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Optical Design with Zemax

Lecture 10: Physical Optical Modelling II

2012-11-22

Herbert Gross

Summer term 2012

2 10 Physical Optical Modelling II

Preliminary time schedule

1. Coatings

2. Coating transmission and phase effects

3. Ghost imaging

4. Straylight

5. Scattering in Zemax

6. Fresnel equations

7. Overview

8. Design and calculation of thin films

9. Simple layers

10.Representations

11.Applications and examples

12.Coatings in Zemax


Contents

10 Physical Optical Modelling II

Ghost Images

Ghost image in photographic lenses:

Reflex film / surface

Ref: K. Uhlendorf, D. Gängler

Different reasons

Various distributions


Straylight and Ghost Images

a b


Scattering of Light

Scattering of light in diffuse media like frog

Ref: W. Osten

Calculation of reflected light

Colour effects due to coatings


Straylight and Ghost Images

Ref.: M. Peschka

sequence 5 - 3

3

5

sequence 6 - 4

4

6

6 - 4

5 - 3

9 - 3

7 - 2

14 - 1115 - 11

20 - 18sequence 13 - 4 sequence 13 - 5

sequence 7 - 2

sequence 20 - 18

sequence 6 - 4


Definition of Scattering

• Physical reasons for scattering:

- Interaction of light with matter, excitation of atomic vibration level dipols

- Resonant scattering possible, in case of re-emission l-shift possible

- Direction of light is changed in complicated way, polarization-dependent

• Phenomenological description (macroscopic averaged statistics)

1. Surface scattering:

1.1 Diffraction at regular structures and boundaries:

gratings, edges (deterministic: scattering ?)

1.2 Extended area with statistical distributed micro structures

1.3 Single micros structure: contamination, imperfections

2. Volume scattering:

2.1 Inhomogeneity of refractive index, striae, atmospheric turbulence

2.2 Ensemble of single scattering centers (inclusions, bubble)

Therefore more general definition:

- Interaction of light with small scale structures

- Small scale structures usually statistically distributed (exception: edge, grating)

- No absorption, wavelength preserved

- Propagation of light can not be described by simple means (refraction/reflection)

1. Surface scattering

1.1 Edge diffraction

1.2 Scattering at topological structures of surfaces

Dimensions: micro roughness – macroscopic ripple due to manufacturing errors

1.3 Scattering at single localized defects (contamination, micro defects)

perturbation of phase- and amplitude

2. Particle scattering :

2.1 Rayleigh regime , d << l

2.2 Theory of Rayleigh-Debye , d < l

2.3 Mie-scattering, spherical particles d > l

3. Volume scattering

3.1 Scattering at refractive index inhomogeneities,

atmospheric turbulence, striae in glass

3.2 Scattering at crystal boundaries (ceramic)

3.3 Scattering in statistical dense material/particle ensemble

biological tissue, multiple scattering events


Scattering Mechanisms

Geometry regular - statistical distributed

Single - multi scattering

Density of scatterers low - high, independence, saturation, change of illumination

Near - far field

Scaling, size of scatterers vs. wavelength, micro - macro

Coherence, scattering vs. re-emission

Polarization dependence

Discret scatterers vs. continuous n-variations

Absorption

Diffraction vs. geometrical approach

Steady state vs time dependence

Wavelength dispersion of material parameters

Finite volume size - boundary conditions


Aspects of Scattering

Geometry simplified

Boundaries simplified, mostly at infinity

Isotropic scattering characteristic

Perfect statistics of distributed particles

Multiple scattering neglected

Discretization of volume

Angle dependence of phase function simplified

Scattering centers independent

Scatterers point like objects

Spatially varying material parameters ignored

Field assumed to be scalar

Decoherence effects neglected

Absorption neglected

Interaction of scatterers neglected

l-dispersion of material data neglected


Approximations in Scattering Models


Modelling of Volume Scattering

Calculation:

1. Geometrical approximation:

Raytrace with Monte-Carlo-method

time consuming, non-smooth results

2. Wave optical with beam propagation

Scalar approach only for large scales

3. Diffusion theory:

In strongly scattering media with isotropic behavior; tissue

off axis

bubble

collimated

gaussian beam

Length scale below 1 cm:

Tatarski function due to

viscosity

PSD

Lengths scale up to 5 m:

Kolmogorov spectrum

PSD

Length scale above:

