Design and Correction of optical Systems

Part 14: Optical system classification

Summer term 2012

Herbert Gross

1

Overview

1. Basics 2012-04-18

2. Materials 2012-04-25

3. Components 2012-05-02

4. Paraxial optics 2012-05-09

5. Properties of optical systems 2012-05-16

6. Photometry 2012-05-23

7. Geometrical aberrations 2012-05-30

8. Wave optical aberrations 2012-06-06

9. Fourier optical image formation 2012-06-13

10. Performance criteria 1 2012-06-20

11. Performance criteria 2 2012-06-27

12. Measurement of system quality 2012-07-04

13. Correction of aberrations 1 2012-07-11

14. Optical system classification 2012-07-18

2012-04-18

14.1 Overview and classification

14.2 Achromate

14.3 Collimator

14.4 Microscope optics

14.5 Photographic optics

14.6 Zoom lenses

14.7 Telescopes

14.8 Miscellaneous

14.9 Lithographic projection systems

Content

Field-Aperture-Diagram

0.20 0.4 0.6 0.80°

4°

8°

12°

16°

20°

24°

28°

32°

36°

NA

w

40°

micro100x0.9

doubleGauss

achromat

Triplet

micro40x0.6

micro10x0.4

Sonnar

Biogon

splittriplet

Distagon

disc

projectionGauss

diodecollimator

projection

Petzval

micros-copy

collimatorfocussing

photographic

projection constantetendue

lithographyBraat 1987

lithography2003

� 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

1. Photo objective lens

2. Microscope objective lens

3. Binocular

4. Infrared afocal system

Typical Example Systems 1

5. Relay optics

6. Scan-objective lens

7. Collimator objective lens

Typical Example Systems 2

possible surfaces under test

8. Projector lens

9. Telescope

10. Lithography projection

lens

Typical Example Systems 3

M1

M2

M3

11. Illumination collector system

12. Illumination condenser system

13. Head mounted display

Typical Example Systems 4

eyepupil

image

totalinternal

reflection

free formedsurface

free formed

surface

field angle 14°

14. Stereo microscope

15. Zoom system

Typical Example Systems 5

eyepiece

tube

system zoom

system objectplane

eye

common

axis

stereo

angle

common

objectivelens

f = 61

f = 113

f = 166

� Achromate:

- Axial colour correction by cementing two

different glasses

- Bending: correction of spherical aberration at the

full aperture

- Aplanatic coma correction possible be clever

choice of materials

� Four possible solutions:

- Crown in front, two different bendings

- Flint in front, two different bendings

� Typical:

- Correction for object in infinity

- spherical correction at center wavelength

with zone

- diffraction limited for NA < 0.1

- only very small field corrected

Achromate

solution 1 solution 2

Crown in

front

Flint in

front

Achromate: Realization Versions

� Advantage of cementing:

solid state setup is stable at sensitive middle surface with large curvature

� Disadvantage:

loss of one degree of freedom

� Different possible realization

forms in practice

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 ν-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

21FFF +=

0

2

2

1

1=+

νν

FF

FF ⋅

−

=

1

2

1

1

1

ν

νFF ⋅

−

=

2

1

2

1

1

ν

ν

case without solution,

only sperical minimum

case with 2 solutions

case with

one solutionand coma

correction

∆∆∆∆s'rim

R1

Achromate: Correction

� Cemented achromate:6 degrees of freedom:3 radii, 2 indices, ratio ν1/ν2

� Correction of spherical aberration:diverging cemented surface with positivespherical contribution for nneg > npos

� Choice of glass: possible goals1. aplanatic coma correction2. minimization of spherochromatism3. minimization of secondary spectrum

� Bending has no impact on chromaticalcorrection:is used to correct spherical aberrationat the edge

� Three solution regions for bending1. no spherical correction2. two equivalent solutions3. 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

λλλλ = 486 nm

λλλλ = 587 nm

λλλλ = 656 nm

sinu'

∆∆∆∆y'

Achromate

� Residual aberrations of an achromate

� Clearly seen:

1. Distortion

2. Chromatical magnification

3. Astigmatism

Collimation

D

source

θθθθG/2divergence

f

u

� Collimating source radiation:

Finite divergence angle is reality

� Geometrical part due to finite size :

� Diffraction part:

� Defocussing contribution to divergence

f

DG ====θ

DD

λθ ====

uf

zsin

2⋅⋅⋅⋅−−−−====

∆∆θ

Collimator Optics

spherical

coma

astigmatism

curvature

distortion

1 2 3 sum

-0.1

0

0.1

-5

0

5

-2

0

2

-2

0

2

-4

-2

0

2

4

4

� Monochromatic doublet

� Correction only spherical and coma:

Seidel surface contributions

Limiting : astigmatism and curvature

� Enlarged aperture : meniscus added

Collimator Optics

0.2

0.5

0.1

0

0.05

0.15

Wrms

w [°]0 0.1 0.2 0.3 0.4

diffraction limit

NA = 0.124NA = 0.187NA = 0.277

a) NA = 0.124

b) NA = 0.187

c) NA = 0.277

� Enlarging numerical aperture by aplanatic-concentric meniscus lenses

� Extreme good correction of spherical aberration

Microscopy - Image Planes and Pupils

� Upper row : image planes

� Lower row : pupil planes

� Köhler setup

Upright-Microscope

� Sub-systems:

1. Detection / Imaging path

1.1 objective lens

1.2 tube with tube lens and

binocular beam splitter

1.3 eyepieces

1.4 optional equipment

for photo-detection

2. Illumination

2.1 lamps with collector and filters

2.2 field aperture

2.3 condenser with aperture stop

eyepiece

photocamera

tube lens

objectivelens

lamp

lamp

collector

collector

condensor

intermediateimage

binocularbeamsplitter

object

film plane

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

Microscope Objective Lens: Flattening

� Three different classes:

1. No effort

2. Semi-flat

3. Completely flatD

S

rel.field

0 0.5 0.707 1

1

0.8

0.6

0.4

0.2

0

diffractionlimit

plane

semiplane

notplane

Microscope Objective Lens

� Possible setups for flattening

the field

� Goal:

- reduction of Petzval sum

- keeping astigmatism corrected

d)achromatized

meniscus lens

a)single

meniscuslense

e)

twomeniscuslenses

achromatized

b)twomeniscus

lenses

c)symmetricaltriplet

f)

modIfiedachromatizedtriplet solution

Microscopic Objective Lens

mechanical

setup

� Families of photographic lenses

� Long history

� Not unique

Classification

Singlets

LandscapeAchromatic

Landscape

Petzval, Portrait

Petzval,Portrait flat R-Biotar

Petzval

PetzvalProjection

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 AsphericII

IR Camera Lens

Catadioptric

UV Lens

PlasticAspheric 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

RapidRectilinear

Aplanat

Dagor

Dagor

reversed

Angulon

Protar

AntiplanetUnar

Quasi-Symmetrical Doublets

Tessar

� Tessar

� Double Gauss

� Super Angulon

Photographic Lenses

� Distagon

� Tele system

� Wide angle

Fish-eye

� Example lens 2

� Distagon

Retrofocus Lenses

� Nikon 210°

� Pleon

(air reconnaissance)

Fish-Eye-Lens

Change of Focal Length

� Distance t increased

� First lens fixed

moved

lenschanged

distance

t changed focal

length f

Change of Focal Length

� Distance t increased

� Image plane fixed

two lenses moved

t f

image

plane

Performance Variation over z

� System layout

f = 200 mm

f = 100 mm

f = 50 mm

f = 67 mm

f = 133 mm

f1 f

2f3 f

4

t2

Performance Variation over z

Seidel

surface

contrib.

coma distortion axial chromatical lateral chromatical

lens 1

lens 2

lens 3

sum

spherical aberration

1 2 3 4 5

1 2 3 4 5

1 2 3 4 5

1 2 3 4 5

-0.1

0

0.1

-0.1

0

0.1

-0.1

0

0.1

-0.1

0

0.1

1 2 3 4 5

1 2 3 4 5

1 2 3 4 5

1 2 3 4 5

-0.2

-0.1

0

0.1

0.2

-0.2

-0.1

0

0.1

0.2

-0.2

-0.1

0

0.1

0.2

-0.2

-0.1

0

0.1

0.2

1 2 3 4 5

-5

0

5

1 2 3 4 5

-5

0

5

1 2 3 4 5

-5

0

5

1 2 3 4 5

-5

0

5

1 2 3 4 5

-5

0

5

1 2 3 4 5

-5

0

5

1 2 3 4 5

-5

0

5

1 2 3 4 5

-5

0

5

1 2 3 4 5

-0.5

0

0.5

1 2 3 4 5

-0.5

0

0.5

1 2 3 4 5

-0.5

0

0.5

1 2 3 4 5

-0.5

0

0.5

� Zoom lens

� Three moving groups

Zoom Lens

e)f' = 203 mmw = 5.64°F# = 16.6

d)f' = 160 mmw = 7.13°F# = 13.7

c)f' = 120 mmw = 9.46°F# = 10.9

b)f' = 85 mmw = 13.24°F# = 8.5

a)f' = 72 mmw = 15.52°F# = 7.7

group 1 group 2 group 3

Basic Refractive Telescopes

� Kepler typ:

- internal focus

- longer total track

- Γ > 0

� Galilei typ:

- no internal focus

- shorter total track

- Γ < 0

Telescopepupil

intermediatefocus

Eyepiece

Eye pupil

telescope focal length fT

eyepiece focal length f

ETelescopepupil

Eye pupil

telescope focal length fT

eyepiece focal length f E

a) Kepler/Fraunhofer

b) Galilei

Catadioptric Telescopes

� Maksutov compact

� Klevtsov

M1

M2

L1

L2L3 L4, L5

M1

L1, L2

M2

Astronomical Telescope

Primary and

secondary mirror

Telecentric Systems

∆∆∆∆wtele

[°]

y'/y'max

0 0.2 0.4 0.6 0.8 1-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

chiefray

centre ray

axis

3°

5°

486 nm 587 nm 656 nm

� Typical :

system layout with two groups

� Telecentricity error due to vignetting

� Telecentricity forces large diameters

Relay Systems: Endoscopes

� Transport over large distances

� Combination of several relay subsystems

� Large field-angle objective lens

� Applications: Technical or medical

� Different subsystems:

objective 1. relay 2. relay 3. relay

0.5

486 nm

587 nm656 nm

0.4

00 0.4

Wrms

[λλλλ]

0.8 1.2 21.6

y'[mm]

0.3

0.2

0.1

diffraction limit

Handy Phone Objective lenses

� Examples

Ref: T. Steinich

Beam Guiding Systems

ΓΓΓΓ = 5

ΓΓΓΓ = 5

ΓΓΓΓ = 4

ΓΓΓΓ = 50

ΓΓΓΓ = 4

a)

b)

c)

d)

e)

adjustment

� Transport of laser light over large

distances

� Adaptation of beam diameter

� Solutions :

Telescopes of Kepler or Galilei type

Beam Guiding Systems

dark colours : Kepler / bright colours : Galilei

-0.02

0

0.02

-0.01

0

0.01

-2

0

2

-2

0

2

-1

0

1

spherical

coma

astigmatism

curvature

distortion

sum4321

� Comparison:

Kepler:

- internal focus

- large overall length

Galilei:

- shorter length

- better correction

Navarro Eye Model

� Wide angle model for larger fields

� Parameters for all accomodations

� Description of chromatical aberrations

30°

20°

15°

0°

0°

459 nm 550 nm 632 nm

15°

20°

30°

Optical Illusion

The rings seems

to move

Abbe Orthoscopic Eyepiece

� Distortion corrected

� General problems with eyepieces:

- remote eye pupil

- typical eye relief 22 mm

-1.000 0.000 1.000

0.250

0.500

0.750

1.000

LONGITUDINALSPHERICAl ABER.

DIOPTER

-3.000 0.000 3.000

2.000

4.000

6.000

8.000

tan sag

ASTIGMATICFIELD CURVES

DIOPTER

-20.00 0.00 20.00

2.000

4.000

6.000

8.000

DISTORTION

Distortion (%)

0°

10°

18°

20 a

rcm

in

Scan System

� Non-telecentric

� Scan angle 2x30°

� Monochromatic

� F-θ-corrected

a) standard distortion

-10%

1

0.5

y/ymax

b) f-θθθθ-distortion

0 10% -0.2% 0 0.2%

1

0.5

y/ymax

0

0.1

0.08

0.06

0.04

0.02

0

Wrms

[λλλλ]

15° 30°θθθθ

c) wave aberration

0° 5° 10°

20°

15°

24° 28° 30.4°

Lithographic Lenses

System with

1. Illumination (horizonthal)

2. Mask projection (vertical)

Lithographic Lens Example Layouts

reticle

mask

stop

mask

reticle

stop

1. relay group

2. relay group

reticle

wafer

mirrorwith relay

group

intermediateimage

Lithographic Optics

� EUV α-Tool 2008

Summary of Important Topics

� A possible classification of optical systems is a sorting into field size and aperture size

� Aperture, field size and width of wavelength range are responsable for complexity

� Achromate: chromatical and spherical correction

� Achromate: additional degree of freedom allows for coma correction or reduction of

spherochromatism

� Achromate: different realization options possible

� There exist quite different types of optical systems with individual specific problems

50

Outlook

Next lecture: Special lectures and applications in the context of optical design

Date: Winter term / October 2012