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Optical Design with Zemax

Lecture 13: Physical Optical Modelling

2013-02-05

Herbert Gross

Summer term 2012

2 13 Physical Optical Modelling

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. Gaussian beams

2. Physical optical propagation

3. Polarization raytrace

4. Polarization transmission

5. Coatings - overview

6. Coating transmission and phase effects

7. Design and calculation of thin films

8. Simple layers

9. Applications and examples

10.Coatings in Zemax


Contents

Expansion of the intensity distribution around the waist I(r,z)

13 Physical Optical Modelling

Gaussian Beams

z

asymptotic

lines

x

hyperbolic

caustic curve

wo

w(z)

R(z)

o

zo

4

2

2

2

1

2

2

2 1

2),(

o

To

z

zzw

r

o

To

e

z

zzw

PzrI

2

0 1)(

o

T

z

zzwzw

00000

zzw

o

o


Gaussian Beams, Definitions and Parameter

Paraxial TEM00 fundamental mode

Transverse intensity is gaussian

Axial isophotes are hyperbolic

Beam radius at 13.5% intensity

Only 2 independent beam parameter of the set:

1. waist radius wo

2. far field divergence angle o

3. Rayleigh range zo

4. Wavelength o

Relations

5

222

1

12

)(

2),0(

o

To

z

zzw

P

zw

PzrI

2

0

0

0

0

2

wwz o

o

I(z) / I0(z)

z / zo

-6 -4 -2 0 2 4 60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Gaussian Beam, Axial Intensity

Axial intensity: Lorentz function

Characteristic depth of the waist region:

Rayleigh range

6

T

oT

zz

zzzzR

2

)(

R / z0

z / zo

0 1 2 3 4 5 60

1

2

3

4

5

6


Gaussian Beams, Radius of Curvature

Gaussian beams have a spherical wavefront

Radius of curvature:

In the waist the phase is plane

The spherical wave is not concentric

to the waist center

In the distance of the Rayleigh range, the

curvature of the phase has ist maximum

7

f

zfz

zzz

TT

oTT

1

1

1112'


Transform of Gaussian Beams

Diffraction effects are taken into account

Geometrical prediction corrected in the waist region

No singulare focal point: waist with finite width

Focal shift: waist located towards the system, intra focal shift

Transform of paraxial beam

propagation

z'T / f

zT / f

-6 -5 -4 -3 -2 -1 0 1 2 3 4-4

-3

-2

-1

0

1

2

3

4

5

6

zo / f = 0.1

zo / f = 0.2

zo / f = 0.5

zo / f = 1

zo / f = 2

geometrical

limit zo / f = 0

8

2

21

2

1

21 )0,(

cL

rr

ezrr

2

1

2

1

c

o

L

w

2

2 11

c

o

L

wM


Gauß-Schell Beam: Definition

Partial coherent beams:

1. intensity profile gaussian

2. Coherence function gaussian

Extension of gaussian beams with similar description

Additional parameter: lateral coherence length Lc

Normalized degree of coherence

Beam quality depends on coherence

Approximate model do characterize multimode beams

9


Solution Methods of the Maxwell Equations

Maxwell-

equations

diffraction

integrals

asymptotic

approximation

Fresnel

approximation

Fraunhofer

approximation

finite

elements

finite

differences

exact/

numerical1st

approximation

direct

solutions of

the PDE

spectral

methods

plane wave

spectrum

vector

potentials

2nd

approximation

finite element

method

boundary

element

method

hybrid method

BEM + FEM

Debye

approximation

Kirchhoff-

integral

Rayleigh-

Sommerfeld

1st kind

Rayleigh-

Sommerfeld

2nd kind

mode

expansion

boundary

edge wave

10

Method Calculation Properties / Applications

Kirchhoff

diffraction integral E r

iE r

e

r rdF

i k r r

FAP

( ) ( ' )'

'

