sigfit user training thermo-optic analysis in sigfit

SigFit User Training

Thermo-Optic Analysis in SigFit

by

Copyright Sigmadyne, Inc.

Introduction

• Refractive index is a function of temperature

– Changes in temperature of transmissive optics cause optical performance errors in

addition to induced surface deformation effects

– Variation in index with temperature described by dn/dT

– dn/dT is a function of temperature and wavelength

– Often considered constant over expected temperature variation

– Relative dn/dT index change relative to air changing at same temperature as

medium

– Absolute dn/dT index change relative to vacuum


Thermo-Optic Properties

• Published material property data

– Tables given in glass catalogs

– Sellmier-type equation uses constants of dispersion for absolute dn/dT as a

function of temperature and wavelength


Includes effect of change in temperature

of medium as well as glass.

( )( )

( ) ( )( )2

2 0 1

0 1 2 2 2

, , 1 2( , )2 3

2 , ,

rel ref ref refabsref ref

TKrel ref ref

n T p E E T Tdn TD D T T D T T

dT n T p

− + − = + − + − + −


• Published material property data (cont)

– dn/dT dispersion relations have various combinations of power terms in wavelength

– SigFit currently supports following form


Reference 1

( )( )6 2 4 6

0 1 2 310absdn

C C C CdT

− − − −= + + +

Corning Fused Silica Corning Calcium Flouride


• Conversion between relative and absolute dn/dT

• Absolute vs relative dn/dT

– Use of relative dn/dT assumes medium is air and is changing temperature with

glass → this is NOT what we want

– Constant reference relative dn/dT assumes no effect of changing medium

temperature

– Constant reference relative dn/dT is equal to absolute dn/dT for nmed close to unity

• Use absolute dn/dT unless refractive index of

medium is significant

– If effect of medium is significant it should be modeled as lenses

( )( )

2 28

2 2

3

2949810 255401 6432.8 10 1

146 1 41 1, , 1

1 3.4785 10 15air refn T p

T

−

−

+ + + −

− − = ++ −

( ) ( )

( )

( ), , , , ,1

, ,

rel abs med

med

dn T p dn T dn T p

dT dT n T p dT

= −

( )

( )( )

( )

( )2

, , 1

, ,, ,

abs abs

medmed

n T dn T

dT n T pn T p

=

is expressed in um

T is expressed in C

100.000− 50.000− 0.000 50.000 100.0001.0002

1.0004

1.0006

1.0008

1.0010

1.0012

Temperature (C)

Ref

ract

ive

Ind

ex o

f Air

=0.1 um

=10.0 um

( ) ( )( )

( ) ( )( )( )2,,

,,,

,,

1,,,

pTn

Tn

dT

pTdn

pTndT

Tdn

dT

pTdn

med

absmed

med

absrel

−=

nrel = index relative to air

nabs = index relative to vacuum

nmed = nabs of medium

Includes effect of change in temperature of medium as well as glass.


SigFit

Thermo-Optic Analysis Methods

• Two basic methods

– Integrated OPD maps (Fast an approximate in optical analysis)

– User defined gradient index (Slow and accurate in optical analysis)


OPD Map

Integration

Polynomial

Fitting or Array

Interpolation

Predicted Temperatures Integrated OPD Maps

3D Temperature Profiles

dn/dT(T,)

Optical Analysis Model

SigFit

SigFit

Integrated OPD Map Method

• OPD map created for entrance surface of each lens element

– Integration paths start at entrance surface nodes and

extend along a cone defined by entrance and exit

apertures

– OPD numerically integrated along paths using shape

function interpolation of temperatures

• Map of integrated OPD may be fit with polynomial coefficients

or interpolated to rectangular array

• Map applied to entrance surface of lens element in optical

model

Ain Aout

Integration Paths

T1 T2

T3T4

Li

Ti-1

Ti+1

Ti

1

NINT

i i

i

OPD n L=

= ( )

