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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

11

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

18

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