coma correction in the case of symmetry
But magnification m = -1 not useful in most practical cases
11 Correction I
Coma Correction: Symmetry Principle
Pupil section: meridional sagittal
Image height: y’ = 19 mm
Transverse
Aberration:
Symmetry principle
0.5 mm
'y0.5 mm
'y
(a)
(b)
From : H. Zügge
12
Combined effect, aspherical case prevent correction
11 Correction I
Coma Correction: Stop Position and Aspheres
aspheric
aspheric
aspheric
0.5 mm
'y
Sagittal
coma
0.5 mm
'y
Sagittal
comaPlano-convex element
exhibits spherical aberration
Spherical aberration corrected
with aspheric surface
Ref : H. Zügge
13
11 Correction I
Distortion and Stop Position
positive negative
Sign of distortion for single lens:
depends on stop position and
sign of focal power
Ray bending of chief ray defines
distortion
Stop position changes chief ray
heigth at the lens
Ref: H.Zügge
Lens Stop location Distortion Examples
positive rear V > 0 tele photo lens
negative in front V > 0 loupe
positive in front V < 0 retrofocus lens
negative rear V < 0 reversed binocular
14
Bending effects astigmatism
For a single lens 2 bending with
zero astigmatism, but remaining
field curvature
11 Correction I
Astigmatism: Lens Bending
Ref : H. Zügge
20
-0. 01 0-0.02-0. 03 0.01-0. 04
Surface 2
Surface 1
Sum
Curvature of surface 1
15
10
5
0
-5
Astigmatism
Seidel coefficients
in []
ST
-2.5 0 2.5
ST S T ST ST
-2.5 0 2.5 -2.5 0 2.5 -2.5 0 2.5 -2.5 0 2.5
15
11 Correction I
Petzval Theorem for Field Curvature
Petzval theorem for field curvature:
1. formulation for surfaces
2. formulation for thin lenses (in air)
Important: no dependence on
bending
Natural behavior: image curved
towards system
Problem: collecting systems
with f > 0:
If only positive lenses:
Rptz always negative
k kkk
kkm
ptz rnn
nnn
R '
''
1
j jjptz fnR
11
optical system
object
plane
ideal
image
plane
real
image
shell
R
16
11 Correction I
Petzval Theorem for Field Curvature
Goal: vanishing Petzval curvature
and positive total refractive power
for multi-component systems
Solution:
General principle for correction of curvature of image field:
1. Positive lenses with:
- high refractive index
- large marginal ray heights
- gives large contribution to power and low weighting in Petzval sum
2. Negative lenses with:
- low refractive index
- samll marginal ray heights
- gives small negative contribution to power and high weighting in Petzval sum
j jjptz fnR
11
fh
h
f j
j 11
1
17
11 Correction I
Flattening Meniscus Lenses
Possible lenses / lens groups for correcting field curvature
Interesting candidates: thick mensiscus shaped lenses
1. Hoeghs mensicus: identical radii
- Petzval sum zero
- remaining positive refractive power
2. Concentric meniscus,
- Petzval sum negative
- weak negative focal length
- refractive power for thickness d:
3. Thick meniscus without refractive power
Relation between radii
Fn d
nr r d'
( )
( )
1
1 1
r r dn
n2 1
1
21
211
'
'1
rr
d
n
n
fnrnn
nn
R k kkk
kk
ptz
r2
d
r1
2
2)1('
rn
dnF
drr 12
drrn
dn
Rptz
11
)1(1
0
)1(
)1(1
11
2
ndnrrn
dn
Rptz
18
Group of meniscus lenses
Effect of distance and
refractive indices
11 Correction I
Correcting Petzval Curvature
r 2r 1
collimated
n n
d
3020 5010
-3
10-1
10-2
1/Rpet [1/mm]
40r
1
[mm]10
K5 / d=15 mm
SF66 / d=15 mm
K5 / d=25 mm
From : H. Zügge
19
11 Correction I
Field Curvature
Correction of Petzval field curvature in lithographic lens
for flat wafer
Positive lenses: Green hj large
Negative lenses : Blue hj small
Correction principle: certain number of bulges
j j
j
n
F
R
1
j
j
jF
h
hF
1
20