0

iT

iT

dnn d

d

=

OPD Map

Integration

Polynomial

Fitting or Array

Interpolation

Predicted Temperatures Integrated OPD Maps



• Multispectral optical analysis not possible with OPD map

method

– OPD maps generated for each wavelength in Evaluation

Wavelength list in Solution module OR single

wavelength in Solution Options if evaluation wavelength

list does not exist

– Can only include one wavelength set of OPD maps at a

time in optical analysis

• If multispectral analysis results are important, then use user

defined gradient index method



• Multispectral optical analysis not possible with OPD map

method

– OPD maps generated for each wavelength in Evaluation

Wavelength list in Solution module OR single wavelength

in Solution Options if evaluation wavelength list does not

exist

– Can only include one wavelength set of OPD maps at a

time in optical analysis

• Form of OPD map for Zemax Optic Studio is phase, not OPD

– phase = OPD / wavelengthSigFit

– OPD = phase × wavelengthZEMAX

– wavelengthZEMAX must be equal to wavelengthSigFit

• If multispectral analysis results are important, then use user

defined gradient index method



Limitations of Integrated OPD Map Method

• Integration paths are not based on optical ray traces

– Users must use apertures to tune paths to approximate ray

footprints

• Integrations performed with fixed rays do not account for effects of field

– Larger variations in ray angles with field will result in larger

variations in paths through the lenses over field

Integration Path

Ray A

Ray B

Figures showing rays of light intersecting the same surface

point but from different field points. The figure on the right

has less variation in incident angle over the full range of

fields.Ray A is subject to less error than

Ray B in the OPD integration made

along the integration path.

Ain Aout

Integration Paths

• Optical analysis queries dynamic link library for refractive index/gradients as rays are

traced

• Dependency on wavelength is allowed to support multispectral


User Defined Gradient Index Lens

Dynamic Link Library

(Supplied with SigFit)

3D Temperature Profiles

dn/dT(T,)

Optical Analysis Model

Surface ID

Location

Base Refractive Index

Wavelength

Database Filename

Refractive Index

Refractive Index

Gradients

SigFitDatabase File

User Defined Gradient Index Lens

• Dynamic link libraries to support user defined gradient index representation are

supplied with SigFit

– Copy to locations shown below


Optical Analysis

SoftwareSigFit Supplied DLLs

Directory To Which User Should Copy

DLL File for Use

Code V

{SigFit_Install_Directory}\CODEV_Support\UserGRIN\sigfit_codev_udg_3dp.dll

{CODEV_Install_Directory}\umr{SigFit_Install_Directory}\CODEV_Support\UserGRIN\sigfit_codev_udg_interp.dll

Zemax Optic Studio

{SigFit_Install_Directory}\ZEMAX_Support\UserGRIN\sigfit_zemax_udg_3dp.dll {ZEMAX_Install_Directory}\DLL\Surfaces

or {MyDocuments

Path}\Zemax\DLL\Surfaces{SigFit_Install_Directory}\ZEMAX_Support\UserGRIN\sigfit_zemax_udg_interp.dll

Preparing the Optical Analysis

• Multiple surfaces must be used in Zemax Optic Studio to take multiple data types

– Surfaces taking phase results from DNDT or DNDS must have no material change

from prior surface

– Surface 2 takes the surface deformation results and contains the material boundary

– Surface 3 and 4 take the stress-optic and thermo-optic results, respectively, by

getting changed to Zernike Phase Surfaces by the files SigFit will write


Before Application of SigFit Results

After Application of SigFit Results

Note proper placement of thicknesses

on last surface in surface stack

Preparing the Optical Analysis

• Multiple surfaces must be used in Zemax Optic Studio to take multiple data types (cont)

– Surfaces taking GRIN results from DNDT must have no material change from prior

surface

– GRIN surfaces must have the thickness of the lens so must be last in the "entrance

surface stack"

– Dummy surfaces must follow surface to accept GRIN results (e.g., surface 4 and 5)

– Complex surfaces (user-defined surfaces and Zernike sag) may not

immediately follow GRIN surfaces


Before Application of SigFit Results After Application of SigFit Results

Note proper placement of thicknesses

on surfaces for gradient index results

Defining a Thermo-Optic Analysis

• Choose Thermo-optic from SigFit analysis type dialog

or


Edit analysis type of existing

surface deformation analysis will

preserve surface definitions


• Define the optical analysis wavelengths in nm in the Evaluation Wavelengths table in

the Solution module

– Specify all wavelengths required in the optical analysis

– Generates one set of integrated OPD map results for optical analysis for each

wavelength

– Used by user defined gradient index representation to efficiently characterize

wavelength dependence of dn/dT and refractive index

– At least three wavelengths required by Code V user defined gradient index

representation

– Will be used by future wavelength dependency features



Material Properties

• Wavelength dependency of refractive index and wavelength and temperature

dependency of thermo-optic properties may be added by reference to objects in Data

module



Material Properties

• Two forms of dispersion relationships allow specification of wavelength dependent

index; tabular form is also allowed by reference to a table of index vs. wavelength in nm

