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Medical Photonics Lecture
Optical Engineering
Lecture 11: Optical Design
2017-01-12
Herbert Gross
Winter term 2016
2
Contents
No Subject Ref Date Detailed Content
1 Introduction Gross 20.10. Materials, dispersion, ray picture, geometrical approach, paraxial approximation
2 Geometrical optics Gross 03.11. Ray tracing, matrix approach, aberrations, imaging, Lagrange invariant
3 Components Kempe 10.11. Lenses, micro-optics, mirrors, prisms, gratings
4 Optical systems Gross 17.11. Field, aperture, pupil, magnification, infinity cases, lens makers formula, etendue, vignetting
5 Aberrations Gross 24.11. Introduction, primary aberrations, miscellaneous
6 Diffraction Gross 01.12. Basic phenomena, wave optics, interference, diffraction calculation, point spread function, transfer function
7 Image quality Gross 08.12. Spot, ray aberration curves, PSF and MTF, criteria
8 Instruments I Kempe 15.12. Human eye, loupe, eyepieces, photographic lenses, zoom lenses, telescopes
9 Instruments II Kempe 22.12. Microscopic systems, micro objectives, illumination, scanning microscopes, contrasts
10 Instruments III Kempe 05.01. Medical optical systems, endoscopes, ophthalmic devices, surgical microscopes
11 Optic design Gross 12.01. Aberration correction, system layouts, optimization, realization aspects
12 Photometry Gross 19.01. Notations, fundamental laws, Lambert source, radiative transfer, photometry of optical systems, color theory
13 Illumination systems Gross 26.01. Light sources, basic systems, quality criteria, nonsequential raytrace
14 Metrology Gross 02.02. Measurement of basic parameters, quality measurements
Modelling of Optical Systems
Principal purpose of calculations:
System, data of the structure(radii, distances, indices,...)
Function, data of properties,
quality performance(spot diameter, MTF, Strehl ratio,...)
Analysisimaging
aberration
theorie
Synthesislens design
Ref: W. Richter
Imaging model with levels of refinement
Analytical approximation and classification
(aberrations,..)
Paraxial model
(focal length, magnification, aperture,..)
Geometrical optics
(transverse aberrations, wave aberration,
distortion,...)
Wave optics
(point spread function, OTF,...)
with
diffractionapproximation
--> 0
Taylor
expansion
linear
approximation
3
Log w
Log NA0.02 0.05 0.10 1.00.500.20
0.5°
1.0°
2.0°
5.0°
10°
20°
50°
100°
Retrofocus
objective
0.2°
Tessar
Cooke-triplet
Double-
Gauss
objective
Petzval-
objective
landscape
objective
Schmidt-
Cassegrain
telescope
3-mirror
telescope
Schmidt
telescope
Microscope
objective
Ritchey-Cretien
telescope
Cassegrain
telescope
DiskobjectiveAchromate
Paraboloid
telescope
Fisheye
objective
Classification in Field and Aperture Size
Overview and sorting
Different types of systems
Diagram of W. Smith:
aperture vs field size
Spectral properties not concidered
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
Throughput as field-
aperture product
Additional dimension:
spectral bandwidth
Classification: -Lw-Diagram
Lw
Photography
Microscopy
Astronomy
LithographyInterferometer
lensmetrology lens
Surface Contributions: Example
7
Seidel aberrations:
representation as sum of
surface contributions possible
