Design and Correction of optical Systems

Part 2: Materials

Summer term 2012

Herbert Gross

1

Part 2: Materials - Contents

2.1 Introduction

2.2 Dispersion

2.3 Transmission

2.4 Glasses

2.5 Plastics

2.6 Crystals

2.7 Liquids and Gases

2.8 Metals

Overview

� Important types of optical materials:

1. Glasses

2. Crystals

3. Liquids

4. Plastics, cement

5. Gases

6. Metals

� Optical parameters for characterization of materials

1. Refractive index, spectral resolved n(λ)

2. Spectral transmission T(λ)

3. Reflectivity R

4. Absorption

5. Anisotropy, index gradient, eigenfluorescence,…

� Important non-optical parameters

1. Thermal expansion coefficient

2. Hardness

3. Chemical properties (resistence,…)

Dispersion

n(λλλλ)

ni(λλλλ)

λλλλo

normal normalanomal

λλλλ

n

� Dispersion:

Refractive index changes with wavelength

� Normale dispersion: larger index n for shorter wavelengths,

Ray bending of blue rays stonger than red

�Notice:

Diffraction dispersion is anomalous

with dn/dλ > 0

The different sign allows for chromatic

correction in diffractive elements.

( ) ( )21 λλ nnn −=∆

d n

d λ< 0

Important Test Wavelengths

λλλλ in [nm] Name Color Element

248.3 UV Hg

280.4 UV Hg

296.7278 UV Hg

312.5663 UV Hg

334.1478 UV Hg

365.0146 i UV Hg

404.6561 h violett Hg

435.8343 g blau Hg

479.9914 F' blau Cd

486.1327 F blau H

546.0740 e grün Hg

587.5618 d gelb He

589.2938 D gelb Na

632.8 HeNe-Laser

643.8469 C' rot Cd

656.2725 C rot H

706.5188 r rot He

852.11 s IR Cä

1013.98 t IR Hg

1060.0 Nd:YAG-Laser

Spectral Lines

Selected atomic lines of the sun spectrum used for test purposes

λ λ λ λ [nm]400 450 500 550 600 650 700 750

K H G F E D12

C AB

h g fe d c b12a

Chromatical Evaluation of Optical Systems

� Chromatical performance evaluation of optical systems:

Usage of one main (central) wavelength and two secondary wavelenghts

� Additional definition of wvalengths at the boundaries of the used spectral range, e.g.

- one further wavelength near to the UV edge (g, i)

- one further wavelength near to the IR-edge (s,t)

Main wavelength 1st secondary wavelength 2nd secondary wavelength

e 546.07 green F' 480.0 bue C' 643.8 red

d 587.56 yellow F 486.1 blue C 656.3 red

Dispersion

� Description of dispersion:

Abbe number

� Visual range of wavelengths:

� Typical range of glasses

νe = 20 ...120

� Two fundamental types of glass:

Crone glasses:

n small, ν large

Flint glasses

n large, ν small

( )( )

ν λλ

=−

−

n

n nF C

1

' '

νe

e

F C

n

n n=

−

−

1

' '

Dispersion

Material with different dispersion values:

� Different curvature of the dispersion curve

� Stronger change of index over wavelength for large dispersion

� Inversion of index sequence at the boundaries of the spectrum possible

refractive index n

F6

SK18A

λλλλ

1.675

1.7

1.65

1.625

1.60.5 0.75 1.0 1.25 1.751.5 2.0

Dispersion Equation

� Experimental determination of

refractive indices for discrete

wavelengths

� Fit of model based or empirical

dispersion function

� Interpolation for desired wavelength

� Types of dispersion formulas:

1. Empirical, no extrapolation

allowed

2. Based on physical oscillator

model, extrapolation possible

in certain rangeλλλλ

n

400 600 800 1000 1200 1400 1600 1800 2000 2200 24001.48

1.49

1.5

1.51

1.52

1.53

1.54

measured data points

model curve of dispersion

∑−

+=j j

j

o

knn

22

22

ωω

Dispersion Formulas

� Schott formula

empirical

� Sellmeier

Based on oscillator model

� Bausch-Lomb

empirical

� Herzberger

Based on oscillator model

� Hartmann

Based on oscillator model

n a a a a a ao= + + + + +− − − −1

2

2

2

3

4

4

6

5

8λ λ λ λ λ

n A B C( )λλ

λ λ

λ

λ λ= +

−+

−

2

212

2

222

n A B CD E

Fo

o

( )

