www.iap.uni-jena.de

Medical Photonics Lecture

Optical Engineering

Lecture 11: Optical Design

2017-01-12

Herbert Gross

Winter term 2016

2

Contents

No Subject Ref Date Detailed Content

1 Introduction Gross 20.10. Materials, dispersion, ray picture, geometrical approach, paraxial approximation

2 Geometrical optics Gross 03.11. Ray tracing, matrix approach, aberrations, imaging, Lagrange invariant

3 Components Kempe 10.11. Lenses, micro-optics, mirrors, prisms, gratings

4 Optical systems Gross 17.11. Field, aperture, pupil, magnification, infinity cases, lens makers formula, etendue, vignetting

5 Aberrations Gross 24.11. Introduction, primary aberrations, miscellaneous

6 Diffraction Gross 01.12. Basic phenomena, wave optics, interference, diffraction calculation, point spread function, transfer function

7 Image quality Gross 08.12. Spot, ray aberration curves, PSF and MTF, criteria

8 Instruments I Kempe 15.12. Human eye, loupe, eyepieces, photographic lenses, zoom lenses, telescopes

9 Instruments II Kempe 22.12. Microscopic systems, micro objectives, illumination, scanning microscopes, contrasts

10 Instruments III Kempe 05.01. Medical optical systems, endoscopes, ophthalmic devices, surgical microscopes

11 Optic design Gross 12.01. Aberration correction, system layouts, optimization, realization aspects

12 Photometry Gross 19.01. Notations, fundamental laws, Lambert source, radiative transfer, photometry of optical systems, color theory

13 Illumination systems Gross 26.01. Light sources, basic systems, quality criteria, nonsequential raytrace

14 Metrology Gross 02.02. Measurement of basic parameters, quality measurements

Modelling of Optical Systems

Principal purpose of calculations:

System, data of the structure(radii, distances, indices,...)

Function, data of properties,

quality performance(spot diameter, MTF, Strehl ratio,...)

Analysisimaging

aberration

theorie

Synthesislens design

Ref: W. Richter

Imaging model with levels of refinement

Analytical approximation and classification

(aberrations,..)

Paraxial model

(focal length, magnification, aperture,..)

Geometrical optics

(transverse aberrations, wave aberration,

distortion,...)

Wave optics

(point spread function, OTF,...)

with

diffractionapproximation

--> 0

Taylor

expansion

linear

approximation

3

Log w

Log NA0.02 0.05 0.10 1.00.500.20

0.5°

1.0°

2.0°

5.0°

10°

20°

50°

100°

Retrofocus

objective

0.2°

Tessar

Cooke-triplet

Double-

Gauss

objective

Petzval-

objective

landscape

objective

Schmidt-

Cassegrain

telescope

3-mirror

telescope

Schmidt

telescope

Microscope

objective

Ritchey-Cretien

telescope

Cassegrain

telescope

DiskobjectiveAchromate

Paraboloid

telescope

Fisheye

objective

Classification in Field and Aperture Size

Overview and sorting

Different types of systems

Diagram of W. Smith:

aperture vs field size

Spectral properties not concidered

Field-Aperture-Diagram

0.20 0.4 0.6 0.80°

4°

8°

12°

16°

20°

24°

28°

32°

36°

NA

w

40°

micro

100x0.9

double

Gauss

achromat

Triplet

micro

40x0.6micro

10x0.4

Sonnar

Biogon

split

triplet

Distagon

disc

projection

Gauss

diode

collimator

projection

Petzval

micros-

copy

collimator

focussing

photographic

projection constant

etendue

lithography

Braat 1987

lithography

2003

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

Throughput as field-

aperture product

Additional dimension:

spectral bandwidth

Classification: -Lw-Diagram

Lw

Photography

Microscopy

Astronomy

LithographyInterferometer

lensmetrology lens

Surface Contributions: Example

7

Seidel aberrations:

representation as sum of

surface contributions possible

Gives information on correction

of a system

Example: photographic lens

1

23 4

5

6 8 9

10

7

Retrofocus F/2.8

Field: w=37°

SI

Spherical Aberration

SII

Coma

-200

0

200

-1000

0

1000

-2000

0

2000

-1000

0

1000

-100

0

150

-400

0

600

-6000

0

6000

SIII

Astigmatism

SIV

Petzval field curvature

SV

Distortion

CI

Axial color

CII

Lateral color

Surface 1 2 3 4 5 6 7 8 9 10 Sum

Basic Idea of Optimization

iteration

path

topology of

meritfunction F

x1

x2

start

Topology of the merit function in 2 dimensions

Iterative down climbing in the topology

8

Mathematical description of the problem:

n variable parameters

m target values

Jacobi system matrix of derivatives,

Influence of a parameter change on the

various target values,

sensitivity function

Scalar merit function

Gradient vector of topology

Hesse matrix of 2nd derivatives

Nonlinear Optimization

x

)(xf

j

iji

x

fJ

21

)()(

m

i

ii xfywxF

j

jx

Fg

kj

kjxx

FH

2

9

Types of constraints

1. Equation, rigid coupling, pick up

2. One-sided limitation, inequality

3. Double-sided limitation, interval

Numerical realizations :