Gives information on correction
of a system
Example: photographic lens
1
23 4
5
6 8 9
10
7
Retrofocus F/2.8
Field: w=37°
SI
Spherical Aberration
SII
Coma
-200
0
200
-1000
0
1000
-2000
0
2000
-1000
0
1000
-100
0
150
-400
0
600
-6000
0
6000
SIII
Astigmatism
SIV
Petzval field curvature
SV
Distortion
CI
Axial color
CII
Lateral color
Surface 1 2 3 4 5 6 7 8 9 10 Sum
Basic Idea of Optimization
iteration
path
topology of
meritfunction F
x1
x2
start
Topology of the merit function in 2 dimensions
Iterative down climbing in the topology
8
Mathematical description of the problem:
n variable parameters
m target values
Jacobi system matrix of derivatives,
Influence of a parameter change on the
various target values,
sensitivity function
Scalar merit function
Gradient vector of topology
Hesse matrix of 2nd derivatives
Nonlinear Optimization
x
)(xf
j
iji
x
fJ
21
)()(
m
i
ii xfywxF
j
jx
Fg
kj
kjxx
FH
2
9
Types of constraints
1. Equation, rigid coupling, pick up
2. One-sided limitation, inequality
3. Double-sided limitation, interval
Numerical realizations :
1. Lagrange multiplier
2. Penalty function
3. Barriere function
4. Regular variable, soft-constraint
Boundary Conditions and Constraints
x
F(x)
permitted domain
F0(x) p
small
penalty
function
P(x)
p large
xmaxx
min
x
F(x)
permitted domain
F0(x)
barrier
function
B(x)
p large
p small
10
Goal of optimization:
Find the system layout which meets the required performance targets according of the
specification
Formulation of performance criteria must be done for:
- Apertur rays
- Field points
- Wavelengths
- Optional several zoom or scan positions
Selection of performance criteria depends on the application:
- Ray aberrations
- Spot diameter
- Wavefornt description by Zernike coefficients, rms value
- Strehl ratio, Point spread function
- Contrast values for selected spatial frequencies
- Uniformity of illumination
Usual scenario:
Number of requirements and targets quite larger than degrees od freedom,
Therefore only solution with compromize possible
Optimization Merit Function in Optical Design
11
Merit function:
Weighted sum of deviations from target values
Formulation of target values:
1. fixed numbers
2. one-sided interval (e.g. maximum value)
3. interval
Problems:
1. linear dependence of variables
2. internal contradiction of requirements
3. initail value far off from final solution
Types of constraints:
1. exact condition (hard requirements)
2. soft constraints: weighted target
Finding initial system setup:
1. modification of similar known solution
2. Literature and patents
3. Intuition and experience
Optimization in Optical Design
g f fj j
ist
j
soll
j m
2
1,
12
Characterization and description of the system delivers free variable parameters
of the system:
- Radii
- Thickness of lenses, air distances
- Tilt and decenter
- Free diameter of components
- Material parameter, refractive indices and dispersion
- Aspherical coefficients
- Parameter of diffractive components
- Coefficients of gradient media
General experience:
- Radii as parameter very effective
- Benefit of thickness and distances only weak
- Material parameter can only be changes discrete
Parameter of Optical Systems
13
Constraints in the optimization of optical systems:
1. Discrete standardized radii (tools, metrology)
2. Total track
3. Discrete choice of glasses
4. Edge thickness of lenses (handling)
5. Center thickness of lenses(stability)
6. Coupling of distances (zoom systems, forced symmetry,...)
7. Focal length, magnification, workling distance
8. Image location, pupil location
9. Avoiding ghost images (no concentric surfaces)
10. Use of given components (vendor catalog, availability, costs)
Constraints in Optical Systems
14
Illustration of not usefull results due to
non-sufficient constraints
Lack of Constraints in Optimization
negative edge
thickness
negative air
distance
lens thickness to largelens stability
to small
air space
to small
15
Typical merit function of an achromate
Three solutions, only two are useful
Optimization Landscape of an Achromate
aperture
reduced
good
solution
1
2
3
r1
r2
16
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
17
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
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
Optimization: Starting Point
object imageintermediate
imagepupil
f1
f2 f
3f4
f5
19
p1
p2
A
A'
B'
B
C'
D'
Optimization and Starting Point
The initial starting point
determines the final result
Only the next located solution
without hill-climbing is found
20
Effectiveness of correction
features on aberration types
Correction Effectiveness
Aberration
Primary Aberration 5th Chromatic
Spherical A
berr
ation
Com
a
Astigm
atism
Petz
val C
urv
atu
re
Dis
tort
ion
5th
Ord
er
Spherical
Axia
l C
olo
r
Late
ral C
olo
r
Secondary
Spectr
um
Sphero
chro
matism
Lens Bending (a) (c) e (f)
Power Splitting
Power Combination a c f i j (k)
Distances (e) k
Lens P
ara
mete
rs
Stop Position
Refractive Index (b) (d) (g) (h)
Dispersion (i) (j) (l)
Relative Partial Disp. Mate
rial
GRIN
Cemented Surface b d g h i j l
Aplanatic Surface
Aspherical Surface
Mirror
Specia
l S
urf
aces
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
21
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
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
22
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
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
23
Microscopic Objective Lens
Incidence angles for chief and
marginal ray
Aperture dominant system
Primary problem is to correct
spherical aberration
marginal ray
chief ray
incidence angle
0 5 10 15 20 2560
40
20
0
20
40
60
microscope objective lens
24
Photographic lens
Incidence angles for chief and
marginal ray
Field dominant system
Primary goal is to control and correct
field related aberrations:
coma, astigmatism, field curvature,
lateral color
incidence angle
chief
ray
Photographic lens
1 2 3 4 5 6 7 8 9 10 11 12 13 14 1560
40
20
0
20
40
60
marginal
ray
25
Sensitivity of a System
Ref: H.Zügge surfaces
Representation of wave
Seidel coefficients []
Double Gauss 1.4/50
26
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:
27
Symmetrical Dublet
f = 200 mm
f = 100 mm
f = 50 mm
f = 20 mm
f = 15 mm
No
focal 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
Lens bending
Lens splitting
Power combinations
Distances
Structural Changes for Correction
(a) (b) (c) (d) (e)
(a) (b)
Ref : H. Zügge
28
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
Aplanatic Surfaces
s'
0 50 100 150 200 250 300-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
Saplanatic
concentricvertex
oblate ellipsoidoblate ellipsoid prolate ellipsoidhyperboloid+ power series + power series+ power series + power series
sp
he
re
sp
he
re
Aplanatic surfaces: zero spherical aberration:
1. Ray through vertex
2. concentric
3. Aplanatic
Condition for aplanatic
surface:
Virtual image location
Applications:
1. Microscopic objective lens
2. Interferometer objective lens
s s und u u' '
s s' 0
ns n s ' '
rns
n n
n s
n n
ss
s s
'
' '
'
'
'
30
Aplanatic lenses
Combination of one concentric and
one aplanatic surface:
zero contribution of the whole lens to
spherical aberration
Not useful:
1. aplanatic-aplanatic
2. concentric-concentric
bended plane parallel plate,
nearly vanishing effect on rays
Aplanatic Lenses
A-A :
parallel offset
A-C :
convergence enhanced
C-C :
no effect
C-A :
convergence reduced
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
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
33
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
