www.iap.uni-jena.de

Optical Design with Zemax

Lecture 11+2: Correction

2013-07-07/12

Herbert Gross

Summer term 2013

2

Preliminary Schedule

1 12.04. Introduction

Introduction, Zemax interface, menues, file handling, preferences, Editors, updates,

windows, coordinates, System description, Component reversal, system insertion,

scaling, 3D geometry, aperture, field, wavelength

2 19.04. Properties of optical systems I Diameters, stop and pupil, vignetting, Layouts, Materials, Glass catalogs, Raytrace,

Ray fans and sampling, Footprints

3 26.04. 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 03.05. Aberrations I Representation of geometrical aberrations, Spot diagram, Transverse aberration

diagrams, Aberration expansions, Primary aberrations,

5 17.05. Aberrations II Wave aberrations, Zernike polynomials, Point spread function, Optical transfer

function

6 24.05. Optimization I

Principles of nonlinear optimization, Optimization in optical design, Global

optimization methods, Solves and pickups, variables, Sensitivity of variables in

optical systems

7 31.05. Optimization II Systematic methods and optimization process, Starting points, Optimization in Zemax

8 07.06. Imaging Fundamentals of Fourier optics, Physical optical image formation, Imaging in Zemax

9 20.06. Illumination Introduction in illumination, Simple photometry of optical systems, Non-sequential

raytrace, Illumination in Zemax

10 28.06. Advanced handling Make double pass, Material index fit, Report graphics, Universal plot, Slider, Visual

optimization, IO of data, Multiconfiguration, Macro language

11 05.07. Correction I Symmetry principle, Lens bending, Correcting spherical aberration, Coma, stop

position, Astigmatism, Field flattening, Chromatical correction, Design method

12 12.07. 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

1. Miscellaneous

2. Index fit

3. Universal plots

4. Slider and visual optimization

5. Multi configuration

6. Lens catalogs

7. Macro language

8. Data IO

9. Coupling of Zemax with Matlab

3

Contents

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

4

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

5

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

6

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

7

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

8

Sensitivity of a System

Ref: H.Zügge surfaces

Representation of wave

Seidel coefficients [l]

Double Gauss 1.4/50

9

Lens bending

Lens splitting

Power combinations

Distances

Structural Changes for Correction

(a) (b) (c) (d) (e)

(a) (b)

Ref : H. Zügge

10

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

l l

l

2

1

3

11

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

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

14

Splitting of lenses and appropriate bending:

1. compensating surface contributions

2. Residual zone errors

3. More relaxed

setups preferred,

although the

nominal error is

larger

Correcting Spherical Aberration : Power Splitting

2.0 mm

0.2 mm

(a)

(b)

(c)

(d)

(e)

0.2 mm

0.2 mm 0.2 mm

Ref : H. Zügge

15

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

16

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

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

17

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

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

18

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

19

Perfect coma correction in the case of symmetry

But magnification m = -1 not useful in most practical cases

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

20

Combined effect, aspherical case prevent correction

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

21

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

Coma Correction: Achromat

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

22

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

23

Bending effects astigmatism

For a single lens 2 bending with

zero astigmatism, but remaining

field curvature

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 [l]

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

24

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

25

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

26

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

27

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

28

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

Flattening Field Lens

29

Microscope Objective Lens

Possible setups for flattening

the field

Goal:

- reduction of Petzval sum

- keeping astigmatism corrected

d)

achromatized

meniscus lens

a)

single

meniscus

lense

e)

two

meniscus

lenses

achromatized

b)

two

meniscus

lenses

c)

symmetrical

triplet

f)

modIfied

achromatized

triplet solution

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

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

31

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

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

Achomatic solutions in the Glass Diagram

Achromat

flint

negative lens

crown

positive lens

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

l = 486 nm

l = 587 nm

l = 656 nm

sinu'

y'

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

Axial Colour: Achromate and Apochromate

l

e

F'

C'

achromateapochromate

residual error

apochromate

644

480

546

residual error

achromate

-100 0 100

singlet

s'

lens

36

Anormal partial dispersion and normal line

Axial Colour: Apochromate

37

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

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

38

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

Buried Surface

39

Principles of Glass Selection in Optimization

field flattening

Petzval curvature

color

correction

index n

dispersion

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

40

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

41

Field Lens im Endoscope

Ref : H. Zügge

42

Influence of Stop Position on Performance

Ray path of chief ray depends on stop position

spotstop positions

43

Example photographic lens

Small axial shift of stop

changes tranverse aberrations

In particular coma is strongly

influenced

stop

Effect of Stop Position

Ref: H.Zügge

44

Splitted achromate

Aspherical surface

Higher Order Aberrations: Achromate, Aspheres

achromat broken contact

0.0250-0.025

1

aspheric

a

0.010-0.01

1

0.0020-0.002

1

1

0.0002

1

0.00001

1

0.002

zone

zone zone

air space

ray

Ref : H. Zügge

45

Additional degrees of freedom for correction

Exact correction of spherical aberration for a finite

number of aperture rays

Strong asphere: many coefficients with high orders,

large oscillative residual deviations in zones

Location of aspherical surfaces:

1. spherical aberration: near pupil

2. distortion and astigmatism: near image plane

Use of more than 1 asphere: critical, interaction and

correlation of higher oders

SPH

tan u'

corrected

points

residual

spherical

aberration

Aspherical Surfaces

46

Improvement by higher orders

Generation of high gradients

Aspherical Expansion Order

r

y(r)

0 0.2 0.4 0.6 0.8 1-100

-50

0

50

100

12. order

6. order

10. order8. order

14. order

2 4 6 8 10 12 1410

-1

100

101

102

103

order

kmax

Drms

[mm]

Aspheres: Correction of Higher Order

Correction at discrete sampling

Large deviations between

sampling points

Larger oscillations for

higher orders

Better description:

slope,

defines ray bending

y y

residual spherical

transverse aberrations

Corrected

points

with

�y' = 0

paraxial

range

�y' = c dzA/dy

zA

perfect

correcting

surface

corrected points

residual angle

deviation

real asphere with

oscillations

points with

maximal angle

error

Lens with diffractive structured

surface: hybrid lens

Refractive lens: dispersion with

Abbe number = 25...90

Diffractive lens: equivalent Abbe

number

Combination of refractive and

diffractive surfaces:

achromatic correction for compensated

dispersion

Usually remains a residual high

secondary spectrum

Broadband color correction is possible

but complicated

refractive

lens

red

blue

green

blue

red

green

red

bluegreen

diffractive

lens

hybrid

lens

R D

453.3

CF

dd

ll

l

Achromatic Hybrid Lens

Dispersion by grating diffraction:

Abbe number

Relative partial dispersion

Consequence :

Large secondary spectrum

-P-diagram

Diffractive Optics: Dispersion

330.3''

CF

ee

ll

l

2695.0''

'

',

CF

Fg

FgPll

ll

normal

line

e

0.8

0.6

0.4

0.2-20 0 4020 60 80

DOE

SF59SF10

F4KzFS1

BK7

PgF'

Combination of DOE

and aspherical carrier

Diffractive Optics: Singlet Solutions

50 mm

0s'

y'

yp

yp

-0.5 mm50 mm

0s'

y'

yp

yp

-0.5 mm50 mm

0s'

y'

yp

yp

-0.5 mm50 mm

0s'

y'

yp

yp

-0.5 mm

diffractive

surface,

carrier

aspherical

refractive

surface,

aspherical

diffractive

surface, phase

aspherical

all 2. order

d

d

d

d,a

a

Data :

- l = 193 nm

- NA = 0.65

- b = 50

- sfree = 7.8 mm

Properties:

- short total track

- extreme large free working distance

- few lenses

Hybrid - Microscope Objective Lens

diffractive

element

1. Step :

Generation of high-NA on axis

Development of Microscopic Lens

d) 3 a-c meniscus

lenses

e) 3 a-c meniscus

lenses and 1 c-c

meniscus lens

NA = 0.589

NA = 0.589

NA = 0.214

b) 1 a-c meniscus

lens

c ) 2 a-c meniscus

lenses NA = 0.371

numerical aperture :

NA = 0.119

a ) without meniscus

lens

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2. Step :

Optimization on axis

Correcting thickness

Introducing free working distance

Inserting finite field

Development of Microscopic Lens

axis

correction

1. version :

2. and 4. lens to thin,

field 20 mm

2. version :

free working

distance to short,

field 50 mm

3. version :

field 100 mm

54

3. Step :

Improvements

Additional degrees of freedom

Material changes

Avoiding strong bendings

Optimization of lens-thickness

Comparison of variants

Fine-tuning

Development of Microscopic Lens

55

Overview of the steps of development

Development of Microscopic Lens

1. Correction on axis,

quality good

2. Correction with field,

compact,

quality not sufficient

3. Correction with triplet,

some surfaces obsolet,

quality not sufficient

4. Correction with one

doublet and larger air

distances, quality not

sufficient

5. Correction with two

doublets, quality nearly

good enough

6. Further optimization

with glass choices,

better field uniformity

7. with working distance

and telecentricity

56