imageshell
flatimage
fieldlens
Effect of a field lens for flattening the image surface
1. Without field lens 2. With field lens
curved image surface image plane
11 Correction I
Flattening Field Lens
21
Compensation of axial colour by
appropriate glass choice
Chromatical variation of the spherical
aberrations:
spherochromatism (Gaussian aberration)
Therefore perfect axial color correction
(on axis) are often not feasable
11 Correction I
Axial Colour: Achromate
BK7 F2
n = 1.5168 1.6200
= 64.17 36.37
F = 2.31 -1.31
BK7 N-SSK8F2
n = 1.5168 1.6177
= 64.17 49.83
F = 4.47 -3.47
BK7
n= 1.5168 = 64.17
F= 1
(a) (b) (c)
-2.5 0z
r p1
-0.20
1
z
0.200
r p
-100 1000
1
r p
z
486 nm
588 nm
656 nm
Ref : H. Zügge
22
Achromate:
- Axial colour correction by cementing two
different glasses
- Bending: correction of spherical aberration at the
full aperture
- Aplanatic coma correction possible be clever
choice of materials
Four possible solutions:
- Crown in front, two different bendings
- Flint in front, two different bendings
Typical:
- Correction for object in infinity
- spherical correction at center wavelength
with zone
- diffraction limited for NA < 0.1
- only very small field corrected
11 Correction I
Achromate
solution 1 solution 2
Crown in
front
Flint in
front
11 Correction I
Achromate: Realization Versions
Advantage of cementing:
solid state setup is stable at sensitive middle surface with large curvature
Disadvantage:
loss of one degree of freedom
Different possible realization
forms in practice
edge contact cemented
a) flint in front
edge contact cemented contact on axis broken, Gaussian setup
b) crown in front
11 Correction I
Achromate : Basic Formulas
Idea:
1. Two thin lenses close together with different materials
2. Total power
3. Achromatic correction condition
Individual power values
Properties:
1. One positive and one negative lens necessary
2. Two different sequences of plus (crown) / minus (flint)
3. Large -difference relaxes the bendings
4. Achromatic correction indipendent from bending
5. Bending corrects spherical aberration at the margin
6. Aplanatic coma correction for special glass choices
7. Further optimization of materials reduces the spherical zonal aberration
21 FFF
02
2
1
1
FF
FF
1
21
1
1
FF
2
12
1
1
case without solution,
only sperical minimum
case with 2 solutions
case with
one solution
and coma
correction
s'rim
R1
11 Correction I
Achromate: Correction
Cemented achromate: 6 degrees of freedom: 3 radii, 2 indices, ratio 1/2
Correction of spherical aberration: diverging cemented surface with positive spherical contribution for nneg > npos
Choice of glass: possible goals 1. aplanatic coma correction 2. minimization of spherochromatism 3. minimization of secondary spectrum Bending has no impact on chromatical correction: is used to correct spherical aberration at the edge Three solution regions for bending 1. no spherical correction 2. two equivalent solutions 3. one aplanatic solution, very stable
11 Correction I
Achomatic solutions in the Glass Diagram
Achromat
flint
negative lens
crown
positive lens
11 Correction I
Achromate
Achromate
Longitudinal aberration
Transverse aberration
Spot diagram
rp
0
486 nm
587 nm
656 nm
0.1 0.2
s'
[mm]
1
axis
1.4°
2°
486 nm 587 nm 656 nm
= 486 nm
= 587 nm
= 656 nm
sinu'
y'
Bending of an achromate
- optimal choice: small residual spherical
aberration
- remaining coma for finite field size
Splitting achromate:
additional degree of freedom:
- better total correction possible
- high sensitivity of thin air space
