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___________________________________________________________________________________________________

SigFit

Reference Manual

Version 2015R1a

___________________________________________________________________________________________________

March 12, 2015

Sigmadyne, Inc.

803 West Avenue

Rochester, NY 14611

www.sigmadyne.com

SigFit 2015R1a

Table of Contents

Installation and Uninstallation............................................................................................................................................ 9

1.1 Upgrading the SigFit Applications ................................................................................................................................ 9

1.2 Installation Requirements .............................................................................................................................................. 9

1.3 Installation of the SigFit Application ............................................................................................................................ 9

1.3.1 Changing the License Type of an Existing SigFit Client Installation ................................................................ 15

1.3.2 Installation of the MSC PATRAN Plotting Template Files ............................................................................... 15

1.3.3 Installation of the Macro Files for ANSYS Mechanical APDL ......................................................................... 16

1.3.4 Installation of the Macro File for ANSYS Workbench ...................................................................................... 16

1.3.5 Installation of the ABAQUS ODB API Library ................................................................................................ 16

1.3.6 Installation of the CODEV User Defined Gradient Index Lens DLL ................................................................ 16

1.4 Installation of Sigmadyne FLEXnet Licensing ........................................................................................................... 16

1.5 Installation of Dongle Security Drivers ....................................................................................................................... 17

1.6 Uninstallation of the SigFit Application ...................................................................................................................... 21

2 Documentation ................................................................................................................................................................. 22

2.1 SigFit Reference Manual (SigFit-Ref-Man-v2015r1a.pdf) ......................................................................................... 22

2.2 SigFit Dictionary (SigFit-Dictionary-v2015r1a.pdf) ................................................................................................... 22

2.3 SigFit Examples Manual (SigFit-Exp-Man-v2015r1.pdf) ........................................................................................... 22

3 Introduction ...................................................................................................................................................................... 23

3.1 Integrated Analysis ...................................................................................................................................................... 23

3.2 Features ....................................................................................................................................................................... 24

3.2.1 Standard Features (Standard) ............................................................................................................................. 24

3.2.2 Active Control (Optional) .................................................................................................................................. 25

3.2.3 Harmonic/Random/Transient Response (Optional) ........................................................................................... 25

3.2.4 Stress Birefringence, Thermo-Optic, Stress-Optic and Aero-Optic Analysis (Optional)................................... 25

3.2.5 Equation Writing (Optional) .............................................................................................................................. 26

3.3 Overview of Using VSigFit ......................................................................................................................................... 26

3.3.1 The Role of VSigFit ........................................................................................................................................... 26

3.3.2 Overall Layout of VSigFit ................................................................................................................................. 26

3.3.3 Starting VSigFit ................................................................................................................................................. 28

3.3.4 Opening an Existing Analysis Definition .......................................................................................................... 28

3.3.5 Opening a New Analysis Definition .................................................................................................................. 28

3.3.6 Defining an Analysis .......................................................................................................................................... 28

3.3.7 Saving an Analysis ............................................................................................................................................. 32

3.3.8 Validating an Analysis Definition ...................................................................................................................... 32

3.3.9 Running SigFit from VSigFit ............................................................................................................................. 33

3.4 Flow Chart of SigFit Calculation Engine .................................................................................................................... 34

4 Interfaces .......................................................................................................................................................................... 36

4.1 User Interface .............................................................................................................................................................. 36

4.1.1 Graphical User Interface (VSigFit) .................................................................................................................... 36

4.1.2 SigFit Input File ................................................................................................................................................. 36

4.1.3 SigFit Output Files ............................................................................................................................................. 36

4.2 Interface to FEA Software ........................................................................................................................................... 48

4.2.1 Model Data Required by SigFit ......................................................................................................................... 49

4.2.2 Disturbance Results Data Required by SigFit .................................................................................................... 50

4.2.3 Interface to NASTRAN ..................................................................................................................................... 50

4.2.4 Interface to ANSYS Mechanical APDL and ANSYS Workbench .................................................................... 51

4.2.5 Interface to ABAQUS ........................................................................................................................................ 55

4.2.6 Interface to SolidWorks Simulation ................................................................................................................... 55

4.2.7 Interface to COSMOS ........................................................................................................................................ 58

4.2.8 Interface to CGNS.............................................................................................................................................. 59

4.3 Interface to Graphical Software ................................................................................................................................... 59

4.3.1 Interface to MSC.Patran ..................................................................................................................................... 59

4.3.2 Interface to FEMAP ........................................................................................................................................... 59