Karman spectrum

PSD

LogC

n2

(k)F

F --> const

Karman

large scale

Kolmogorov

inertial subrange

F =a k 311

F =a ek2

Viskose

Dissipation

Tatarski

k

kko iinner scaleouter scale

2

F ik

k

Ta eb

3

11

F kbTa

6

11

2

22 4

F

o

KaL

kb


Atmospheric Turbulence

Analytical solutions:

Spherical particles

1. generalized Lorentz-Mie theory, near and far field

2. multi sphere configurations

3. layered structures

Spheroids

Cylinders

1. single cylinders, with oblique incidence, near and far field

2. stacked cylinders

3. multi cylinder configurations, perpendicular incidence

Numerical solutions in time domain:

Arbitrary geometies

Finite difference time domain method (FDTD), only small volumes ( 2mm3), Dx = l/20

Pseudospectral method (PSTD) , Dx = l/4

Stationary solutions:

Discrete dipole approximation for arbitrary geomtries

T-matrix method


Available Solutions Maxwell Theory

Ref: A. Kienle

Different surface geometries:

Every micro-structure generates

a specific straylight distribution


Light Distribution due to Surface Geometry

x

y

Smooth

surface

Specular

reflex

No scattering

x

y

Regular

grating

Discrete

pattern of

diffraction

orders

x

y

Irregular

grating

Continuous

linear scatter

pattern

x

yStatistical

isotropic

surface

Broad scatter

spot

Ref.: J. Stover, p.10

Scattering at rough surfaces:

statistical distribution of light scattering

in the angle domain

Angle indicatrix of scattering:

- peak around the specular angle

- decay of larger angle distributions

depends on surface treatment

qq

is

dP

dLog

q

qscattering angle

special polishing

Normal polishing

specular angle


Phenomenology of Surface Scattering

Roughness

of optical

surfaces,

Dependence of

treatment

technology

10 4

10 2

10 0

10 -2

10 -610 -4 10 -2 10 0

10 +2

Grinding

Polishing

Computercontrolledpolishing

Diamond turning

Plasmaetching

Ductilemanufacturing

Ion beam finishing

Magneto-rheological treatment

roughnessrms [nm]

material removalqmm / s


Roughness of Optical Surfaces


Surface Characterization

h(x)

x

C(Dx)

Dx

PSD(k)

k

A(k)

k

FFT FFT

| |2

< h1h

2 >

correlation

square

dxeyxhkA ikx

L

0

),()(

DD dxxxhxhL

xC )()(1

)(

topology

spectrum

autocorrelation

power spectral

density

2

)(1

)( dxexhL

kF ikx

PSD


Spatial Frequency of Surface Perturbations

Power spectral density of the perturbation

Three typical frequency ranges,

scaled by diameter D

1. Long range, figure error

deterministic description

resolution degradation

2. Mid frequency, critical

model description complicated

3. Micro roughness

statistical description

decrease of contrast

limiting lineslope m = -1.5...-2.5

log A2

Four

long range

low frequency

figure

Zernike

mid

frequencymicro

roughness

1/l

oscillation of

the polishing

machine

12/D1/D 40/D

Description of scattering characteristic of a surface: BSDF

(bidirectional scattering distribution function)

Straylight power into the solid angle dW

from the area element dA relative to

the incident power Pi

The BSDF works as the angle response

function

Special cases: formulation as convolution

integral

W

ddP

dP

dP

dLF

i

s

i

sBSDF

qcos

ndW

solid angle

areaelement

scattered power

dPs

normal

incidentpower

dPi

qi

sq

W iiiiiiBSDF dPFP qqqqq cos),(,,,),(


BSDF of a Surface

Exponential correlation

decay

PSD is Lorentzian function

Gaussian coerrelation

Fractal surface with

Hausdorf parameter D

K correlation model

parameter B, s


Model Functions of Surfaces

C x erms

x

c( )

2

F s

sPSD

rms c

c

( )

1

1

2

2

C x erms

x

c( )

2

1

2

2

F s ePSD

c rms

s c

( )

2

2

4

2

F s

n

n

K

sPSD

n

n( )

1

2

21

2 2

1

F s

A

s BPSD C

( )/

12

2


Sources of Stray Light

Ref: B. Goerz

Definition of scattering at every surface

in the surface properties

Possible options:

1. Lambertian scattering indicatrix

2. Gaussian scattering function

3. ABg scattering function

4. BSDF scattering function

5. User defined

More complex problems only make sense in

the non-sequential mode of Zemax,

here also non-optical surfaces (mechanics) can be included

Surface and volume scattering possible

Optional ray-splitting possible

Relative fraction of scattering light can be specified


Scattering in Zemax

Surface scattering:

Projection of the scattered ray on the surface, difference x to the specular ray: x

Volumne scattering:

Angle scattering description by probability P

Lambertian scattering:

isotropic

Gaussian scattering

ABg model scatter

Henyey-Greenstein volume scattering

(biological tissue model)

Rayleigh scattering


Scattering in Zemax

2

2

)(

x

BSDF eAxF

gBSDFxB

AxF

)(

2/32

2

cos214

1)(

qq

gg

gP

ql

q 2

4cos1

8

3)( P

Data file with scattering functions: ABg-data.dat

File can be edited


Scattering in Zemax

Tools / Catalogs / ABg Scatter Data Catalogs

Specification and definition of scattering

parameters:

wavelength, angle, A, B, g

Tools / Catalogs / SCatter Function Viewer

Graphical representation of the scattering function


Scattering in Zemax

Simple example: single focussing lens

Gaussian scattering characteristic at

one surface

Geometrical imaging of a bar pattern

Image with / without Scattering

Scattering must be activated in settings

Blurring increases with growing -value


Scattering in Zemax

Example from samples with non-sequential mode

Important sampling accelerates the calculation


Scattering in Zemax

Volume scattering example

Stokes shift is possible for fluorescence


Scattering in Zemax

Fresnel Formulas

n n'

incidence

reflection transmission

interface

E

B

i

i

E

B

r

r

E

Bt

t

normal to the interface

i

i'i

a) s-polarization

n n'

incidence

reflection

transmission

interface

B

E

i

i

B

E

r

r

B

E t

t

normal to the interface

i'i

i

b) p-polarization

Schematical illustration of the ray refraction ( reflection at an interface

The cases of s- and p-polarization must be distinguished

30

Fresnel Formulas

Electrical transverse polarization

TE, s- or -polarization, E perpendicular to incidence plane

Magnetical transverse polarization

TM, p- or p-polarization, E in incidence plane

Boundary condition of Maxwell equations

at a dielectric interface:

continuous tangential component of E-field

Amplitude coefficients for

reflected field

transmitted field

Reflectivity and transmission

of light power

TEe

rTE

E

Er

1 TE

TEe

tTE r

E

Et 1

' TMTM r

n

nt

nn EE 2211

tt EE 21

TMe

rTM

E

Er

2rP

PR

e

r 2

cos

'cos't

in

in

P

PT

e

t

||

31

Fresnel Formulas: Stokes Relations

1 rt

1cos

'cos|||| r

i

it

Relation between the amplitude coefficients for reflection/transmission:

1. s-components:

field components additive

minus sign due to phase jump

2. p-components:

energy preservation but change of

area size due to projection,

correction factor, no additivity of

intensities

field

amplitudes

incidence reflection

transmission

Ei

Er

Et

cross section

area

continuous

tangential

component

32

Fresnel Formulas

Coefficients of amplitude for reflected rays, s and p

Coefficients of amplitude for transmitted rays, s and p

tzez

tzezE

kk

kk

inin

inin

innin

innin

ii

iir

'cos'cos

'cos'cos

sin'cos

sin'cos

)'sin(

)'sin(

222

222

tzez

tzezE

knkn

knkn

inin

inin

innnin

innnin

ii

iir

22

22

2222

2222

||'

'

'coscos'

'coscos'

sin'cos'

sin'cos'

)'tan(

)'tan(

tzez

ezE

kk

k

inin

in

innin

in

inin

int

2

'cos'cos

cos2

sin'cos

cos2

'cos'cos

cos2

222

tzez

ezE

knkn

kn

inin

in

innnin

inn

inin

int

22

2

2222||

'

'2

'coscos'

cos2

sin'cos'

cos'2

'coscos'

cos2

33

Fresnel Formulas

Typical behavior of the Fresnel amplitude coefficients as a function of the incidence angle

for a fixed combination of refractive indices

i = 0

Transmission independent

on polarization

Reflected p-rays without

phase jump

Reflected s-rays with

phase jump of

(corresponds to r<0)

i = 90°

No transmission possible

Reflected light independent

on polarization

Brewster angle:

completely s-polarized

reflected light

r

r

t

t

i

Brewster

34

Fresnel Formulas: Energy vs. Intensity

Fresnel formulas, different representations:

1. Amplitude coefficients, with sign

2. Intensity cefficients: no additivity due to area projection

3. Power coefficients: additivity due to energy preservation

r , t

0 10 20 30 40 50 60 70 80 90-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

i

t

r

r

t

R , T

i0 10 20 30 40 50 60 70 80 90

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

T(In)

T(In)

R(In)

R(In)

R , T

i0 10 20 30 40 50 60 70 80 90

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

T

T

R

R

35

Fresnel Formulas

Reflectivity and transmittivity of power

Arbitrary azimuthal angle of polarization: decompositioin of components

In case of vanishing absorption:

Energy preservation

Special case of normal incidence

Typical values for some glasses and optical materials in air

)'(sin

)'(sin2

2

ii

iiR

)'(tan

)'(tan2

2

||ii

iiR

)'(sin

2cos'2sin2 ii

iiT

)'(cos)'(sin

'2sin2cos22||

iiii

iiT

ee RRR 22

|| sincos ee TTT 22

|| sincos

1TR

2

'

'

nn

nnR

2'

'4

nn

nnT

n R

1.4 2.778 %

1.5 4.0 %

1.8 8.16 %

2.4 16.96 %

36

Optical multi layer systems / thin layers:

Change of reflection, transpossion, polarization

Application in optical systems:

1. improved transmissioin

2. avoiding false light and ghosts

Thin layer stacks:

1. interference at many interface planes

2. the layer thickness is in the range of the wavelength

3. calculation is quite complex

Types of coatings:

1. AR coatings

2. HR coatings (mirrors)

3. spectral edge filter

4. spectral band filter

5. beam splitter

6. polarizing coatings

7. color filtering

Introduction and Overview

Types of Coatings

T

l

selective

filter

positive

T

l

selective

filter

negative

R

l

polarization

beam splitter

p s

T

l

band pass

filter

T

l

edge filter

low pass

T

l

edge filter

high pass

R

l

AR coating

R

l

HR coating

R

l

broadband

beam splitter

Comparison of coatings with different number of layers:

1. without coating

2. single layer

3. double layer

4. multi-layer

Comparison of Coatings

l

5

4

3

2

1

0

400 500 600 700 800 900

R in %

uncoated

mono layer

coating

double layer

coating

multi layer

coating

Principle of calculation of a thin layer system:

1. decomposition of field components at the plane interfaces

2. continuity condition of Fresnel equations

3. resulting matrix of layer sequence

4. calculation of th eigenwert values

sspp eEeEE

sspp eHeHH

EenH k

0

0

m

Field Components in Layers

y

z

x

Es

Ep

E

Ers

Etp

Ets

Etp

Et

Er

q

q q'

incidence

plane

incident

reflected

transmitted

Optical impedance in vacuum

Impedance of a system stack for both

polarizations

Equivalent phase delay of a layer

for incidence angle q

Reflectivity of amplitude

Transmission of amplitude

E

HZ o

0

0m

qqm

coscos0

0 nZ

n

E

HZ op

qqm

coscos

0

0 nZnE

HZ os

o

dn

l

q

cos2

inc

os

ref

oss

E

Er

2

2

sinc

os

ref

oss r

E

ER

inc

os

trans

gs

o

g

sE

E

n

nt

2

2

sinc

os

trans

gs

o

g

s tE

E

n

nT

Calculation of Thin Layer Stacks

Field components:

1. entrance and exit of a layer

2. E and H-field

3. forward and backward

propagating wave

4. both polarization components

Continuity conditions at the interface

planes

Solution of linear system equations

Also valid for absorbing media

Matrix Model of Stack Calculation

d1

n0

n1

ng

Ei0 Er0

Eg

Luft

Layer No 1

substrate

d2n2

dj-1nj-1

djnj

dj+1nj+1

dmnm

q1

q2

qj-1

qj

qj+1

qm

q0

qg

Layer No j-1

Layer No 2

Layer No

m

Layer No j

Layer No j+1

Ejt- Ejr-

Ejr+Ejt+

Ej-1,t+

Ej-1,t- Ej-1,r-

Ej-1,r+

Ej+1,t+

Ej+1,t- Ej+1,r-

Ej+1,r+

Transfer matrices

- for one layer

- for both polarizations

p and s

Matrix of complete stack

(representation with B)