Small Fresnel numbers,

Numerical computation slow

Fourier method of

plane waves )(ˆˆ)'(21 xEFeFxE zvi

II

Large Fresnel numbers

Fast algorithm

Split step beam

propagation

Wave equation: derivatives approximated

En

yxnkE

z

Eik

z

E

o

1

),(2

2

222

2

2

Near field

Complex boundary geometries

Nonlinear effects

Raytracing Ray line law of refraction

r r sj j j j 1 sin '

'sini

n

ni

System components with a aberrations

Materials with index profile

Coherent mode

expansion

Field expansion into modes

n

nn xcxE )()( dxxxEc nn )()( *

Smooth intensity profiles

Fibers and waveguides

Incoherent mode

expansion

Intensity expansion into coherent modes

n

nn xcxI2

)()(

Partial coherent sources


Wave Optical Coherent Beam Propagation

11

Different ranges of edge or slit diffraction as a function of the Fresnel number /

distance:

1. Far field

Fraunhofer

weak structure

small NF ≤ 1

2. Fresnel

Quadratic

approximation

of phase

ripple structure

medium NF > 1

3. Near field

Behind slit

large NF >> 1


Diffraction Ranges

NF = 10000

NF = 1000

NF = 100

NF = 20

NF = 5

NF = 1

z [mm]far field

Fraunhofer

Fresnel

regime

near field

coherent plane wave

slit

intensity near left edge

12

Fresnel number : critical number for separation of approximation ranges

Setup with two stops in distance L

Fraunhofer diffraction, farfield,

Dominant effect of diffraction:

NF < 1

Fresnel diffraction with

considerable influence of

diffraction: NF = 1

Geometrical-optical range witj neglectable diffraction, near field :

NF >> 1

L

a1

a2

final

plane

stop

start plane

stop

spherical wave

from axis point P

sagittal

height p

P

L

aaNF

21


Fresnel Number

13


Fourier-Based Propagators

Changing form the spatial into the frequence domain

Expanding the complex field into plane waves by Fourier transform

Propagation of each plane wave by a simple phase shift

After propagation returning into spatial domain

Between starting and final plane the field is unknown (one step method)

0

2

2,,

k

zik

xx

x

ezkEzzkE

z

xs

x

free space /

ABCD segment

spatial

domain

Fourier-

transform

inverse Fourier

transform

spatial

domain

plane waves

frequency domain

x

one step

starting

plane

final plane

14


Propagation by Plane / Spherical Waves

Expansion field in simple-to-propagate waves

1. Spherical waves 2. Plane waves

Huygens principle spectral representation

rdrErr

erE

rrik

2

'

)('

)'(

x

x'

z

E(x)

eikr

r

)(ˆˆ)'( 1 rEFeFrE xy

zik

xyz

x

x'

z

E(x)

eik z z

15

Basis: 1. superposition of solutions

2. separability of coordinates

Plane wave

Spectral expansion

A(k): plane wave spectrum

Dispersion relation: Ewald sphere

Transverse expansion

Main idea:

- Field decomposition in plane waves

- Switch into Fourier space of spatial frequencies

- Propagation of plane wave as simple phase factor

- Back transform into spatial domain

- Superposition of plane wave with modified phase


Plane Wave Expansion

kdekArE rki

)(

2

13

trkietrE

,

2

2222

o

zyxc

nkkkk

E x y z A k k z e dk dkx y

i xk yk

x y

x y, , ( , , )

1

22

k k k k k kT z x y z

A k k z E x y z e dxdyx y

i xk ykx y, , ( , , )

16

Propagation of plane waves:

pure phase factor

1. exact sphere

2. Fresnel quadratic approximation

Evanescent waves

components damped in z

important only for near field setups

Propagation algorithm

x-y-sections are coupled

Paraxial approximation

x-y-section decoupled


Plane Wave Expansion

A k k z A k k A k k ex y x y

ik z

x y

ik zk

k

k

kz

x x

, , , , , ,

0 01

2 2

22

22

0,,

0,,,, 2

yx

yx

vvzizik

yx

kkk

iz

zik

yxyx

eevvA

eekkAzkkA

evanescentkkforkkkik yxyxz ,0222

0

22

),(ˆˆ

),(ˆˆ)','(

222/121

1

yxEFeF

yxEFeFyxE

xy

vviz

xy

xy

zik

xy

yx

z

),(ˆˆ)','(22

1 yxEFeFyxE xy

vvzi

xyyx

17


Richards-Wolf Vectorial Diffraction integral

Transfer from entrance to exit pupil in high-NA:

1. Geometrical effect due to projection

(photometry): apodization

with

Tilt of field vector components

y'

R

u

dy/cosudy

y

rrE

E

yE

xE

y

xs

Es

eEy e

y

y'

x'

u

R

entrance

pupil

image

plane

exit

pupil

n

NAus sin

4 220

1

1

rsAA

2cos11

11

2 22

22

0

rs

rsAA

18


High-NA Focusing

Total apodization

corresponds astigmatism

Example calculations

4 22

2222

0

12

2cos1111),(),(

rs

rsrsrArA linx

-1 -0.5 0 0.5 10

0.5

1

1.5

2

-1 -0.5 0 0.5 10

0.5

1

1.5

2

-1 -0.5 0 0.5 10

0.5

1

1.5

2

-1 -0.5 0 0.5 10

0.5

1

1.5

2

NA = 0.5 NA = 0.8 NA = 0.97NA = 0.9

r

A(r)

x

y

19

Pupil


Vectorial Diffraction at high NA

Linear Polarization

20


High NA and Vectorial Diffraction

Relative size of vectorial effects as a function of the numerical aperture

Characteristic size of errors:

I / Io

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 110

-6

10-5

10-4

10-3

10-2

10-1

100

NA

axial

lateral

error axial lateral

0.01 0.52 0.98

0.001 0.18 0.68

21

Setting of initial beam and

sampling parameters


Beam Propagation in Zemax

22

Individual control of parameters

at every surface

Model of calculation:

1. propagator from surface to

surface

2. estimation of sampling by pilot

gaussian beam

3. mostly Fresnel propagator with

near-far-selection

4. re-sampling possible

5. polarization, finite transmission,...

possible



23

Example:

Focussing of a tophat beam with

one-sided truncation



24


Description of Polarization

Parameter Properties

1

Polarization

ellipse

Elliptczity ,

Rotation angle only complete polarization

2

Complex

parameter

Parameter

only complete polarization

3

Jones vector

Components of the field

E

only complete polarization

4

Stokes vector

Stokes parameter So to

S4 also for partial polarization

5

Poincare sphere

Points on and inside

sphere

only graphical

representation

6

Coherence matrix

2x2 - matrix C

also for partial polarization

25

Decomposition of the field strength E

into two components in x/y or s/p

Relative phase angle between

components

Polarization ellipse

Linear polarized light

Circular polarized light

y

x

i

y

i

x

y

x

eA

eA

E

EE

0

xy

0

10E

1

00E

sin

cos0E

iErz

1

2

1

iElz

1

2

1


Jones Vector

2

22

sincos2

yx

yx

y

y

x

x

AA

EE

A

E

A

E

26

Jones representation of full polarized field:

decomposition into 2 components

Cascading of system components:

Product of matrices

Transmission of intensity


Jones Calculus

1121 EJJJJE nnn

os

op

ppps

spss

s

p

oE

E

JJ

JJ

E

EEJE ,

System 1 :

J1

E1 System 2 :

J2

E2 System 3 :

J3

E3 System n :

Jn

En-1 EnE4

1

*

12 EJJEI

27

Three basic types of components, that change the polarization:

1. Change of amplitude: polarizer / analyzer

2. Change of phase: retarder

3. Change of orientation: rotator

)()0()()( DJDJ


Jones Matrices

p

s

trans t

tJ

10

01

2

2

0

0

i

i

ret

e

eJ

cossin

sincos)(rotJ

28

Jones matrix changes Jones vector

Müller matrix changes Stokes vector

Change of coherence matrix

Procedure for real systems:

1. Raytracing

2. Definition of initial polarization

3. Jones vector or coherence matrix local on each ray

4. transport of ray and vector changes at all surfaces

5. 3D-effects of Fresnel equations on the field components

6. Coatings need a special treatment

7. Problems: ray splitting in case of birefringence

JCJC'