1. Lagrange multiplier

2. Penalty function

3. Barriere function

4. Regular variable, soft-constraint

Boundary Conditions and Constraints

x

F(x)

permitted domain

F0(x) p

small

penalty

function

P(x)

p large

xmaxx

min

x

F(x)

permitted domain

F0(x)

barrier

function

B(x)

p large

p small

10

Goal of optimization:

Find the system layout which meets the required performance targets according of the

specification

Formulation of performance criteria must be done for:

- Apertur rays

- Field points

- Wavelengths

- Optional several zoom or scan positions

Selection of performance criteria depends on the application:

- Ray aberrations

- Spot diameter

- Wavefornt description by Zernike coefficients, rms value

- Strehl ratio, Point spread function

- Contrast values for selected spatial frequencies

- Uniformity of illumination

Usual scenario:

Number of requirements and targets quite larger than degrees od freedom,

Therefore only solution with compromize possible

Optimization Merit Function in Optical Design

11

Merit function:

Weighted sum of deviations from target values

Formulation of target values:

1. fixed numbers

2. one-sided interval (e.g. maximum value)

3. interval

Problems:

1. linear dependence of variables

2. internal contradiction of requirements

3. initail value far off from final solution

Types of constraints:

1. exact condition (hard requirements)

2. soft constraints: weighted target

Finding initial system setup:

1. modification of similar known solution

2. Literature and patents

3. Intuition and experience

Optimization in Optical Design

g f fj j

ist

j

soll

j m

2

1,

12

Characterization and description of the system delivers free variable parameters

of the system:

- Radii

- Thickness of lenses, air distances

- Tilt and decenter

- Free diameter of components

- Material parameter, refractive indices and dispersion

- Aspherical coefficients

- Parameter of diffractive components

- Coefficients of gradient media

General experience:

- Radii as parameter very effective

- Benefit of thickness and distances only weak

- Material parameter can only be changes discrete

Parameter of Optical Systems

13

Constraints in the optimization of optical systems:

1. Discrete standardized radii (tools, metrology)

2. Total track

3. Discrete choice of glasses

4. Edge thickness of lenses (handling)

5. Center thickness of lenses(stability)

6. Coupling of distances (zoom systems, forced symmetry,...)

7. Focal length, magnification, workling distance

8. Image location, pupil location

9. Avoiding ghost images (no concentric surfaces)

10. Use of given components (vendor catalog, availability, costs)

Constraints in Optical Systems

14

Illustration of not usefull results due to

non-sufficient constraints

Lack of Constraints in Optimization

negative edge

thickness

negative air

distance

lens thickness to largelens stability

to small

air space

to small

15

Typical merit function of an achromate

Three solutions, only two are useful

Optimization Landscape of an Achromate

aperture

reduced

good

solution

1

2

3

r1

r2

16

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

17

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

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

19

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

20

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

21

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

22

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

23

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

24

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 color

incidence 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

25

Sensitivity of a System

Ref: H.Zügge surfaces

Representation of wave

Seidel coefficients []

Double Gauss 1.4/50

26

Variable focal length

f = 15 ...200 mm

Invariant:

object size y = 10 mm

numerical aperture NA = 0.1

Type of system changes:

- dominant spherical for large f

- dominant field for small f

Data:

27

Symmetrical Dublet

f = 200 mm

f = 100 mm

f = 50 mm

f = 20 mm

f = 15 mm

No

focal length [mm]

Length [mm]

spherical c9

field curvature c4

astigma-tism c5

1 200 808 3.37 -2.01 -2.27

2 100 408 1.65 1.19 -4.50

3 50 206 1.74 3.45 -7.34

4 20 75 0.98 3.93 2.31

5 15 59 0.20 16.7 -5.33

Lens bending

Lens splitting

Power combinations

Distances

Structural Changes for Correction

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

(a) (b)

Ref : H. Zügge

28

Removal of a lens by vanishinh of the optical effect

For single lens and

cemented component

Problem of vanishinh index:

Generation of higher orders

of aberrations

29

Lens Removal

1) adapt second radius of curvature 2) shrink thickness to zero

a) Geometrical changes: radius and thickness

b) Physical changes: index

Aplanatic Surfaces

s'

0 50 100 150 200 250 300-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

Saplanatic

concentricvertex

oblate ellipsoidoblate ellipsoid prolate ellipsoidhyperboloid+ power series + power series+ power series + power series

sp

he

re

sp

he

re

Aplanatic surfaces: zero spherical aberration:

1. Ray through vertex

2. concentric

3. Aplanatic

Condition for aplanatic

surface:

Virtual image location

Applications:

1. Microscopic objective lens

2. Interferometer objective lens

s s und u u' '

s s' 0

ns n s ' '

rns

n n

n s

n n

ss

s s

'

' '

'

'

'

30

Aplanatic lenses

Combination of one concentric and

one aplanatic surface:

zero contribution of the whole lens to

spherical aberration

Not useful:

1. aplanatic-aplanatic

2. concentric-concentric

bended plane parallel plate,

nearly vanishing effect on rays

Aplanatic Lenses

A-A :

parallel offset

A-C :

convergence enhanced

C-C :

no effect

C-A :

convergence reduced

31

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

32

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

33

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

34

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

35

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

36

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

37

Influence of Stop Position on Performance

Ray path of chief ray depends on stop position

spotstop positions

38

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

39

Field Lens im Endoscope

Ref : H. Zügge

40

Evolution of Eyepiece Designs

Monocentric

Plössl

Erfle

Von-Hofe

Erfle diffractive

Wild

Erfle type(Zeiss)

BerteleScidmore

Loupe

Erfletype

Bertele

Kellner

Ramsden

Huygens

Kerber

König

Nagler 1

Nagler 2

Bertele

Aspheric

Dilworth

Families of photographic lenses

Long history

Not unique

Classification

Singlets

Landscape

Achromatic

Landscape

Petzval, Portrait

Petzval,Portrait flat R-Biotar

Petzval

Petzval

Projection

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 Aspheric

II

IR Camera Lens

Catadioptric

UV Lens

Plastic

Aspheric 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

Rapid

Rectilinear

Aplanat

Dagor

Dagor

reversed

Angulon

Protar

AntiplanetUnar

Quasi-Symmetrical Doublets

Tessar

43

Medium Magnification Microscopic lenses

Development of Lithographic Lenses

b) Refractive spherical systems

a) Early systemsg) EUV

mirror

systems

M1

M3

M2

M4

M4

M3

M1

M2

M5

M6

M1

M2

M3

M4

M5

M6

M8

M6

c) Refractive with aspheres and immersion

d) Catadioptric cube

systems

e) Multi-axis catadioptric systems

f) Uni-axis catadioptric

systems

Modified Workflow in Instrument Development

Historical:

sequential workflow

Modern:

complex workflow with feedback and

relationships

Optical design

Tolerancing

Mechanical

Design

Manufacturing

components

Integration

Adjustment

Development

Metrology

phys-opt

Simulation

Researchlab

Control of

buyed

components

Software

Tests

Optical Design

Tolerancing

Mechanical

Design

Manufacturing

Assembly

Adjustment

Development

Performance

Check

Introduction to Tolerancing

Specifications are usually defined for the as-built system

Optical designer has to develop an error budget that cover all influences on

performance degradation as

- design imperfections

- manufacturing imperfections

- integration and adjustment

- environmental influences

No optical system can be manufactured perfectly (as designed)

- Surface quality, scratches, digs, micro roughness

- Surface figure (radius, asphericity, slope error, astigamtic contributions, waviness)

- Thickness (glass thickness and air distances)

- Refractive index (n-value, n-homogeneity, birefringence)

- Abbe number

- Homogeneity of material (bubbles and inclusions)

- Centering (orientation of components, wedge of lenses, angles of prisms, position of components)

- Size of components (diameter of lenses, length of prism sides)

- Special: gradient media deviations, diffractive elements, segmented surfaces,...

Tolerancing and development of alignment concepts are essential parts of the optical

design process 46 Ref: K. Uhlendorf

Data Sheet

Tolerances: Typical Values

Diameter Tolerance Unit <10 mm 10...20

mm

20...30

mm

Center thickness mm 0.02 0.03 0.03

Centering Tilt angle sek 60 60 60

Decenter/offset m 15 15 15

Roughness nm 15 10 10

Spherical/radius spherical rings 3 4 5

astigmatism rings .5 1 1

Asphericity Global deviation m 1 1.2 1.5

Global asphericity m 0.25 0.45 0.60

Local deviation m 0.025 0.05 0.075

Slope error rad 0.0005 0.0005 0.0005

Example Microscopic lens

Adjusting:

1. Axial shifting lens : focus

2. Clocking: astigmatism

3. Lateral shifting lens: coma

Ideal : Strehl DS = 99.62 %

With tolerances : DS = 0.1 %

After adjusting : DS = 99.3 %

Adjustment and Compensation

Ref.: M. Peschka

49

Adjustment and Compensation

Ref.: M. Peschka

50

Sucessive steps of improvements

Drawing of Microscopic Lens with Housing