– Sellmeier form

– Dispersion form


𝑛𝑟𝑒𝑙(𝜆) =𝐵1𝜆2

𝜆2 − 𝐶1+

𝐵2𝜆2

𝜆2 − 𝐶2+

𝐵3𝜆2

𝜆2 − 𝐶3+ 1

𝑛𝑟𝑒𝑙(𝜆) = 𝐴0 + 𝐴1𝜆4 + 𝐴2𝜆2 + 𝐴3𝜆−2 + 𝐴4𝜆−4 + 𝐴5𝜆−6 + 𝐴6𝜆−8 + 𝐴7𝜆−10

Note that Schott uses the B and C values shown in the

equation while Ohara uses A and B values, respectively.

Sellmeier Index Dispersion

Coefficients from Schott

Glass Catalog

• Specifying thermo-optic properties in Data module

– Sellmeier: Sellmeier coefficients give temperature and

wavelength dependence

– Specification of reference temperature is often not clear in

glass catalogs; browse glass catalog in optical software or

contact glass manufacturer


Material Properties

Example Sellmeier Specification in Data Module


( )( )

( ) ( )( )2

2 0 1

0 1 2 2 2

, 1 2( , )2 3

2 ,

rel ref refabsref ref

TKrel ref

n T E E T Tdn TD D T T D T T

dT n T

− + − = + − + − + −

NOTE: TK expressed in microns for

equation evaluation.Sellmeier dn/dT Dispersion

Coefficients from Schott

Glass Catalog


Material Properties

• Specifying temperature dependent thermo-optic properties in table file

– Reference to table ID to be found in table file

– Table file name specified in Data module

– Values are instantaneous dn/dT, NOT secant

– Glass catalog data like the below is secant data between

temperatures shown

– Use such tabular data for constant dn/dT, not a

temperature dependent table unless you derive

instantaneous values from it


( )0

iT

iT

dnn d

d

=

Example Table Specifications in Data Module

Temperature

units consistent

with FE

temperature

units


Base Refractive Index for Code V and User Defined Gradient Index Results

• If using the user defined gradient index lens feature with Code V it is important to

specify the FE temperature units, the environment pressure and the index of refraction

in SigFit


Refractive Index Sellmier Data in Data Module

Constant index may be used for monochromatic analysis.

Constant index over wavelength will generate erroneous

answers for use of user defined gradient index lens and

multispectral analysis in Code V because private glass

representing thermo-optic behavior will not have nominal

index wavelength dependence.

Constant Index of Refraction Wavelength Dependent Index of Refraction

(Required for Multispectral UDG Results)

( )( )

( ) ( )( )2

2 0 1

0 1 2 2 2

, 1 2( , )2 3

2 ,

rel ref refabsref ref

TKrel ref

n T E E T Tdn TD D T T D T T

dT n T

− + − = + − + − + −

FEA temperature units and

environment pressure are

defined in Solution module

• Optic SID on entrance surface definitions must target correct surface in optical model

– When sending results to Zemax Optic Studio separate surfaces must be used in

the optical model to represent thermo-optic results


Surface Definition Optic SID


• Optic SID on surface definition may target same surface in optical model as targeted by

results of surface error


Surface Definition Optic SID


• Specification of apertures on the surface definitions controls definition of integration

paths for generation of integrated OPD map

• Apertures also limit nodes included in 3D polynomial fit of index profile for user defined

gradient index results


Surface Apertures and Control of Integration Paths


Ain Aout

Integration Paths

• Lenses are defined by entrance surface, exit surface and 3D elements


Lens Definitions

Entrance and exit surface IDs

Sets number of integration steps

for each integration path

through the lens for OPD

integration method

Temperature at which lens exhibits

no temperature induced OPD,

typically temperature at which

system is aligned or tested.

Integration Path

Exit Surface ShapeFinite Element

Integration Point

Tolerance Region

Nondimensional tolerance

used to determine if integration

point is within an element

Reference to 3D elements

associated with the lens; similar

to definition of surfaces


Gradient step size is the step size in

optic units for gradient index lens

representation of thermo-optic errors


Lens Definition

• Property Association (NASTRAN)

– Data in LENDEF table refers to ranges of PSOLID property IDs of 3D elements

Choose type of association for “Define Lens By”Define association data in LENDEF table.

This example associates Lens 10001 with

Property ID 10001.