SMS

'

EJE

'


Propagation of Polarization

29

Change of field strength:

calculation with polarization matrix,

transmission T

Diattenuation

Eigenvalues of Jones matrix

Retardation: phase difference

of complex eigenvalues

To be taken into account:

1. physical retardance due to refractive index: P

2. geometrical retardance due to geometrical ray bending: Q

Retardation matrix


Diattenuation and Retardation

EE

EPPE

E

EPT

T

*

*

2

2

minmax

minmax

TT

TTD

2/12/12/12/12/1 wewwJ

i

ret

21 argarg

totaltotalPQR

1

30


Polarization

Polarization of a donat mode in the focal region:

1. In focal plane 2. In defocussed plane

Ref: F. Wyrowski

31

Model:

1. definition of a starting polarization

2. every ray carries a Jones vector of polarization, therefore a spatial variation of polarization

is obtained.

3. at any interface, the field is decomposed into s- and p-component in the local system

4. changes of the polarization component due to Fresnel formulas or coatings:

- amplitude, diattenuation

- phase, retardance

Spatial variations of the polarization phase accross the pupil are aberrations,

the interference is influenced and Psf, MTF, Strehl,... are changed


Polarization in Zemax

32

Starting polarization

Polarization influences:

1. surfaces, by Fresnel formulas or coatings

2. direct input of Jones matrix surfaces with



EJE

'

y

x

imreimre

imreimre

y

x

y

x

E

E

DiDCiC

BiBAiA

E

E

DC

BA

E

E

'

'

33

Analysis of system polarization:

1. pupil map shows the spatial variant

polarization ellipse

2. The transmission fan shows the variation of

the transmission with the pupil height

3. the transmission table showes the mean

values of every surface



34

Single ray polarization raytrace:

detailed numbers of

- angles

- field components

- transmission

- reflection

at all surfaces



35

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

menue options



36


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

37


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

38


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

39

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


Overview on Coatings

40


Types of Coatings

T

selective

filter

positive

T

selective

filter

negative

R

polarization

beam splitter

p s

T

band pass

filter

T

edge filter

low pass

T

edge filter

high pass

R

AR coating

R

HR coating

R

broadband

beam splitter

41

Comparison of coatings with different number of layers:

1. without coating

2. single layer

3. double layer

4. multi-layer


Comparison of Coatings

5

4

3

2

1

0

400 500 600 700 800 900

R in %

uncoated

mono layer

coating

double layer

coating

multi layer

coating

42

Optical impedance in vacuum

Impedance of a system stack for both

polarizations

Equivalent phase delay of a layer

for incidence angle

Reflectivity of amplitude

Transmission of amplitude

E

HZ o

0

0

coscos0

0 nZ

n

E

HZ op

coscos

0

0 nZnE

HZ os

o

dn

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

43

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

1

2

j-1

j

j+1

m

0

g

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+

44

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

pj

pj

jj

j

j

j

jj

j

pj

pj

H

E

ni

n

i

H

E

,

,

,1

,1

cossincos

sincos

cos

m

m

jm

j

j

B

EM

B

E

1231,1 ... MMMMMMM mmjm

ggo

gs nZ

cos

0

cos0

0

0 nZ os


Transfer Matrices

45

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 o /

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

46

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

47

Single layer with thickness /4

Matrix

Destructive interference

of the two backwards

propagating waves:

no reflected light

0

004/

lo

l

niZ

nZ

i

M


Single /4 Layer

d

n0

nl

ng

ER0 ER1

ET0

air

layer

substrat

48

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 /4 Layer

R0.1

0.05

0.01

0

0.02

0.03

0.04

0.06

0.07

0.08

0.09

in nm300 400 500 600 700 800 900 1000

49

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 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

50

Dielectric HR coating

Problems:

1. absorbing substrates (metal mirrors)

2. Polarization splitting for

oblique incidence


Example: HR Coating

1

0.8

0.6

0.4

0.2

0

400 500 600 700 800 900

R

51

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


Coating Analysis in Zemax

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