Impedance of air and substrate

must be taken into account

sj

sj

jjjj

j

jj

j

sj

sj

H

E

ni

n

i

H

E

,

,

,1

,1

cossincos

sincos

cos

q

q

pj

pj

jj

j

j

j

jj

j

pj

pj

H

E

ni

n

i

H

E

,

,

,1

,1

cossincos

sincos

cos

q

q

m

m

jm

j

j

B

EM

B

E

1231,1 ... MMMMMMM mmjm

ggo

gs nZ qm

cos

0

qm

cos0

0

0 nZ os

Transfer Matrices

Single layer matrix

Reflectivity of complete system

for s and p polarization

Transmission of complete system

for s and p polarization

Matrix approach:

- analysis method

- optimization by NLSQ-algorithms

- problem: periodicity of phase

In principle solution only for

1. one wavelength

2. one incidence angle

Typically the spectral performance is shown as a function of lo / l

2221

1211

cossin

sincos

MM

MM

Zi

Z

i

M

jjj

j

j

j

j

22211211

22211211

MZMMZZMZ

MZMMZZMZr

sgsgsoso

sgsgsoso

s

22211211

2

MZMMZZMZ

Zt

sgsgsoso

sos

Final Calculations Step

Periodicity of phase:

dependence of performance on thickness

Period is the wavelength

Special thicknesses:

waves in phase,

no effect of the thin layer

stack

Influence of the Layer Thickness

R

0 1 2 3 4 5 6 7 8 90

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

nl = 2.30

nl = 1.70

nl = 1.50

nl = 1.35

nl = 1.22

Fresnel formulas:

reflectivity in general depends on

1. incidence angle

2. polarization

Degredation for broad band

and incidence angle interval

i

l / l o

lDesign

iDesign

R = 0.1

R = 0.0

R = 0.2

R = 0.3

R = 0.4

R = 0.4

R = 0.5

R = 0.5

R = 0.6R = 0.6

R = 0.7

Dependence on Incidence Angle and Polarization

s-polarization

p-polarization

total

R in %

i in °

Special example:

13 layer with

L : n = 1.45

H : n = 2.35

Example Coating

R

0.4 0.6 0.8 1 1.2 1.4 1.60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

i = 20° p

i = 20° s

i = 30° p

i = 30° s

l / l

Typical coating:

stack of low-high-materials (LH) with thickness l / 4

Remaining sidelobs outside of a centrals spectral interval

Suppression of sidelobs:

additional initial and final

layer with l/8

Sidelobs

R

l / l0.4 0.6 0.8 1 1.2 1.4 1.60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

without

l/8-bands

with

l/8-bands

Example Coating

R

l /l 0.4 0.6 0.8 1 1.2 1.4 1.6

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

i = 0°

i = 10°

i = 20°

i = 40°

i = 30°

Special example:

4 layer with thickness l/4

L : n = 1.45

H : n = 2.35

Reflectivity for different

incidence angles

Single layer with thickness l/4

Matrix

Destructive interference

of the two backwards

propagating waves:

no reflected light

0

004/

lo

l

niZ

nZ

i

M l

Single l/4 Layer

d

n0

nl

ng

ER0 ER1

ET0

air

layer

substrat

Reflectivity of amplitude

Phase condition

corresponds to l/4

Amplitude condition:

identical amplitude

Problem:

on a glass with n = 1.5

a layermaterial of

n=1.23 is needed

lnd

4

l

gol nnn

sincos

sincos2

2

innnnnn

innnnnnr

lgogol

lgogol

Single l/4 Layer

l / 4

no nl ng

air layer substrat

Spectral behavior:

single zero of reflectivity at the desired design wavelength

Residual reflectivity for violation of the amplitude condition

(non-ideal refractive index) 2

2

2

sin

lso

lsogle

nnn

nnnR

Single l/4 Layer

R0.1

0.05

0.01

0

0.02

0.03

0.04

0.06

0.07

0.08

0.09

l in nm300 400 500 600 700 800 900 1000

Double layer: several solutions possible

One simple solution: thickness

Corresponding amplitude condition

Residual reflectivity

2

2

1

2

20

2

1

2

20

nnnn

nnnnR

g

g

double

4/2211 l dndn

g

o

n

n

n

n

2

1

Double Layer

d1

d2

n0

n1

n2

ns

ER0 ER1 ER2

ET0

air

layer 1

layer 2

substrat

Scheme:

Typical broad spectral performance

for reflectivity

Multi Layer

n2

substrat

n3

n4

n5

n6

n7

n8

n1 air

R0.1

0.05

0.01

0

0.02

0.03

0.04

0.06

0.07

0.08

0.09

l in nm300 400 500 600 700 800 900 1000

Especially simple layout:

periodical stack with pair

of materials

a(LH)mg

a : air

L : low-index material

H : high-index material

g : glass substrate

m : number of pairs

Approximation of residual reflectivity

Advantageous:

1. large ratio of indices

2. high number of layer pairs

m

H

L

H

g

n

n

n

nR

241

Periodical Layer of 2 Materials

l / l

R

1

00 1 2

0.5

envelope

m = 5

m = 3

m = 2

Comfortable choice:

layer thickness l/4

Peak reflectivity

Spectral width of the reflectivity

interval:

growing with increased n-ratio

2

2

2

max

m

H

L

g

o

m

H

L

g

o

n

n

n

n

n

n

n

n

R


nH / nL

Dl / l

1 1.5 2 2.5 3 3.5 40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Performance dependence for different material combinations


m0 5 10 15 20 25 30

10-3

10-2

10-1

100

Log T

ng = 1.50

nL = 1.38

nH = 1.70

ng = 1.50

nL = 1.38

nH = 5.10

ng = 1.50

nL = 1.38

nH = 2.35

ng = 2.20

nL = 1.42

nH = 2.35

ng = 1.80

nL = 1.42

nH = 1.70

ng = 2.20

nL = 2.80

nH = 5.10

Combination of layers with real refractive indices can be used to generate arteficial indices

Equivalent Layers

d = l / 4 n = 1.62

n = 2.15

n = 1.38

d = l / 2

d = l / 4

n = 1.38

n = 1.35

n = 2.35

n = 2.35

d = l / 4

d = l / 4

no = 1

d = l / 2

ns = 1.52

n = 1.38

n = 2.35

n = 1.38

ideal equivalent

Graphical visualization of thin layer effects in the complex impedance plane

Every layer is represented by an arc

The arc length corresponds to the phase

Absorbing materilals are represented by spiral curves

Initial and final point must be on the real axis

Exception:metals with complex substrate index

Impedance Diagram

Re Y

Im Y

1 3 42

Layer 1

n = 2.35

Layer 2

n = 1.35

1.52

0.5016 3.633

-1.50

+1.0

Re Y

Im Y

1 3 42

no ng

solution 1

solution 2

Graphical illustration of layer stacks in the complex plane of the reflectivities

Every layer is represented by an arrow with

1. length, corresponds to amplitude

2. direction, corresponds to phase

Im(r)

Re(r)r

1 r2

rres

r'2

r''2

r'res

r''res

Reflectivity Diagram

AR coating:

vectorial sum of vectors must vanish

Re r

Im r

r1

r2

r3

r4

r5

rgesamt

Reflectivity Diagram

Re

Im

Material Typ Refractive

index n

Spectral

range

Magnesiumfluorid L 1.38 UV - nIR

Cerfluorid L 1.62

Aluminiumoxid 1.62 UV - nIR

Cryolite 1.35 UV - nIR

Siliziumdioxid 1.48

Magnesiumoxid L 1.72

Zirkonium Dioxid H 2.00 UV - nIR

Hafniumdioxid H 1.98

Titandioxid H 2.45 vis - nIR

Zinksulfid H 2.30 vis - nIR

Cerdioxid 2.20 vis - nIR

Thoriumfluorid 1.52 UV - nIR

Silizium Monoxid 1.95 vis - nIR

Silizium 3.50 nIR - IR

Germanium 4.20 nIR - IR

Zinkselenid 2.44 nIR - IR

Cadmiumtellurid 2.69 nIR - IR

Bleitellurid 5.5 IR

Tellur H 4.80

Lithiumfluorid L 1.37

Coating Materials

Multi-beam interference analogous to the Fabry-Perot

Extrem narrow spectral transmission

Calculation of transmission:

Airy formula

cos21

)1(2

2

RR

RIT

Interference Coating

T

F-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

R = 0.900

R = 0.950

R = 0.980

R = 0.990

R = 0.999

Transmission in Optical Systems

Residual reflectivity of the (identical) surfaces in an optical system with n surfaces:

Overall transmission of energy:

Transmission decreases

nonlinear

Practical consequences:

1. loss of signal energy

2. contrast reduction in

case of imaging

3.occurence of ghost images

n0 10 20 30 40 50 60

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

T

R = 1 %

R = 2 %

R = 4 %

R = 6 %R = 10 %

n

ges RT 1

64

Example of a concrete multi-layer stack

Example Coating

R

l / l0.4 0.6 0.8 1 1.2 1.4 1.60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Dielectric HR coating

Problems:

1. absorbing substrates (metal mirrors)

2. Polarization splitting for

oblique incidence

Example: HR Coating

l

1

0.8

0.6

0.4

0.2

0

400 500 600 700 800 900

R

Requirements:

1. steep edge

2. high reflectivity R on one side

3. high transmission T on

the other side

4. no oscillations

Application:

cold mirror, blocking of

infrared light

Thin Layer as Edge Filter

l

1

0.8

0.6

0.4

0.2

0

400 600 800 1000 1200 1400

T in %

Superposition of two edge filters:

Band pass

Transmission of a selcted

spectral range

Thin Film Layers for Bandpass Filtering

l

1

0.8

0.6

0.4

0.2

0

400 600 800 1000 1200 1400

T in %

stack 1

stack 2

resulting band

pass

spectral

transmission

Special coloring properties by spectral filtering

Example application:

selective spectral transmission

for subtractive color printing

Color Filtering

l

1.0

0.75

0.50

0.25

0

300 400 500 600 700

T in %

yellow magenta cyan

Special coating for polarization splitting into s and p

Application: cubic beam splitter

Polarizing Beam Splitting Coating

layer

L / H

pp

s

s

glass

glass

R

l / l1 1.20.80.6 1.4 1.60.4 1.80.2

s-polarization

p-polarization0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Last column in the lens data

manager:

coating on the surface

One-Step-Coating of the

complete system in:

Tools/Catalogs/

Add Coationgs to all Surfaces

On every surface:

specification of coating data

form data file

coating.dat

File can be edited in:

Tools/Catalogs/Edit Coating File


Coatings in Zemax

Syntax of the coating file,

Tools/Catalogs/Coating Listing

1. Material specifications:

different indices of the substrate

2. coatings:

all layers: material, thickness in waves

material must be given

3. ideal coatings:

described by transmission value

4. coatings specified by table

explicite values of Rs, Rp, Ts, Tp for each

wavelength and incidence angle

5. encripted coatings

(binary format)


Coatings in Zemax

MATE BK7

0.4 1.5308485 0

0.46 1.5244335 0

0.5 1.5214145 0

0.7 1.5130640 0

0.8 1.5107762 0

1.0 1.5075022 0

2.0 1.4945016 0

COAT AR

MGF2 .25

COAT HEAR1

MGF2 .25

ZRO2 .50

CEF3 .25

COAT I.05

COAT I.50

COAT I.95

TABLE PASS45

ANGL 0.0

WAVE 0.55 1.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0

ANGL 45.0

WAVE 0.55 0.0 0.0 1.0 1.0 0.0 0.0 0.0 0.0

ANGL 90.0

WAVE 0.55 1.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0

ENCRYPTED ZEC_HEA673

ENCRYPTED VISNIR

ENCRYPTED ZEC_UVVIS

ENCRYPTED ZEC_HEA613

COAT CZ2301,45

MGF2_G 0.08450000 1 0

XIV 0.02640000 1 0

MGF2_G 0.01280000 1 0

XIV 0.07600000 1 0

MGF2_G 0.01380000 1 0

XIV 0.02930000 1 0

MGF2_G 0.03260000 1 0

XIV 0.01070000 1 0

Selection of coating/polarization analysis

Tapering of coatings is possible:

radial polynomial of cosine-shaped

spatial thickness variation

Import of professional coating software

data is possible

Given coatings can be incorporated into the

optimization to a certain flexibility

- thickness scaling

- offset of refractive index

- offset of extinction coefficient


Coatings in Zemax

Detailed polarization analyses are possible at the individual surfaces by using the coating

menue options

9 Physical Optical Modelling I

Coating Analysis in Zemax

Optical Design with Zemax - Institute of Applied Physics · 2012-11-21 · 3. ABg scattering...

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