34
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
35
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
36
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
37
Influence of Stop Position on Performance
Ray path of chief ray depends on stop position
spotstop positions
38
field lens in
intermediate
image plane
lens L1
lens L2
chief ray
marginal ray
original
pupilshifted pupil
Field Lenses
Field lens: in or near image planes
Influences only the chief ray: pupil shifted
Critical: conjugation to image plane, surface errors sharply seen
39
Field Lens im Endoscope
Ref : H. Zügge
40
Evolution of Eyepiece Designs
Monocentric
Plössl
Erfle
Von-Hofe
Erfle diffractive
Wild
Erfle type(Zeiss)
BerteleScidmore
Loupe
Erfletype
Bertele
Kellner
Ramsden
Huygens
Kerber
König
Nagler 1
Nagler 2
Bertele
Aspheric
Dilworth
Families of photographic lenses
Long history
Not unique
Classification
Singlets
Landscape
Achromatic
Landscape
Petzval, Portrait
Petzval,Portrait flat R-Biotar
Petzval
Petzval
Projection
Quasi-Symmetrical Angle
Pleon
Panoramic
Lens
Extrem Wide Angle
Fish Eye
VivitarRetrofocus II
Wide Angle Retrofocus
Distagon
SLR
Flektogon
Retrofocus
PlasmatKino-Plasmat
Ultran
Noctilux
Quadruplets
Double Gauss
Biotar / Planar
Double Gauss II
Celor
Compact
Special
Plastic Aspheric
II
IR Camera Lens
Catadioptric
UV Lens
Plastic
Aspheric I
Telephoto
Telecentric II
Telecentric I
Super-Angulon
Hologon
MetrogonTopogon
Hypergon
Pleogon
Biogon
Triplet
Triplets
Inverse Triplet
Heliar Hektor
Pentac
Sonnar
Ernostar II
Less Symmetrical
Ernostar
Orthostigmatic
Symmetrical Doublets
Periskop
Rapid
Rectilinear
Aplanat
Dagor
Dagor
reversed
Angulon
Protar
AntiplanetUnar
Quasi-Symmetrical Doublets
Tessar
43
Medium Magnification Microscopic lenses
Development of Lithographic Lenses
b) Refractive spherical systems
a) Early systemsg) EUV
mirror
systems
M1
M3
M2
M4
M4
M3
M1
M2
M5
M6
M1
M2
M3
M4
M5
M6
M8
M6
c) Refractive with aspheres and immersion
d) Catadioptric cube
systems
e) Multi-axis catadioptric systems
f) Uni-axis catadioptric
systems
Modified Workflow in Instrument Development
Historical:
sequential workflow
Modern:
complex workflow with feedback and
relationships
Optical design
Tolerancing
Mechanical
Design
Manufacturing
components
Integration
Adjustment
Development
Metrology
phys-opt
Simulation
Researchlab
Control of
buyed
components
Software
Tests
Optical Design
Tolerancing
Mechanical
Design
Manufacturing
Assembly
Adjustment
Development
Performance
Check
Introduction to Tolerancing
Specifications are usually defined for the as-built system
Optical designer has to develop an error budget that cover all influences on
performance degradation as
- design imperfections
- manufacturing imperfections
- integration and adjustment
- environmental influences
No optical system can be manufactured perfectly (as designed)
- Surface quality, scratches, digs, micro roughness
- Surface figure (radius, asphericity, slope error, astigamtic contributions, waviness)
- Thickness (glass thickness and air distances)
- Refractive index (n-value, n-homogeneity, birefringence)
- Abbe number
- Homogeneity of material (bubbles and inclusions)
- Centering (orientation of components, wedge of lenses, angles of prisms, position of components)
- Size of components (diameter of lenses, length of prism sides)
- Special: gradient media deviations, diffractive elements, segmented surfaces,...
Tolerancing and development of alignment concepts are essential parts of the optical
design process 46 Ref: K. Uhlendorf
Data Sheet
Tolerances: Typical Values
Diameter Tolerance Unit <10 mm 10...20
mm
20...30
mm
Center thickness mm 0.02 0.03 0.03
Centering Tilt angle sek 60 60 60
Decenter/offset m 15 15 15
Roughness nm 15 10 10
Spherical/radius spherical rings 3 4 5
astigmatism rings .5 1 1
Asphericity Global deviation m 1 1.2 1.5
Global asphericity m 0.25 0.45 0.60
Local deviation m 0.025 0.05 0.075
Slope error rad 0.0005 0.0005 0.0005
Example Microscopic lens
Adjusting:
1. Axial shifting lens : focus
2. Clocking: astigmatism
3. Lateral shifting lens: coma
Ideal : Strehl DS = 99.62 %
With tolerances : DS = 0.1 %
After adjusting : DS = 99.3 %
Adjustment and Compensation
Ref.: M. Peschka
49
Adjustment and Compensation
Ref.: M. Peschka
50
Sucessive steps of improvements
Drawing of Microscopic Lens with Housing