Aplanatic glass choice:
vanishing coma
Cases:
a) simple achromate,
sph corrected, with coma
b) simple achromate,
coma corrected by bending, with sph
c) other glass choice: sph better, coma reversed
d) splitted achromate: all corrected
e) aplanatic glass choice: all corrected
11 Correction I
Coma Correction: Achromate
0.05 mm
'y0.05 mm
'y0.05 mm
'y
Pupil section: meridional meridional sagittal
Image height: y’ = 0 mm y’ = 2 mm
Transverse
Aberration:
(a)
(b)
(c)
Wave length:
Achromat
bending
Achromat, splitting
(d)
(e)
Achromat, aplanatic glass choice
Ref : H. Zügge
11 Correction I
Achromate
Residual aberrations of an achromate
Clearly seen:
1. Distortion
2. Chromatical magnification
3. Astigmatism
Residual spherochromatism of an achromate
Representation as function of apeture or wavelength
11 Correction I
Spherochromatism: Achromate
longitudinal aberration
0
rp
0.080.04 0.12z
defocus variation
pupil height :
rp = 1
rp = 0.707
rp = 0.4
rp = 0
0-0.04 0.080.04
587
656
486z
1
486 nm
587 nm
656 nm
31
Effect of different materials
Axial chromatical aberration
changes with wavelength
Different levels of correction:
1.No correction: lens,
one zero crossing point
2.Achromatic correction:
- coincidence of outer colors
- remaining error for center
wavelength
- two zero crossing points
3. Apochromatic correction:
- coincidence of at least three
colors
- small residual aberrations
- at least 3 zero crossing points
- special choice of glass types
with anomalous partial
dispertion necessery
11 Correction I
Axial Colour: Achromate and Apochromate
e
F'
C'
achromateapochromate
residual error
apochromate
644
480
546
residual error
achromate
-100 0 100
singlet
s'
lens
32
Anormal partial dispersion and normal line
11 Correction I
Axial Colour: Apochromate
33
Pg,F
0.5000
0.5375
0.5750
0.6125
0.6500
90 80 70 60 50 40 30 20
F2
F5
K7
K10
LAFN7
LAKN13
LAKL12
LASFN9
SF1
SF10
SF11
SF14
SF15
SF2
SF4
SF5
SF56A
SF57
SF66
SF6
SFL57
SK51
BASF51
KZFSN5
KZFSN4
LF5
LLF1
N-BAF3
N-BAF4
N-BAF10
N-BAF51N-BAF52
N-BAK1
N-BAK2
N-BAK4
N-BALF4
N-BALF5
N-BK10
N-F2
N-KF9
N-BASF2
N-BASF64
N-BK7
N-FK5
N-FK51N-PK52
N-PSK57
N-PSK58
N-K5
N-KZFS2
N-KZFS4
N-KZFS11
N-KZFS12
N-LAF28
N-LAF2
N-LAF21N-LAF32
N-LAF34
N-LAF35
N-LAF36
N-LAF7
N-LAF3
N-LAF33
N-LAK10
N-LAK22
N-LAK7
N-LAK8
N-LAK9
N-LAK12
N-LAK14
N-LAK21
N-LAK33
N-LAK34
N-LASF30
N-LASF31
N-LASF35
N-LASF36
N-LASF40
N-LASF41
N-LASF43
N-LASF44
N-LASF45
N-LASF46
N-PK51
N-PSK3
N-SF1
N-SF4
N-SF5
N-SF6
N-SF8
N-SF10
N-SF15
N-SF19
N-SF56
N-SF57
N-SF64
N-SK10
N-SK11
N-SK14
N-SK15
N-SK16
N-SK18N-SK2
N-SK4
N-SK5
N-SSK2
N-SSK5
N-SSK8
N-ZK7
N-PSK53
N-PSK3
N-LF5
N-LLF1
N-LLF6
BK7G18
BK7G25
K5G20
BAK1G12
SK4G13
SK5G06
SK10G10
SSK5G06
LAK9G15
LF5G15
F2G12
SF5G10
SF6G05
SF8G07
KZFS4G20
GG375G34
normal
line
Choice of at least one special glass
Correction of secondary spectrum:
anomalous partial dispersion
At least one glass should deviate
significantly form the normal glass line
11 Correction I
Axial Colour : Apochromate
656nm
588nm
486nm
436nm1mm
z0-0.2mm
z-0.2mm
2030405060708090
N-FK51
N-KZFS11
N-FS6
(1)
(2)
(3)
(1)+(2) T
PgF
0,54
0,56
0,58
0,60
0,62
34
Cemented surface with perfect refrcative index match
No impact on monochromatic aberrations
Only influence on chromatical aberrations
Especially 3-fold cemented components are advantages
Can serve as a starting setup for chromatical correction with fulfilled monochromatic
correction
Special glass combinations with nearly perfect
parameters
d 1d 2 d 3
Nr Glas nd nd d d
1 SK16 1.62031 0.00001 60.28 22.32
F9 1.62030 37.96