( )

λ λ λλ

λ

λ λλ

λ λ

= + + + +

− +−

2 4

2

2

2 22

2 2

( )mmit

aaaan

o

oo

o

µλ

λλλλλλ

168.0

)(222

3

22

22

1

=

−+

−++=

λλλ

−+

−+=

5

4

3

1)(a

a

a

aan o

Relative Partial Dispersion

� Relative partial dispersion :

Change of dispersion slope with λ

� Definition of local slope for selected

wavelengths relative to secondary

colors

� Special selections for characteristic

ranges of the visible spectrum

λ = 656 / 1014 nm far IR

λ = 656 / 852 nm near IR

λ = 486 / 546 nm blue edge of VIS

λ = 435 / 486 nm near UV

λ = 365 / 435 nm far UV

( ) ( )P

n n

n nF C

λ λ

λ λ1 2

1 2=

−

−' '

λλλλ

n

400 600 800 1000700500 900 1100

e : 546 nm

main color

F' : 480 nm

1. secondarycolor

g : 435 nmUV edge

C' : 644 nm

s : 852 nm

IR edge

t : 1014 nm

IR edge

C : 656 nmF : 486 nm

d : 588 nm

i : 365 nm

UV edge

i - g

F - C

C - s

C - t

F - e

g - F

2. secondarycolor

1.48

1.49

1.5

1.51

1.52

1.53

1.54

n(λλλλ)

Relative Partial Dispersion

� Typical behavior of glasses:

Flint (e.g. SF9) glasses have stronger dispersion than crown glasses (e.g. LaK21)

� Larger difference of refractive index over the visible spectrum

λλλλ

dn/dλλλλ

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

SF9

LaK21

∆∆∆∆nSF9

∆∆∆∆nLaK21

Normal Line

� The relative partial dispersion changes approximately linear with the dispersion for glasses

� Nearly all glasses are located on the normal line in a P-ν-diagram

� Glasses apart from the normal line shows anomalous partial dispersion

these material are important for chromatical correction of higher order

2,12,12,1 λλλλλλ ν baP d +⋅=

21212121 λλλλλλλλ ν PbaP d ∆++⋅=

Normal Line

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

νννν

normal

line

Transmission

� Internal transmission:

only volume absorption, without losses at the interfaces

� Typical characterization:

transmission of a plate with finite width 25 mm

calculation of the transmission of a sample

with arbitrary thickness

� Glasses: strong edge at the UV side

� Definition of edge position

1. 50% value

2. mean value of 20% and 80% value

d

in

outd e

I

IT

⋅−== α

( ) mm

d

mmd TT 2525

=

λλλλ

T

200 400 500 600 700 8000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

50 % -

Definition

20 / 80 % -

Definition

Transmission

� Typical transmission of glass

� Three ranges:

1. steep UV edge

2. high transmission

plateau in the visible

3. slow edge towards

the IR

λλλλ inµµµµm

T (d=10mm)

UV-edgeionization

of the

atoms

IR-edgeabsorption

by residualwater

window withtransmission T > 0.99

0.50 1.51.0 2 2.50.90

0.925

0.975

0.95

1.0

NIRVIS

Transmission

� Absolute transmission of a sample,

Only energy in-out-ratio

Losses at the interfaces (Fresnel) are incorporated

� Internal transmission of a sample,

only volume losses, interface efects removed

0I

IT =

0i

i

I

IT =

I(x)

x

Io

Iio

IIi

n

Transmission: Glasses

� Transmission of

glasses

� plate with thickness

d = 10 mm

in mλλλλµµµµ

T (d=10mm)

TiF6

KzFSN4

LaK33

BK7

LaF2

SK4

FK52

Transmission: IR- and UV Materials

Transmission of UV- and IR-materials (with Fresnel losses at interfaces)

T

Log λ λ λ λ

in µ µ µ µm

ZnS3mm

IRG 5 mm

Suprasil 3mm

CdTe

4mm

ZnSe

3mm

Ge

3mm

GaAs

3mm

IRG 1002mm

100

50

0

visualrange

infrared

3 - 5infrared

8 - 12

0.1

Glass

� Glass blocks

� Striae in glass

Ref: P. Hartmann / Schott

Glass Diagram 2010

� Usual representation of

glasses:

diagram of refractive index

vs dispersion n(ν)

� Left to right:

Increasing dispersion

decreasing Abbe number

Glass Diagram: Changes of Numbers

Ref: P. Hartmann / Schott

Data Sheet

Glass:

LAFN7

Part 1

Data Sheet

Glass:

LAFN7

Part 2

Ranges of the Glass Diagram

Crown glasses

ν

νe e

e e

für n

für n

> <

> >

54 7 16028

49 7 16028

. .