SigFit 2015R1a

4.3.3

Interface to ANSYS Mechanical APDL ............................................................................................................ 59

4.3.4 Interface to ANSYS Workbench ........................................................................................................................ 60

4.3.5 Interface to ABAQUS CAE/Viewer .................................................................................................................. 62

4.3.6 Interface to SolidWorks Simulation ................................................................................................................... 62

4.4 Interface to Optical Analysis Software ........................................................................................................................ 62

4.4.1 Topics Common to Importation to any Optical Analysis Software ................................................................... 62

4.4.2 Interface to CODEV .......................................................................................................................................... 63

4.4.3 Interface to ZEMAX .......................................................................................................................................... 63

4.4.4 Interface to OSLO .............................................................................................................................................. 64

4.5 Interface to Microsoft Excel ........................................................................................................................................ 64

5 Theory and Use of SigFit ................................................................................................................................................. 65

5.1 Definition of Solution Options .................................................................................................................................... 65

5.1.1 Output File Naming ........................................................................................................................................... 65

5.1.2 Analysis Type Definition ................................................................................................................................... 65

5.1.3 Wavelength ........................................................................................................................................................ 65

5.1.4 Surface Deformation Direction .......................................................................................................................... 65

5.1.5 Corrected Surface Deformation Calculation (Radial/Axial Correction) ............................................................ 65

5.1.6 Interfacing Software Definitions ........................................................................................................................ 65

5.1.7 Symmetry ........................................................................................................................................................... 66

5.1.8 Model File Specification .................................................................................................................................... 67

5.2 Definition of Coordinate Systems ............................................................................................................................... 67

5.2.1 Defining Coordinate Systems in SigFit .............................................................................................................. 67

5.2.2 Referencing Coordinate Systems Defined in the Finite Element Model............................................................ 68

5.3 Definition of Surfaces.................................................................................................................................................. 68

5.3.1 Definition of Finite Element Model Representation of Surfaces ....................................................................... 68

5.3.2 Surface Coordinate System ID (VCID) and Polynomial Fitting Coordinate System ID (FCID) ....................... 71

5.3.3 Optical Analysis Surface ID .............................................................................................................................. 73

5.3.4 CODEV Surface INT Sign ................................................................................................................................. 74

5.3.5 Material Properties Reference ............................................................................................................................ 74

5.3.6 Material Coordinate System Reference ............................................................................................................. 74

5.3.7 Surface Definition by Meshing in SigFit ........................................................................................................... 74

5.3.8 Surface Geometry Definition ............................................................................................................................. 74

5.3.9 Diffractive Surface Definitions .......................................................................................................................... 79

5.3.10 Surface Aperture Definitions ........................................................................................................................ 81

5.3.11 Surface Obscuration Definitions ................................................................................................................... 82

5.3.12 Surface Area Weighting Definition ............................................................................................................... 82

5.4 Definition of Material Properties ................................................................................................................................. 82

5.5 Definition of Lenses .................................................................................................................................................... 84

5.5.1 Definition of Finite Element Model Representation of Lenses .......................................................................... 84

5.5.2 Definition of Entrance and Exit Surfaces ........................................................................................................... 85

5.5.3 Integration Intervals ........................................................................................................................................... 85

5.5.4 Lens Initial Value ............................................................................................................................................... 85

5.5.5 Search Tolerance ................................................................................................................................................ 86

5.6 Definition of Disturbances .......................................................................................................................................... 86

5.6.1 Finite Element Disturbances .............................................................................................................................. 86

5.6.2 Vector Disturbances ........................................................................................................................................... 86

5.6.3 Polynomial Disturbances ................................................................................................................................... 87

5.6.4 Hitmap (Array) Disturbances ............................................................................................................................. 87

5.6.5 Zernike INT Disturbances .................................................................................................................................. 87

5.6.6 Linear Combinations .......................................................................................................................................... 88

5.7 Surface Displacement Data Definitions: Displacement Vector (dX) and Corrected Surface Displacement (ds

′

) ....... 88

5.8 Rigid Body Motion ...................................................................................................................................................... 90

5.8.1 Calculation of Best Fit Rigid Body Motion ....................................................................................................... 91

5.8.2 Subtraction of Rigid Body Motion ..................................................................................................................... 91

5.8.3 Area Weighting .................................................................................................................................................. 92

5.8.4 Best-Fit Rigid-Body Motion Output for Optical Analysis ................................................................................. 92

SigFit 2015R1a

5.9

Best Fit Radius of Curvature / Best Fit Power............................................................................................................. 95