2 SK5 1.58905 0.00003 61.23 20.26
LF2 1.58908 40.97
3 SSK2 1.62218 0.00004 53.13 17.06
F13 1.62222 36.07
4 SK7 1.60720 0.00002 59.47 10.23
BaF5 1.60718 49.24
11 Correction I
Buried Surface
35
P'
f 's '
d
yy
ba
b
a
k f '
8 Correction II
Telephoto Systems
Combination of a positiv and a negative lens:
Shift of the first principal plane in front of the system
The intersection length is smaller than the focal length: reduction factor k
Typical values: k = 0.6...0.9
Focal lengths:
Overall length
Free intersection length
ff d
f k da
'
' ( )1
f
f d kf d
f kfb
a
a
'
'
L k f '
s k f df '
P'
f '
s '
8 Correction II
Retrofocal System
Combination of a negative and a positive lens:
Shift of the second principal plane behind the system
The intersection length is larger than the focal length
Application: systems for large free working distance
Corresponds to an inverse telephoto system
Retrofocus system results form a telephoto system by inversion
8 Correction II
Telephoto and inverse Telephoto Principle
focal length f
telephoto systemprincipal plane P'
retrofocus systeminverse telephoto
imageplane
11 Correction I
System Design Phases
1. Paraxial layout:
- specification data, magnification, aperture, pupil position, image location
- distribution of refractive powers
- locations of components
- system size diameter / length
- mechanical constraints
- choice of materials for correcting color and field curvature
2. Correction/consideration of Seidel primary aberrations of 3rd order for ideal thin lenses,
fixation of number of lenses
3. Insertion of finite thickness of components with remaining ray directions
4. Check of higher order aberrations
5. Final correction, fine tuning of compromise
6. Tolerancing, manufactability, cost, sensitivity, adjustment concepts
39
Existing solution modified
Literature and patent collections
Principal layout with ideal lenses
successive insertion of thin lenses and equivalent thick lenses with correction control
Approach of Shafer
AC-surfaces, monochromatic, buried surfaces, aspherics
Expert system
Experience and genius
11 Correction I
Optimization: Starting Point
object imageintermediate
imagepupil
f1
f2 f
3f4
f5
40
11 Correction I
Strategy of Correction and Optimization
Usefull options for accelerating a stagnated optimization:
split a lens
increase refractive index of positive lenses
lower refractive index of negative lenses
make surface with large spherical surface contribution aspherical
break cemented components
use glasses with anomalous partial dispersion
41
Lens bending
Lens splitting
Power combinations
Distances
11 Correction I
Correction Methods
(a) (b) (c) (d) (e)
(a) (b)
Ref : H. Zügge
42
Operationen with zero changes in first approximation:
1. Bending a lens.
2. Flipping a lens into reverse orientation.
3. Flipping a lens group into reverse order.
4. Adding a field lens near the image plane.
5. Inserting a powerless thin or thick meniscus lens.
6. Introducing a thin aspheric plate.
7. Making a surface aspheric with negligible expansion constants.
8. Moving the stop position.
9. Inserting a buried surface for color correction, which does not affect the main
wavelength.
10. Removing a lens without refractive power.
11. Splitting an element into two lenses which are very close together but with the
same total refractive power.
12. Replacing a thick lens by two thin lenses, which have the same power as the two refracting
surfaces.
13. Cementing two lenses a very small distance apart and with nearly equal radii.
11 Correction I
Zero-Operations
43