Lens Design II - iap.uni-jena.dedesign+II... · design and aspherics. Diffraction limited systems...
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Lens Design II
Lecture 2: Structural modifications
2018-10-24
Herbert Gross
Winter term 2018
2
Preliminary Schedule Lens Design II 2018
1 17.10. Aberrations and optimization Repetition
2 24.10. Structural modificationsZero operands, lens splitting, lens addition, lens removal, material selection
3 07.11. Aspheres Correction with aspheres, Forbes approach, optimal location of aspheres, several aspheres
4 14.11. FreeformsFreeform surfaces, general aspects, surface description, quality assessment, initial systems
5 21.11. Field flatteningAstigmatism and field curvature, thick meniscus, plus-minus pairs, field lenses
6 28.11. Chromatical correction IAchromatization, axial versus transversal, glass selection rules, burried surfaces
7 05.12. Chromatical correction IISecondary spectrum, apochromatic correction, aplanatic achromates, spherochromatism
8 12.12. Special correction topics I Symmetry, wide field systems, stop position, vignetting
9 19.12. Special correction topics IITelecentricity, monocentric systems, anamorphotic lenses, Scheimpflug systems
10 09.01. Higher order aberrations High NA systems, broken achromates, induced aberrations
11 16.01. Further topics Sensitivity, scan systems, eyepieces
12 23.01. Mirror systems special aspects, double passes, catadioptric systems
13 30.01. Zoom systems Mechanical compensation, optical compensation
14 06.01. Diffractive elementsColor correction, ray equivalent model, straylight, third order aberrations, manufacturing
1. Correction strategy
2. Structural changes
3. Zero operations
4. Material optimization
3
Contents
Effectiveness of correction
features on aberration types
Correction Effectiveness
Aberration
Primary Aberration 5th Chromatic
Sp
he
rica
l A
berr
atio
n
Co
ma
Astig
ma
tism
Pe
tzva
l C
urv
atu
re
Dis
tort
ion
5th
Ord
er
Sp
he
rica
l
Axia
l C
olo
r
Late
ral C
olo
r
Se
co
nd
ary
Sp
ectr
um
Sp
he
roch
rom
atism
Lens Bending (a) (c) e (f)
Power Splitting
Power Combination a c f i j (k)
Distances (e) k
Len
s P
ara
mete
rs
Stop Position
Refractive Index (b) (d) (g) (h)
Dispersion (i) (j) (l)
Relative Partial Disp. Mate
ria
l
GRIN
Cemented Surface b d g h i j l
Aplanatic Surface
Aspherical Surface
Mirror
Sp
ecia
l S
urf
ace
s
Diffractive Surface
Symmetry Principle
Acti
on
Str
uc
Field Lens
Makes a good impact.
Makes a smaller impact.
Makes a negligible impact.
Zero influence.
Ref : H. Zügge
4
Strategy of Correction and Optimization
If the potential of the setup seems to by not improvable, enlarge the number of degrees
of freedom by structural changes of the system
Possible options are:
• add a lens
split a lens by distribution of nearly equal ray bending
split a lens by decomposing it by a positive and negative part
split a lens by decomposing it with two different materials
add especially a field lens
break a cemented component
insert a burried surface
• make a surface aspherical
• make a surface free shaped
• insert a mirror
• replace a lens by a mirror
• implement a diffractive surface
• remove a lens
• cement two lenses
• make an asphere spherical
5
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
‚kick‘, if the optimization is captured in a local minimum
In general:
it is preferred to preserve the achieved (good) result and perform small changes
to let the optimization run again, change the weightings
if the potential of the setup seems to by not improvable, enlarge the number of degrees
of freedom
6
Number of Lenses
Approximate number of spots
over the field as a function of
the number of lenses
Linear for small number of lenses.
Depends on mono-/polychromatic
design and aspherics.