Lens Definition

• Name Association (ANSYS Workbench, ANSYS, ABAQUS, and SolidWorks

Simulation)

– Data in LENDEF1 table refers to named entities

– ANSYS Mechanical APDL: Component names

– ANSYS Workbench: Named Selections

– ABAQUS: Part Instance Name, Element Set Name

– SolidWorks Simulation: Body Name

• ABAQUS also requires specification of the Part Instance in which the finite element

entities are located

Surface associated with Component or Named

Selection “LENS1” in ANSYS


• Fitting module is used to specify polynomials for two fitting purposes

– Specified on entrance surfaces only

– Integrated OPD maps on entrance surfaces

– 3D temperature profiles in lenses for user defined gradient representation

– Uses settings for OPD fitting and additional axial polynomial dependence


Polynomial Fitting

Calculation/subtraction of rigid-body-

motion does not apply to OPD results


Z polynomial dependence for user

defined gradient representations

Defines fitting of integrated OPD maps on

entrance surfaces and XY polynomial

dependence for user defined gradient

representations


Output Requests

• Output of integrated OPD maps or user defined gradient index results can be requested

in Output module

– Integrated OPD maps requested with Refr Indx Output Meth of OPD

– User defined gradient index results requested with Refr Indx Output Meth of DLL

DB



• For user defined gradient index results to be sent to Code V or Zemax Optic Studio

– Request optical output files by checking Optical Files in Output module

– Select 'DLL DB' or 'Both OPD & DB' for Refr Index Output Meth. in the Refractive

Index Effects Settings of the Output module

– This requests generation of the index profile database used by the user defined

gradient index DLL to support the optical analysis

– Select '3D Poly' for Refr Indx Reprsnt Meth in DLL Database Parameters of the

Output module

– This represents the index profiles in the database with 3D polynomial fits as

defined in the Fitting module

– Use of element interpolation choice should only be used on results that cannot

be fit by polynomials as optical ray trace run times can be very long (many

hours)



Output Requests

• Both integrated OPD maps and user defined gradient index results may be generated

in the same run

• This is highly suggested as comparison of the two methods is recommended when

performing initial analyses in order to verify the accuracy of the integrated OPD method


Importing Thermo-Optic OPD Results into Optical Analysis

• Code V

– Wavefront change maps are written in the form of WFR INT files that are imported,

normalized and located by commands in the _opd_ciii.seq file, where iii is the load

case index

– Definition of multiple wavelengths in SigFit will generate multiple macro files

denoted with _w001.seq, _w002.seq, etc. and corresponding sets of INT files

INT S002 double_gauss_dndt_codev_opd_zrn_opd_s002_c001.int

INR S002 2.4991E+01

INX S002 0.0000E+00

INY S002 0.0000E+00

...

S002 C001

ZRN 45 WFR SSZ 1.0 WVL 5.87600E-01

-8.93970E-01 6.12405E-05 -5.51887E-05 -2.75688E-05 4.88318E-01 2.72041E-05

-1.04409E-05 -4.41324E-05 1.42744E-05 1.00089E-05 -4.25910E-05 -2.65105E-06

-5.64319E-02 1.21075E-05 1.48294E-06 -1.39527E-07 7.80432E-06 2.21301E-05

-6.90103E-06 -1.69432E-05 4.78252E-06 -2.67447E-07 3.83963E-05 -2.42086E-05

-6.07245E-03 1.53355E-05 -5.78477E-06 1.35485E-06 0.00000E+00 -2.82228E-06

-9.03938E-06 6.83552E-06 -3.51043E-05 3.46876E-06 1.47567E-05 0.00000E+00

0.00000E+00 -5.04458E-07 -3.44905E-05 -2.70691E-05 3.04194E-03 3.68723E-05

8.62139E-07 3.41177E-06 0.00000E+00

.seq file importing, normalizing and locating ZRN WFR INT file of thermo-optic OPD

Entrance surface of lens


B$="SZERNPHA"

SURP 2,TYPE,B$

SURP 2,EDVA, 43, 1

SURP 2,EDVA, 2.922530000000000E+01, 2

SURP 2,EDVA,-2.774929371582779E-02, 3

SURP 2,EDVA, 1.111777147475203E-06, 4

SURP 2,EDVA,-1.006653263481387E-06, 5

SURP 2,EDVA, 1.618240124966645E-02, 6

SURP 2,EDVA, 2.114195474890794E-07, 7

SURP 2,EDVA, 2.528899912173778E-07, 8

....

