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Optical Design with Zemax

Lecture 11: Correction I

2013-01-22

Herbert Gross

Summer term 2012

2 11 Correction I

Preliminary time schedule

1 16.10. Introduction

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

Coordinate systems and notations, System description, Component reversal, system insertion,

scaling, 3D geometry, aperture, field, wavelength

2 23.10. Properties of optical systems I Diameters, stop and pupil, vignetting, Layouts, Materials, Glass catalogs, Raytrace, Ray fans

and sampling, Footprints

3 30.10. 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 06.11. Aberrations I Representation of geometrical aberrations, Spot diagram, Transverse aberration diagrams,

Aberration expansions, Primary aberrations,

5 13.+27.11. Aberrations II Wave aberrations, Zernike polynomials, Point spread function, Optical transfer function

6 04.12. Advanced handling

Telecentricity, infinity object distance and afocal image, Local/global coordinates, Add fold

mirror, Vignetting, Diameter types, Ray aiming, Material index fit, Universal plot, Slider,IO of

data, Multiconfiguration, Macro language, Lens catalogs

7 11.12. Optimization I Principles of nonlinear optimization, Optimization in optical design, Global optimization

methods, Solves and pickups, variables, Sensitivity of variables in optical systems

8 18.12. Optimization II Systematic methods and optimization process, Starting points, Optimization in Zemax

9 08.01 Imaging Fundamentals of Fourier optics, Physical optical image formation, Imaging in Zemax

10 15.01. Illumination Introduction in illumination, Simple photometry of optical systems, Non-sequential raytrace,

Illumination in Zemax

11 22.01. Correction I

Symmetry principle, Lens bending, Correcting spherical aberration, Coma, stop position,

Astigmatism, Field flattening, Chromatical correction, Retrofocus and telephoto setup, Design

method

12 29.01. 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

13 05.02. Physical optical modelling Gaussian beams, POP propagation, polarization raytrace, coatings

1. Symmetry principle

2. Lens bending

3. Correcting spherical aberration

4. Coma, stop position

5. Astigmatism

6. Field flattening

7. Chromatical correction

8. Retrofocus and telephoto setup

9. Design method

10. Starting points

11 Correction I

Contents

3

11 Correction I

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

4

11 Correction I

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

5

11 Correction I

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

6

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

11 Correction I

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

7

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

11 Correction I

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

8

11 Correction I

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

9

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

11 Correction I

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

10

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

11 Correction I

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

11

Perfect coma correction in the case of symmetry

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

11 Correction I

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

12

Combined effect, aspherical case prevent correction

11 Correction I

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

13

11 Correction I

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

14

Bending effects astigmatism

For a single lens 2 bending with

zero astigmatism, but remaining

field curvature

11 Correction I

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 []

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

15

11 Correction I

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

16

11 Correction I

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

17

11 Correction I

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

18

Group of meniscus lenses

Effect of distance and

refractive indices

11 Correction I

Correcting Petzval Curvature

r 2r 1

collimated

n n

d

3020 5010

-3

10-1

10-2

1/Rpet [1/mm]

40r

1

[mm]10

K5 / d=15 mm

SF66 / d=15 mm

K5 / d=25 mm

From : H. Zügge

19

11 Correction I

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

20

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

11 Correction I

Flattening Field Lens

21

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

11 Correction I

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

22

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

11 Correction I

Achromate

solution 1 solution 2

Crown in

front

Flint in

front

11 Correction I

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

edge contact cemented

a) flint in front

edge contact cemented contact on axis broken, Gaussian setup

b) crown in front

11 Correction I

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

11 Correction I

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

11 Correction I

Achomatic solutions in the Glass Diagram

Achromat

flint

negative lens

crown

positive lens

11 Correction I

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

= 486 nm

= 587 nm

= 656 nm

sinu'

y'

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

Cases:

a) simple achromate,

sph corrected, with coma

b) simple achromate,

coma corrected by bending, with sph

c) other glass choice: sph better, coma reversed

d) splitted achromate: all corrected

e) aplanatic glass choice: all corrected

11 Correction I

Coma Correction: Achromate

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

11 Correction I

Achromate

Residual aberrations of an achromate

Clearly seen:

1. Distortion

2. Chromatical magnification

3. Astigmatism

Residual spherochromatism of an achromate

Representation as function of apeture or wavelength

11 Correction I

Spherochromatism: Achromate

longitudinal aberration

0

rp

0.080.04 0.12z

defocus variation

pupil height :

rp = 1

rp = 0.707

rp = 0.4

rp = 0

0-0.04 0.080.04

587

656

486z

1

486 nm

587 nm

656 nm

31

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

11 Correction I

Axial Colour: Achromate and Apochromate

e

F'

C'

achromateapochromate

residual error

apochromate

644

480

546

residual error

achromate

-100 0 100

singlet

s'

lens

32

Anormal partial dispersion and normal line

11 Correction I

Axial Colour: Apochromate

33

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

11 Correction I

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

34

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

11 Correction I

Buried Surface

35

P'

f 's '

d

yy

ba

b

a

k f '

8 Correction II

Telephoto Systems

Combination of a positiv and a negative lens:

Shift of the first principal plane in front of the system

The intersection length is smaller than the focal length: reduction factor k

Typical values: k = 0.6...0.9

Focal lengths:

Overall length

Free intersection length

ff d

f k da

'

' ( )1

f

f d kf d

f kfb

a

a

'

'

L k f '

s k f df '

P'

f '

s '

8 Correction II

Retrofocal System

Combination of a negative and a positive lens:

Shift of the second principal plane behind the system

The intersection length is larger than the focal length

Application: systems for large free working distance

Corresponds to an inverse telephoto system

Retrofocus system results form a telephoto system by inversion

8 Correction II

Telephoto and inverse Telephoto Principle

focal length f

telephoto systemprincipal plane P'

retrofocus systeminverse telephoto

imageplane

11 Correction I

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

39

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

11 Correction I

Optimization: Starting Point

object imageintermediate

imagepupil

f1

f2 f

3f4

f5

40

11 Correction I

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

41

Lens bending

Lens splitting

Power combinations

Distances

11 Correction I

Correction Methods

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

(a) (b)

Ref : H. Zügge

42

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.

11 Correction I

Zero-Operations

43