Diffraction limited systems
with different field size and
aperture
Number of spots
12000
10000
8000
6000
4000
2000
00 2 4 6 8
Number of
elements
monochromatic
aspherical
mono-
chromatic
poly-
chromatic
14
diameter of field
[mm]
00 0.2 0.4 0.6 0.8
numerical
aperture1
8
6
4
2
106
2 412
8
lenses
single plano
convex lens
two plano
convex lenses
dublet of two
optimal
bended lenses
achromat
dublet with marginal
corrected ray and
residual zone
splitted achromate
achromate with
additional meniscus
four lenses
Wrms = 5.21
Wrms = 1.91
Wrms = 0.91
Wrms = 0.221
Wrms = 0.168
Wrms = 0.026
Wrms = 0.0159
Wrms = 0.0001
Spherical Aberration Correction
Correction of spherical aberration by splitting
the ray bending
Optimal bending of lenses
Splitting of lenses
Smooth reducing of spherical aberration
or marginal correction
8
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
9
10
Even Aberrations in Symmetrical Systems
Aberrations with even symmetry are doubled
Spherical aberration, Astigmatism, field curvature, axial chromatical aberration
Ref: M. Seesselberg
spherical aberration in an symmetrical system
4 4 9 9W c Z c Z
4 4 9 92 2W c Z c Z
4 4 9 9W c Z c Z
doubled values
11
Odd Aberrations in Symmetrical Systems
Ref: M. Seesselberg
Aberrations with odd symmetry are vanishing
Coma, distortion, transverse chromatical aberration
coma in an symmetrical system
8 8 15 15W c Z c Z 8 8 15 15W c Z c Z
0W
vanishing values
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
12
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
13
14
Sensitivity by large Incidence
Small incidence angle of a ray:
small impact of centering error
Large incidence angle of a ray:
- strong non-linearity range of sin(i)
- large impact of decenter on
ray angle
Ref: H. Sun
ideal
surface
location
real surface
location:
decentered
ideal ray
real raysurface
normal
ideal ray
real ray
surface
normal
a) small incidence:
small impact of decenter
b) large incidence:
large impact of decenter
i
i
Distribution of refractive power
good: small W
Symmetry content
good: large S
General trend :
Cost of small W and large S : - long systems
- many lenses
Advantage of wj, sj-diagram :
Identification of strange surfaces
System Structure
N
j
jwN
W1
21j
NN
jjj
jun
y
m
nnw
''1
'
N
j
jsN
S1
21
j
j
j
j
NNstop
jj
jn
u
n
u
unin
in
ms
'
'
''1
1
|wj|
5 10 15 20 25 30 350
0.1
0.2
0.3
0.4
0.5
0.6
0.7
5 10 15 20 25 30 350
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
|sj|
power : W = 0.273
symmetry : S = 0.191
j
j
15
Example:
optimizing W and S with one additional lens
Starting system:
Final design
System Structure
|wj| |s
j|
1 2 3 4 5 6 7 8 9 10 110
0.5
1
1.5
2
1 2 3 4 5 6 7 8 9 10 110
0.2
0.4
0.6
0.8
1
1 2
3 45
67
8 910 11
S = 0.147W = 0.912
|wj| |s
j|
1 2 3 4 5 6 7 8 9 10 110
0.5
1
1.5
2
1 2 3 4 5 6 7 8 9 10 110
0.2
0.4
0.6
0.8
1
1 2
3 45
67
8 910 11
S = 0.147W = 0.912
|wj| |s
j|
1 2 3 4 5 6 7 8 9 10 11 12 130
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6 7 8 9 10 11 12 130
0.5
1
1.5
2
W = 0.586 S = 0.182
1 2
3 4
5 6 789 10 11
12 13
|wj| |s
j|
1 2 3 4 5 6 7 8 9 10 11 12 130
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6 7 8 9 10 11 12 130
0.5
1
1.5
2
W = 0.586 S = 0.182
1 2
3 4
5 6 789 10 11
12 13
16
Field-Aperture-Diagram
0.20 0.4 0.6 0.80°
4°
8°
12°
16°
20°
24°
28°
32°
36°
NA
w
40°
micro
100x0.9
double
Gauss
achromat
Triplet
micro
40x0.6micro
10x0.4
Sonnar
Biogon
split
triplet
Distagon
disc
projection
Gauss
diode
collimator
projection
Petzval
micros-
copy
collimator
focussing
photographic
projection constant
etendue
lithography
Braat 1987
lithography
2003
Classification of systems with
field and aperture size
Scheme is related to size,
correction goals and etendue
of the systems
Aperture dominated:
Disk lenses, microscopy,
Collimator
Field dominated:
Projection lenses,
camera lenses,
Photographic lenses
Spectral widthz as a correction
requirement is missed in this chart
Variable focal length
f = 15 ...200 mm
Invariant:
object size y = 10 mm
numerical aperture NA = 0.1
Type of system changes:
- dominant spherical for large f
- dominant field for small f
Data:
18
Symmetrical Dublet
f = 200 mm
f = 100 mm
f = 50 mm
f = 20 mm
f = 15 mm
Nofocal
length [mm]
Length [mm]
spherical c9
field curvature c4
astigma-tism c5
1 200 808 3.37 -2.01 -2.27
2 100 408 1.65 1.19 -4.50
3 50 206 1.74 3.45 -7.34
4 20 75 0.98 3.93 2.31
5 15 59 0.20 16.7 -5.33
19
Field vs Aperture Correction
Remote pupil system with decreasing field for one wavelength and 4 lenses
Aperture maximum value for overall diffraction limited correction
Large field angles: lenses bended towards pupil
Old achromate move towards usual achromate
