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Optical Engineering

Part 2: Materials, dispersion, glass map

Herbert Gross

Summer term 2020

Wavelengths

Atomic interaction and dispersion

Abbe number

Dispersion formulas

Partial dispersion

Normal line

Glass map

2

Contents

Important Test Wavelengths

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 violet Hg

435.8343 g blue Hg

479.9914 F' blue Cd

486.1327 F blue H

546.0740 e green Hg

587.5618 d yellow He

589.2938 D yellow Na

632.8 HeNe-Laser

643.8469 C' red Cd

656.2725 C red H

706.5188 r red He

852.11 s IR Cä

1013.98 t IR Hg

1060.0 Nd:YAG-Laser

Chromatical Evaluation of Optical Systems

Chromatical performance evaluation of optical systems:

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

Additional definition of wavelengths 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 wavelength1st secondary

wavelength

2nd secondary

wavelength

e 546.07 green F' 480.0 blue C' 643.8 red

d 587.56 yellow F 486.1 blue C 656.3 red

Atomic model for the refractive index:

oscillator approach of atomic field interaction

Sellmeier dispersion formula:

corresponding function

Special case of coupled resonances:

example quartz, degenerated oscillators

Atomic Model of Dispersion

j jjj

jj

iric

f

mc

Nenin

222

22

0

22

22

10-1

100

101

0

1

2

3

4

5

6

7

log

[mm]

nvisible

0.4 0.7

1(UV)

2(UV)

3(IR)

4(IR)

nvis()

j j

j

C

BAn

2

2

2

12

2

222

4

02

j j

j

oC

BBAn

5

refractive

index n

1.65

1.6

1.5

1.8

1.55

1.75

1.7

BK7

SF1

0.5 0.75 1.0 1.25 1.751.5 2.0

1.45

flint

crown

Description of dispersion:

Abbe number

Visual range of wavelengths:

typically d,F,C or e,F’,C’ used

Typical range of glasses

ne = 20 ...100

Two fundamental types of glass:

Crown glasses:

n small, n large, dispersion low

Flint glasses:

n large, n small, dispersion high

n

n

n nF C

1

' '

ne

e

F C

n

n n

1

' '

Dispersion and Abbe number

6

Curvatures cj of the radii of a lens

Focal power at the center wavelength e

for a thin lens

Difference in focal powers for outer

wavelengths F', C'

with the Abbe number

Focal length at the center wavelength

Difference of the focal lengths for outer

wavelengths

Achromatization condition for two thin

lenses close together

Abbe Number and Achromatization

2

2

1

1

1,

1

rc

rc

cnccnF eee )1())(1( 21

e

ee

e

CFCFCF

Fcn

n

nncnnFFF

n

)1(

1)( ''

''''

cnFf

ee

e

)1(

11

e

e

e

FC

CF

FCCF

f

cn

nn

cnn

nnfff

n

2

''

''

''''

)1()1)(1(

''

1

CF

ee

nn

n

n

011

22112

2

1

1 nnnn ff

FFF

7

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

8

n A B C( )

2

212

2

222

n A B CD E

Fo

o

( )

( )

2 4

2

2

2 22

2 2

mmit

aaaan

o

oo

o

m

168.0

)(222

3

22

22

1

5

4

3

1)(a

a

a

aan o

Dispersion formulas

8

Relative partial dispersion :

Change of dispersion slope with

Different curvature of dispersion

curve

Definition of local slope for selected

wavelengths relative to secondary

colors

Special -selections for characteristic

ranges of the visible spectrum

= 656 / 1014 nm far IR

= 656 / 852 nm near IR

= 486 / 546 nm blue edge of VIS

= 435 / 486 nm near UV

= 365 / 435 nm far UV

P

n n

n nF C

1 2

1 2

' '

n

400 600 800 1000700500 900 1100

e : 546 nm

main color

F' : 480 nm

1. secondary

color

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. secondary

color

1.48

1.49

1.5

1.51

1.52

1.53

1.54

n()

Relative Partial Dispersion

9

Partial Dispersion and 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-n-diagram

The slope of the normal line depends

on the selection of wavelengths

Glasses apart from the normal line

shows anomalous partial dispersion

P

these material are important for

chromatical correction of higher order

2,12,12,1 n baP d

21212121 n PbaP d

PgF

80 60 40 20

0.5

0.6

P

0.55

0.45

PCs

n

10

Preferred glass selection for apochromates

11

Relative Partial Dispersion

N-SF1

N-SF6

N-SF57

N-SF66

P-SF68

P-SF67

N-FK51A

N-PK52A

N-PK51

N-KZFS12

N-KZFS4

N-LAF33

N-LASF41

N-LAF37

N-LAF21

N-LAF35

N-LAK10

N-KZFS2

Usual representation of

glasses:

diagram of refractive index

vs dispersion n(n)

Left to right:

Increasing dispersion

decreasing Abbe number

Glass Diagram

12

Ranges of the Glass Diagram

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

1. Crown:

Low index, low dispersion

2. Flint:

High index, high dispersion

n

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

LFLLF

BaLF

LaF

PSK

PK

FK TiK

BKK

SK

BaK

SSK

KF

crown glass

flint glass

BaF

6028.17.49

6028.17.54

ee

ee

nfor

nfor

n

n

6028.17.49

6028.17.54

ee

ee

nfor

nfor

n

n