Importing Thermo-Optic OPD Results into Optical Analysis

• Zemax Optic Studio

– OPD maps are written in the form of phase surface commands in the _opd_ciii.zpl

file, where iii is the load case index

– Coefficients are expressed in waves of the optical analysis

– User must be sure wavelength in SigFit matches wavelength in Zemax Optic

Studio

– Definition of multiple wavelengths in SigFit will generate multiple macro files

denoted with _w001.zpl, _w002.zpl, etc.

Entrance surface of lens Coefficients are expressed in waves of the optical analysis wavelength. User must

be sure wavelength in SigFit matches wavelength in Zemax Optic Studio.


Form of OPD map for Zemax Optic Studio is phase, not OPD

phase = OPD / wavelengthSigFit

OPD = phase × wavelengthZEMAX

wavelengthZEMAX must be equal to wavelengthSigFit

Thermo-Optic Analysis with User Defined Gradient Index Lenses

• Running Code V With Thermo-optic User Defined Gradient Index Results

– Copy dll files from {SigFit_Install_Directory}\CODEV_Support\UserGRIN to

{CODEV_Install_Directory}\umr

– SigFit generates two files

– _cov_udg_ciii.seq file is a macro file that builds a new private glass type for

every lens for which thermo-optic results are generated

– base indices are set from nominal model indices; set environment before

import

– applies the UDG to glass types of entrance surfaces

– _udg_3dp.sdb file is a database file that Code V reads during ray trace

– Be sure Code V working directory is same as directory of macro and .sdb files

– Run macro file with nominal lens loaded

– Loading of macro will take a few seconds and ray traces can be minutes or hours

– Start gradient step size on SigFit lens definition at the nominal lens thickness

divided by 5 and then cut in half and compare answers

– Note gradient step size may be edited in .seq file without rerunning SigFit



• Adjusting gradient step size in macro files can be done in text editor

– Code V .seq file is jobname_cov_udg_ciii.seq

– Must change value for each private glass created by SigFit


num ^surfidx ^surfid(6) ^surfgss(6) ^wvlid ^wvlval îndxval

str ^pwl_command ^prv_indx_command ûdg_command1 ûdg_command2

ûdg_command3 ûdg_command4

str ^wvlstr ^surfidstr ^surfidxstr îndxstr ^glasnamstr

^surfid(1)==2

^surfid(2)==4

^surfid(3)==5

^surfid(4)==8

^surfid(5)==9

^surfid(6)==11

^surfgss(1)== 1.0000000000000000

^surfgss(2)== 1.0000000000000000

^surfgss(3)== 1.0000000000000000

^surfgss(4)== 1.0000000000000000

^surfgss(5)== 1.0000000000000000

^surfgss(6)== 1.0000000000000000


• Running Zemax Optic Studio With Thermo-optic User Defined Gradient Index Results

– Copy dll files from {SigFit_Install_Directory}\ZEMAX_Support\UserGRIN to

{ZEMAX_Install_Directory}\DLL\Surfaces or {MyDocuments

Path}\Zemax\DLL\Surfaces

– Zemax Optic Studio models need special preparation for multiple result types

– SigFit generates two files

– _zmx_udg_ciii.zpl file is a macro file that changes the type of entrance surfaces

to user defined surfaces and loads interface data to database

– _udg_3dp.sdb file is a database file that Zemax Optic Studio reads during ray

trace

– Be sure Zemax Optic Studio ZPL folder is same as directory of macro and .sdb files

– Run macro file with nominal lens loaded

– Loading of macro will take a few seconds and ray traces can be minutes or hours

– Start gradient step size on SigFit lens definition at the nominal lens thickness

divided by 5 and then cut in half and compare answers

– Note gradient step size may be edited in .zpl file without rerunning SigFit



• Adjusting gradient step size in macro files can be done in text editor

– Zemax Optic Studio .zpl file is jobname_zmx_udg_ciii.zpl

– Must change value for each entrance surface modified by SigFit


SURP 004, SDLL, sigfit_zemax_udg_3dp.dll

SURP 004, TYPE, USERSURF

SURP 004, PARM, 1.00000E-01, 1

SURP 004, PARM, 1, 2

SURP 004,PARM,0,3

SURP 4, EDVA,141, 1

SURP 4, EDVA, 68, 2

SURP 4, EDVA, 58, 3

SURP 4, EDVA, 92, 4

...

References

1. SCHOTT Technical Information, “TIE-19: Temperature coefficient of the refractive

index,” January 2008

2. Michels, G. J. and Genberg, V. L, “Analysis of thermally loaded transmissive optical

elements,” Proceedings of SPIE, 8840-11, (2013)