. .

Flint glasses

ν

νe e

e e

für n

für n

< <

< >

54 7 16028

49 7 16028

. .

. .

Two major families of glass types, depending on chemical ingredients:

1. Crown:

Low index, low dispersion

2. Flint:

High index, high dispersion

n

80 70 60 50 40 30 2025354555657585

1.45

1.50

1.55

1.60

1.65

1.70

1.75

1.80

1.85

1.90

1.95

2.00

LaK

LaSF

SF

TiSF

TiF

BaSF

F

LF

LLF

BaLF

LaF

PSK

PK

FK TiK

BKK

SK

BaK

SSK

KF

crown glass

flint

glass

BaF

Chemical Glass Families

Abbr. Name Abbr. Name

Crownglasses

K Kron

Flintglasses

F Flint

BaK Baritkron BaF Baritflint

BaLK Baritleichtkron BaLF Baritleichtflint

BK Borkron BaSF Baritschwerflint

ZK Zinkkron LLF Doppelleichtflint

SK Schwerkron KF Kronflint

SSK Doppelschwerkron KzF Kurzflint

FK Fluorkron LaF Lanthanflint

TiK Tiefkron LaSF Lanthanschwerflint

PK Phosphatkron LF Leichtflint

PSK Phosphatschwerkron SF Schwerflint

LaK Lanthankron TiF Tiefflint

TiSF Schwertiefflint

KzFS Kurzschwerflint

Available Ranges in the Glass Diagram

νννν

n

20 30 40 50 60 70 80 90 1001.4

1.5

1.6

1.7

1.8

1.9

2

20 30 40 50 60 70 80 90 1001.4

1.5

1.6

1.7

1.8

1.9

2

Schott Ohara

� Nearly equal area in the glass diagramm with available materials for all vendors

� No options with Index / dispersion

1. high / high

2. low / low

Plastics

Material Index at 546 nm

Abbenumber

MaxTemp

Therm expan10-6 K-1

Scatterin %

Trans.3mm,

Densityg/cm3

PMMA - Polymethyl-Methacrylat 1.49280 57 90 65 2 92 1.19

PC - Polycarbonat - Makrolon, Lexan 1.59037 30 120 69 4 87 1.20

CR39 - DEGBAC - Gießharz 1.5011 57.8 100 120 1 1.32

PS - Polystyrol 1.590 30.8 80 70 3 89 1.06

DPSC - Diphenyl-sulfidcarbonat 1.612 26.0

CMMA 1.50 56.0

Styrol, SAN 1.566 34.7 95 65 4 90 1.09

SMA 1.585 31.3

SMMA 1.568 33.5

FMS 1.508 34.0

SCMA 1.535 42.5

COC 1.533 56.0

MR8 1.60 42.0

Plastic Materials

Plastics in the

n - ν - diagram

90 80 70 60 50 40 30 20

1.40

1.45

1.50

1.55

1.60

1.65

1.70

1.75

1.80

1.85

1.90

1.95

2.00

refractiveindex n

Abbe number νννν

10

PMMA

CR39o

o

o

o

SAN

PS oPC

CMMAo

o COC oSCMA

oFMS

oSMMA

oSMA

DPSC

o

oMR8

plastics

anorganic

glasses

Properties of Plastic Materials

1. Stress induced birefringence during processing

2. Generation of local inhomogenieties of the refractive index in die casting

3. Water intake (swelling) : change of shape (up to 4%) and decrease in the refractive index

4. Electro-static charge

5. Aging due to cold forming, polymerization, opalescence, yellowing

6. Strong thermal variation of the refractive index

7. Limiting temperature (above the transition temperature the material is destroyed)

100 ... 120 °C

8. For an increased abrasive hardness and for the prevention from charging and

swelling ,special coatings may have to be applied.

