Lens Design I...2 Preliminary Schedule - Lens Design I 2019 1 11.04. Basics Introduction, Zemax...
Transcript of Lens Design I...2 Preliminary Schedule - Lens Design I 2019 1 11.04. Basics Introduction, Zemax...
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Lens Design I
Lecture 10: Optimization II
2019-06-20
Herbert Gross
Summer term 2019
2
Preliminary Schedule - Lens Design I 2019
1 11.04. Basics
Introduction, Zemax interface, menues, file handling, preferences, Editors,
updates, windows, coordinates, System description, 3D geometry, aperture,
field, wavelength
2 18.04. Properties of optical systems IDiameters, stop and pupil, vignetting, layouts, materials, glass catalogs,
raytrace, ray fans and sampling, footprints
3 25.04. Properties of optical systems II
Types of surfaces, cardinal elements, lens properties, Imaging, magnification,
paraxial approximation and modelling, telecentricity, infinity object distance
and afocal image, local/global coordinates
4 02.05. Properties of optical systems IIIComponent reversal, system insertion, scaling of systems, aspheres, gratings
and diffractive surfaces, gradient media, solves
5 09.05. Advanced handling IMiscellaneous, fold mirror, universal plot, slider, multiconfiguration, lens
catalogs
6 16.05. Aberrations IRepresentation of geometrical aberrations, spot diagram, transverse
aberration diagrams, aberration expansions, primary aberrations
7 23.05. Aberrations II Wave aberrations, Zernike polynomials, measurement of quality
8 06.06. Aberrations III Point spread function, optical transfer function
9 13.06. Optimization IPrinciples of nonlinear optimization, optimization in optical design, general
process, optimization in Zemax
10 20.06. Optimization II Initial systems, special issues, sensitivity of variables in optical systems, global
optimization methods
11 27.06. Advanced handling IISystem merging, ray aiming, moving stop, double pass, IO of data, stock lens
matching
12 04.07. Correction ISymmetry principle, lens bending, correcting spherical aberration, coma,
astigmatism, field curvature, chromatical correction
13 11.07. Correction IIField lenses, stop position influence, retrofocus and telephoto setup, aspheres
and higher orders, freeform systems, miscellaneous
1. Initial systems
2. Special issues
3. Sensitivity of variables in optical systems
4. Global methods
3
Contents
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
4
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
5
6
Initial System Influence
Simple system of two lenses
Criterion:
spot on axis, one wavelength
Starting with different radii of curvature:
completly different solutions
Initial Systems for Extreme Field / Aperture
Large aperture: start with corrected marginal ray
Large filed: start with corrected chief ray
7
field
w
aperture
NA
constant
etenduemicroscopic
lenses
wide angle
camera lenses
start with
Shafer:
CR corrected
start with AC-lens:
MR corrected
optimization:
increase field
optimization:
increase
aprture
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
8
Lens bending
Lens splitting
Power combinations
Distances
Structural Changes for Correction
(a) (b) (c) (d) (e)
(a) (b)
Ref : H. Zügge
9
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
10
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
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12
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
Reality:
- as-designed performance: not reached in reality
- as-built-performance: more relevant
Possible criteria:
1. Incidence angles of refraction
2. Squared incidence angles
3. Surface powers
4. Seidel surface contributions
5. Permissible tolerances
Special aspects:
- relaxed systems does not contain
higher order aberrations
- special issue: thick meniscus lenses
Sensitivity and Relaxation
13
performance
parameter
best
as
built
tolerance
interval
local optimal
design
optimal
design
Quantitative measure for relaxation
with normalization
Non-relaxed surfaces:
1. Large incidence angles
2. Large ray bending
3. Large surface contributions of aberrations
4. Significant occurence of higher aberration orders
5. Large sensitivity for centering
Internal relaxation can not be easily recognized in the total performance
Large sensitivities can be avoided by incorporating surface contribution of aberrations
into merit function during optimization
Fh
Fh
F
FA
jjj
jj
1
11
k
j
jA
Sensitivity of a System
14
Sensitivity/relaxation:
Average of weighted surface contributions
of all aberrations
Correctability:
Average of all total aberration values
Total refractive power
Important weighting factor:
ratio of marginal ray heights
1 2 3 4 5 6 7 8 91
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
-50
-40
-30
-20
-10
0
1
0
2
0
3
0
4
0
Sph
1 2 3 4 5 6 7 8 91
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
-50
-40
-30
-20
-10
0
1
0
2
0
3
0
Ko
m
a
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20-2
-1
0
1
2
3
4
Ast
1 2 3 4 5 6 7 8 91
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
-20
-10
0
1
0
2
0
3
0
4
0
CHL
1 2 3 4 5 6 7 8 91
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
0
1
0
2
0
3
0
4
0
5
0
Inz-
Wi
Sph
Coma
Ast
CHL
incidenceangle
k
j
jj FFF2
1
1h
h j
j
Sensitivity of a System
15
16
Design Solutions and Sensitivity
Focussing
3 lens with
NA = 0.335
Spherical
correction
with/without
compensation
Red surface:
main correcting
surface
Counterbeding
every lens in
one direction
17
Relaxed Design
Photographic lens comaprison
Data:
F# = 2.0
f = 50 mm
Field 20°
Same size and quality
Considerably tigher tolerances in the
first solution
Ref: D. Shafer
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
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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 colorincidence 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
19
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
20
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
Simulated Annealing:
temporarily added term to
overcome local minimum
Optimization and adaptation
of annealing parameters
Global Optimization: Escape method of Isshiki
merit
function
F(x)
x
F
global
minimum xglo
local
minimum xloc
conventional
path
merit
function with
additive term
F(x)+Fesc
Fesc 2
0)(
0)(FxF
esc eFxF
= 1 . 0
= 0 .5
= 0 . 01
22
No unique solution
Contraints not sufficient
fixed:
unwanted lens shapes
Many local minima with
nearly the same
performance
Global Optimization
reference design : F = 0.00195
solution 1 : F = 0.000102
solution 2 : F = 0.000160
solution 3 : F = 0.000210
solution 4 : F = 0.000216
solution 5 : F = 0.000266
solution 10 : F = 0.000384
solution 6 : F = 0.000273
solution 7 : F = 0.000296
solution 8 : F = 0.000312
solution 9 : F = 0.000362
solution 11 : F = 0.000470
solution 12 : F = 0.000510
solution 13 : F = 0.000513
solution 14 : F = 0.000519
solution 15 : F = 0.000602
solution 16 : F = 0.000737
23
Saddel points in the merit function topology
Systematic search of adjacend local minima is possible
Exploration of the complete network of local minima via saddelpoints
Saddel Point Method
S
M1
M2
Fo
Example Double Gauss lens of system network with saddelpoints
Saddel Point Method