5.9.1 Calculation of RoC of Flat Surfaces .................................................................................................................. 95

5.9.2 Calculation of dRoC of Initially Curved Surfaces ............................................................................................. 95

5.9.3 Subtraction of dRoC .......................................................................................................................................... 96

5.9.4 Power and Subtraction of Power ........................................................................................................................ 96

5.9.5 Best-Fit Radius of Curvature/Power Output for Optical Analysis ..................................................................... 96

5.10 Polynomial Fitting .................................................................................................................................................. 97

5.10.1 Standard Zernike Polynomials ...................................................................................................................... 98

5.10.2 Fringe Zernike Polynomials ........................................................................................................................ 100

5.10.3 Annular Zernike Polynomials ..................................................................................................................... 100

5.10.4 Aspheric Polynomials ................................................................................................................................. 100

5.10.5 Forbes Polynomials ..................................................................................................................................... 101

5.10.6 XY Polynomials .......................................................................................................................................... 104

5.10.7 Legendre Polynomials ................................................................................................................................. 104

5.10.8 Fourier-Legendre Polynomials for grazing incidence (GRCONIC) surfaces.............................................. 105

5.10.9 Fitting Polynomials to Deformed Surfaces and Optical Path Difference Maps .......................................... 106

5.10.10 Using Polynomial Fits for Representation of Surface Deformation ............................................................ 110

5.10.11 Using Polynomial Fits for Representation of Optical Path Difference ....................................................... 119

5.11 Interpolation .......................................................................................................................................................... 121

5.11.1 Destination Node to Origination Mesh Mapping ........................................................................................ 122

5.11.2 Pixel Center/Pixel Corner Rectangular Array Size Conventions ................................................................ 122

5.11.3 Input Disturbances and Actuator Influence Functions in Rectangular Array Format ................................. 123

5.11.4 Output Disturbances in Rectangular Array Format ..................................................................................... 124

5.11.5 Output Disturbances to an Alternate Set of Nodes ...................................................................................... 130

5.11.6 Calculating Interpolated Values .................................................................................................................. 130

5.12 Active Control ...................................................................................................................................................... 132

5.12.1 Defining the Actuator Influence Functions ................................................................................................. 133

5.12.2 Simulation of Active Control ...................................................................................................................... 133

5.12.3 Actuator Placement Optimization ............................................................................................................... 136

5.13 Monte Carlo Analysis ........................................................................................................................................... 137

5.14 Harmonic / Random / Transient Response with Modal Techniques ..................................................................... 140

5.14.1 Harmonic Response .................................................................................................................................... 140

5.14.2 Random Response ....................................................................................................................................... 143

5.14.3 Modal Transient Response .......................................................................................................................... 145

5.14.4 Damping ...................................................................................................................................................... 146

5.15 Equation Generation ............................................................................................................................................. 147

5.15.1 Equation Generation of Rigid Body Surface Motion .................................................................................. 147

5.15.2 Equation Generation of Line-of-Sight Error (LoS) ..................................................................................... 147

5.15.3 Equation Generation of Polynomial Coefficients ........................................................................................ 148

5.15.4 Equation Generation of Residual Surface Error .......................................................................................... 149

5.16 Refractive OPD Analyses (Thermo-Optic, Stress-Optic, Stress-Induced Birefringence, and Aero-Optic Analyses)

150

5.16.1 Integration Paths Through Lenses ............................................................................................................... 151

5.16.2 Thermo-Optic OPD (dn/dT) Effects ............................................................................................................ 152

5.16.3 Stress-Optic OPD (dn/dσ) Effects ............................................................................................................... 156

5.16.4 Aero-Optic Effect ........................................................................................................................................ 158

5.16.5 Stress-Birefringence Analysis (Photo-Elastic Effect) ................................................................................. 160

5.16.6 Importing BIR and CAO to CODEV .......................................................................................................... 161

5.17 Phase Changes of Diffractive Optics .................................................................................................................... 162

5.17.1 Respresentation of Disturbed Diffractive Surfaces in Optical Analysis Software ...................................... 162

5.18 Combining Multiple Result Types in Optical Analysis ........................................................................................ 165

5.18.1 Combining Multiple Result Types in CODEV ........................................................................................... 165

5.18.2 Combining Multiple Result Types in ZEMAX ........................................................................................... 166

5.19 System Level Performance Predictions ................................................................................................................ 167

5.19.1 Line-of-Sight Error Predictions (LoS) ........................................................................................................ 168

5.19.2 Line-of-Sight (LoS) MTF Predictions ......................................................................................................... 173

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