2 3 4 5 6 7 8 9 100
5
10
15
20
25
30
35
40
45
50
w [°]
D [mm]
Radii of curvature of wide angle camera lenses - symmetrical setups
Mostly radii 'concentric' towards the stop losition
Locations zj of surfaces normalized for comparison
Nearly linear trend, some exceptions near to the pupil
Stop position centered
20
Wide Angle Lenses - Symmetrical
zj
Double Gauss
Pleogon
Rj
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5-250
-200
-150
-100
-50
0
50
100
150
200
250
Biogonzj
stop
Radii of curvature of wide angle camera lenses - asymmetrical setups
No clear trend
Locations zj of surfaces normalized for comparison
Stop position in the rear part
21
Wide Angle Lenses - Asymmetrical
Fisheye
Rj
Distagon
zj-1 -0.8 -0.6 -0.4 -0.2 0 0.2
-300
-200
-100
0
100
200
300Flektogon
stop
22
Wide Angle Camera systems
Wide angle camera with f# = 2 and 120°FoV
Different effort in lens design according to constraints
1. plane sensor, telecentric
2. plane sensor
3. curved sensor
Ref.: I. Stamenov
Relaxed System
Example: achromate with cemented/splitted setup
Equivalent performance
Inner surfaces of splitted version more sensitive
Ref: H. Zügge
a ) Cemented achromate f = 100 mm , NA = 0.1
b ) Splitted achromate f = 100 mm , NA = 0.1
-15
-10
-5
0
5
10
1 2 3
-15
-10
-5
0
5
10
1 2 3 4
Seidel coefficient
spherical aberration
spot enlargement for
0.2 ° surface tilt
surface
index
surface
index
23
Best Location for Correction Changes
The aberration contribution strongly depends on the heights of the marginal / chief ray
at a surface
Spherical aberration can be best corrected with a surface near to the pupil
Astigmatism and distortion can be best corrected with a surface near to the image
Field curvature does not depend on the surface location (see Petzval)
Coma correction depends on marginal and chief ray and thus is more complicated.
Usually a location near to the pupil is more helpful
24
Microscope Objective Lens
Seidel surface contributions
for 100x/0.90
No field flattening group
Lateral color in tube lens corrected
5 10
-0.5
0
0.5
-0.02
0
0.02
-4
-2
0
2
4
-5
0
5
-2
0
2
-0.02
0
0.02
-1
0
1
spherical
coma
astigmatism
curvature
distortion
axial
chromatic
lateral
chromatic
1
518
11
13
sum
25
Smooth changes
Lens bending
Distances
Structural changes:
Lens splitting
Power combinations
Structural and Smooth Changes for Correction
(a) (b) (c) (d) (e)
(a) (b)
Ref : H. Zügge
26
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.
Zero-Operations
27
Adding a meniscus lens with thickness zero:
Two additional degrees of freedom
Generates two adjacent local minima
Different opportunities to generate a
meniscus
28
Optimization
Ref : F. Bociort
Removal of a lens by vanishinh of the optical effect
For single lens and
cemented component
Problem of vanishinh index:
Generation of higher orders
of aberrations
29
Lens Removal
1) adapt second radius of curvature 2) shrink thickness to zero
a) Geometrical changes: radius and thickness
b) Physical changes: index
Special problem in glass optimization:
finite area of definition with
discrete parameters n, n
Restricted permitted area as
one possible contraint
Model glass with continuous
values of n, n in a pre-phase
of glass selection,
freezing to the next adjacend
glass
Optimization: Discrete Materials
area of permitted
glasses in
optimization
n
1.4
1.5
1.6
1.7
1.8
1.9
2
100 90 80 70 60 50 40 30 20n
area of available
glasses
30
Positive lenses with anomalous partial dispersion and high n:
PK51, FK51, FK52, FK54
For monochromatic correction disadvantageous
Negative lenses with anomalous partial dispersion andf low n:
KzFS-glasses
High indices for monochromatic correction:
LaK, LaSF, LaF
expensive, hard to manufacture, disadvantageous for color correction
Low refracting glasses for field flattening in negative lenses:
TiF, TiSAF
expensive, hard to manufacture, disadvantageous for color correction
Basic Principles of Glass Selection
31
Principles of Glass Selection in Optimization
field flattening
Petzval curvature
color
correction
index n
dispersion n
positive
lens
negative
lens
-
-
+
-
+
+
availability
of glasses
Design rules for glass selection
Different design goals:
1. Color correction:
large dispersion
difference desired
2. Field flattening:
large index difference
desired
Ref : H. Zügge
32
Preferred glass selection for apochromates
33
Relative Partial Dispersion
N-SF1
N-SF6
N-SF57
N-SF66
P-SF68
P-SF67
N-FK51A
N-PK52A
N-PK51
N-KZFS12
N-KZFS4
N-LAF33
N-LASF41
N-LAF37
N-LAF21
N-LAF35
N-LAK10
N-KZFS2
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 nd nd
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
Buried Surface
34