9. During the cooling process significant changes occur in the volume caused by shrinking.

There are two different types of plastics

a. thermosets, shrinking 0.4%...0.7%

b. thermoplasts, shrinking 4%...14%

Usage of Plastics in Optical Systems

� Most attractive use of plastics: Consumer optics

- benefit of light weight

- critical cost

- high number of pieces

� Advantages for special components due to manufacturing technique:

- complex surface shapes, arrays, aspheres

- for injection moulding cost of complex shape only for master piece

� Typical products with plastics components:

- Eye glasses

- binoculars

- photographic lenses

- pic-up objective lenses

- illumination systems

Plastics vs Glass Materials

property unit range plastics range glass

refractive index n 1.49 ...1.61 1.44...1.95

dispersion ν 25...57 20...90

uniformity of the refractive index 10-3

...10-4

10-4

...10-6

temperature dependence of the refractive index 10-6*K

-1 -100...-160 -10...+10

Vickers hardness N/mm2 120...190 3000...7000

thermal expansion 10-6*grd

-1 70...100 5...10

thermal conductivity Wm-1grd-1

0.15...0.23 0.5...1.4

internal transmission in the green range 0.97...0.993 0.999

stress - optical coefficient 10-12

Pa-1

40 3

stress- birefringence 5*10-5

...10-3

0

density g/cm3 1.05...1.32 2.3...6.2

water intake % 0.1...0.8 0

Comparison plastics with glasses

UV- and IR - Materials

material refractive

index λλλλ-range (µµµµm) UV IR νννν P

MgF2 1.389 0.12 - 9.0 • •

ZnS 2.25 0.4 - 14.5 • 12.831 0.271

CaF2, calcium fluoride 1.42 0.12 - 11.5 • • 47.53 0.397

ZnSe 2.44 0.5 - 22.0 • 34.20 0.291

MgO 1.69...1.737 0.28 - 9.5 • 53.4

CdTe 2.70 0.9 - 31.0 •

diamond 2.3757 0.25...3.7, 6.0... • (•) 2387 0.469

germanium 4.003 2.0...15 • 701.42 0.556

silicon 3.433 1.2...15 • 420.16 0.523

BaF2 1.474 0.18...12 • • 81.7 0.651

SiO2 , quartz 1.544 0.15...4.0 • (•) 69.9 0.653

Al2O3 , sapphire 1.769 0.17...5.5 • (•) 6.626 0.650

IR - Materials

name composition application toxity processing

germanium Ge 5 can be processed very well

gallium arsenide GaAs 2 toxic

silicon Si 5 high tool wear

zink sulfide ZnS 4 can be processed very well

zink selenide ZnSe 4 slightly toxic can be processed very well

sapphire Al2O3 3

IG2 / AMTIR-1 Ge33As12Se55 3 toxic

IG3 Ge30As13Se32Te25 3 toxic

IG4 Ge10As40Se50 3 toxic

IG5 / AMTIR-3 Ge28Sb12Se60 4 slightly toxic can be processed well

IG6 As40Se60 3 toxic

GASIR1 Ge22As20Se58 3 toxic

GASIR2 Ge20Sb15Se65 3 slightly toxic

calcium fluoride CaF2 3

barium fluoride BaF2 3

lithium fluoride LiF 3

sodium chloride NaCl 2

sodium fluoride NaF 2

potassium bromide KBr 2

potassium chloride KCl 2

potassium iodide KJ 2

KRS 5 TlBr-TlJ 2 toxic

KRS 6 TlBr-TlCl 2 slightly toxic

thallium bromide TlBr 1

thallium iodide TlJ 1

Gases

� Refractive indices near to 1

� Definition of indices relative to vacuum

(usual glasses: relative to air)

� Strong changes of the index with temeprature and pressure

� Examples

( )T

T

p

pnn 0

0

011 ⋅⋅−+=

medium ne ννννe

Air 1.000293246 89.68

Argon 1.00028314 80.90

Chlorine 1.0007840 56.40

Helium 1.00003495 194.17

Ammonia 1.000379 47.38

carbon dioxyde 1.0004506 77.82

oxygen 1.00027227 71.09

nitrogen 1.00029914 89.83

steam 1.0002527 66.50

hydrogen 1.00013937 77.00

Refractive Index of Air

� Empirical formula for the refracdtive index of air at normal pressure as a function of

- wavelength λ in µm

- temprature T in °C

(n-1) 10-6

T = 70 °

T = 50 °

T = 20 °

in mλ µ

[ ]( )2000367.0101803.0476.1

036.26810142

6 −⋅−⋅

++⋅+= −

Tnλλ

Refractive Index of Air

� Formula of Edlen:

Refractive index of air as a function of

T : temperature in °C

p : pressure in torr

x : relative CO2-content

q : partial pressure of water steam

( )[ ]

( )

−⋅⋅−

⋅+

⋅−⋅⋅+⋅⋅

−+

−+⋅⋅−⋅++=

−−

−

2

108

22

8

0384.0802.310

0036610.01

009876.05953.0101

60.93214

/19.38

15518

/1130

233398337.8091100004.05327.011

λ

λλ

qT

Tpp

xn

Liquids

� Examples

� Index of water

λλλλ

n

400 600 800 1000 1200 1400 1600 1800 2000

1.30

1.31

1.32

1.33

1.34

1.35

1.36

200

1.37

medium nd

Ethylalcohol 1.362

Gasoline 1.440

Benzene 1.501

Glycine 1.455

Methyliodide CH2J2 1.742

Carbon sulfate 1.628

Cedar wood oil 1.51

Liquid oxygen 1.221

Liquid hydrogen 1.11

Absorption of Water

� Spectral resolved absorption coefficient of water

Ref: A. Kienle

Technical Liquids

Liquids of the vendor Cargille

020406080100120

νννν-Number

PCs

0,4

0,45

0,5

0,55

0,6

0,65

0,7

0,75

SCHOTT Glasses

Series A

Series AAA

Series AA

Series E

Series I

Series EC31

νννν-Number

Pg,F

0102030405060708090100

Series E

Series I

Series EC31

SCHOTT Glasses

Series A

0,5

0,55

0,6

0,65

0,7

0,75

Abbe normal line

Cements

� Optical cement materials:

- rigid connection of glass components

- typical thickness 0.01 mm without optical

effects

- elasticity for compensation of thermal expansion

differences desired

- typical index n = 1.45…1.55 (epoxy resins)

� Organic cement problems with

- UV transmission

- long term stability

- high energy density

- thermal stability

crown

glassflint

glassn

1.5

1.7

1.6

cement

z

Metals

� Complex refractive index

� Alternative formulation:

attenuation κ

� Relation with conductivity σ

� Typical data of some metals

ir ninn ⋅+=~

( )κ⋅+⋅= inn 1~

( )σνεµω

σπεµ ⋅⋅+⋅=

⋅⋅+⋅= 24~ iin

material n k δδδδ in [µµµµm]

gold 0.402 2.54 0.034

silver 0.129 3.25 0.026

aluminum 0.912 6.56 0.013

tungsten 3.50 2.72 0.032

platinum 2.10 3.67 0.023

silicon 4.12 0.048 1.787

Dispersion of the Refractive Index of Metals

� Typically strong structure of the dispersion

curve with absorption ranges

� Example: Aluminum

� Comparison of different metalsLog λ λ λ λ0.1 µµµµm

10

k

1 µµµµm 10 µµµµm

10-1

10-2

1

n

Vis

λλλλ

R

1 µµµµm500 nm300 nm 2 µµµµm 5 µµµµm

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

10 µµµµm

aluminum, Al

silver, Ag

mercury, Hg

gold, Aucopper, Cu

platinum, Pt

nickel, Ni

chromium, Cr

Summary of Important Topics

� Characterization of optical materials: refractive index n, Abbe number ν (dispersion)

� Abbe number: mean slope of dispersion curve, small ν means large dispersion

� Choice of special wavelengths to describe the dispersion behavior (e.g.: e, F, C)

� Partial dispersion P: more refined description of dispersion: curvature

� Normal glass line: most glasses fulfill P proportional to ν

� Mathematical description of dispersion: Sellmeier formulas, corresponds to modelling

adjacent absorption lines, typically 2-3 terms considered

� Transmission of materials: glasses show UV IR decay, crystals have broader windows

� Glass diagram: n-ν-chart, distinction of

1. crown glasses, n low, ν high, dispersion low

2. flint glasses; n high, ν low, dispersion high

� Plastics materials: for high volume systems, bad performance in comparison to glass

(thermal, index low, straylight, transmission)

� Special behavior, but minor importance in optics: gases, liquids, cements, metals

45

Outlook

Next lecture: Part 3 – Components

Date: Wednesday, 2012-05-02

Contents: 3.1 Lenses - description and parameters

- imaging formulas

3.2 Mirrors

3.3 Prisms - dispersion prims

- reflection prisms

- miscellaneous

3.4 Special components - gratings

- aspheres

- diffractive elements

- taper

- gradient lenses

46