Characterization of surface roughness and shape deviations of aspheric surfaces [Elektronische Ressource] / vorgelegt von Gufran Sayeed Khan

Gufran

Sujets

• Physik

Informations

• Publié par: friedrich-alexander-universitat_erlangen-nurnberg
• Publié le: 01 janvier 2008
• Nombre de lectures: 16
• Langue: English
• Poids de l'ouvrage: 4 Mo

Extrait

Characterization of Surface Roughness and Shape
Deviations of Aspheric Surfaces



Der Naturwissenschaftlichen Fakultät der Friedrich-
Alexander-Universität Erlangen-Nürnberg

Zur Erlangung des Doktorgrades

Vorgelegt von
Gufran Sayeed Khan
aus Moradabad, Indien







Lehrstuhl für Optik
Institut für Optik, Information und Photonik



Erlangen 2008 ii


Als Dissertation genehmigt von der naturwissenschaftlichen Fakultät der
Universität Erlangen-Nürnberg




























Tag der mündlichen Prüfung 31. Januar 2008
Vorsitzender der Promotionskommission Prof. Dr. Eberhard Bänsch
Erstberichterstatter PD Dr. N. Lindlein
Zweiberichterstatter Prof. Dr. R. P. Bajpai



Contents

Zusammenfassung vii

Abstract ix

1 Introduction to Aspheric Optics 1
1.1 Aspheric Optics………………………………………………………………….1
1.1.1 Mathematical Description of Aspherics………………………………...2
1.1.2 Challenges in using Aspherics…………………………………………..3
1.2 Fabrication of Aspherics………………………………………….......................3
1.2.1 Single Point Diamond Turning (SPDT)………………………………...3
1.2.1.1 Advantages of SPDT…………………………………………..4
1.2.1.2 Operating Parameters of SPDT………………………………..5
1.2.1.3 Diamond Turnable Materials…………………………………..5
1.2.2 Grinding and Polishing of Aspherics……………………………………6
1.2.3 Fabrication Errors: Form, Figure and Finish…………………………....7
1.3 Metrology of Aspherics…………………………………………………………8
1.3.1 Surface Roughness by Profilometric Methods……………………….....8
1.3.1.1 Stylus Type Mechanical Profilers…………………………......8
1.3.1.2 Optical Profilers……………………………………………….9
1.3.2 Surface Deviations by Interferometric Methods…………………….....10
1.3.2.1 Null Methods…………………………………………………11
1.3.2.2 Non-null Methods………………………………………….....11

2 DOE based Interferometry 13
2.1 Interference…………………………………………………………………….13
2.2 Fringe Evaluation Techniques…………………………………………............15
2.3 Phase Shifting Interferometry……………………………………………….....16
2.3.1 Three Step Algorithm………………………………………………….17 iv Contents
2.3.2 Four Step Algorithm for the Elimination of Errors due to Nonlinear
Detector Error………………………………………………………….18
2.3.3 Five Step Algorithm for Elimination of Errors due to Linear Phase
Shift Error……………………………………………………………...19
2.3.4 Phase Unwrapping……………………………………………………..19
2.4 DOE based Null Interferometry……………………………………….. ……..20
2.4.1 Reflective or Refractive Null Optics…………………………………..22
2.4.2 Computer Generated Hologram (CGH) Nulls………………………....23
2.4.3 Combination of Null Optics and CGH………………………………...24
2.4.4 Different Architectures with CGH as Null Element…………………...24
2.4.5 Production of CGH………………………………………………….....26

3 Frequency Analysis of Nano-scale Roughness Formation on Single
Point Diamond Turned Optical Surfaces 29
3.1 Introduction……………………………………………………………….....29
3.2 Statistical Parameters for Roughness Evaluation…………….…….....30
3.2.1 Arithmetic Average Roughness (R )…………………………………...30 a
3.2.2 Root Mean Square Roughness (R )………………………………….....30 q
3.2.3 Peak-to-Valley Roughness (R )………………………………………...31 t
3.2.4 Limitations of Height Dependent Parameters……………………….....31
3.3 Surface Roughness Generation during Single Point
Diamond Turning…………………………………………………….………...32
3.3.1 Theoretical Surface Finish during Turning………………………….....32
3.3.2 Effects of Tool Feed Rate……………………………………………...34
3.3.3 Effects of Relative Vibration between the Tool and the Workpiece…..35
3.3.4 Material Induced Vibrations…………………………………………...36
3.4 Power Spectral Density (PSD)…………………………………………..……..36
3.4.1 Calculation of PSD…………………………………………….……….37
3.4.2 Parseval’s Theorem………………………………………………..…...38
3.4.3 Average PSD…………………………………………………………..38
3.5 Autocorrelation Analysis………………………………………………............38
3.6 Experimental Results………………………………………………………......39
3.6.1 Machining Details and Analysis……………………………….……....39 Contents v
3.6.2 Results and Discussion……………………………………….………..40
3.6.2.1 Power Spectral Density Analysis with Varying Tool Feed…..41
3.6.2.2 Identification of the Contributions of Different Effects to
the Surface Roughness…………………………………….…42
3.6.2.3 Autocorrelation Study………………………………….….….44
3.6.2.4 Averaging Algorithms for PSD……………………………....45
3.6.2.5 Effects of the Spindle Rotational Speed on Surface
Quality…………………………………………………….….46
3.7 Conclusions…………………………………………………………………….47

4 Quasi Absolute Testing of Rotationally Invariant Aspherics:
Simulation Studies 49
4.1 Absolute Test…………………………………………………………………..49
4.1.1 Three Position Test for Spheres……………………………………......50
4.1.2 Quasi Absolute Test of Aspherics: Measurement Principle…………....51
4.2 Combined Diffractive Optical Elements……………………………………….52
4.2.1 Calculation of the Aspheric Phase Function……………………….......53
4.2.2 Calculation of the Spherical Phase Function…………………………..54
4.2.3 Encoding the Two Phase Functions…………………………………....55
4.3 Design Considerations for the Combo-DOE : Simulation Studies…………….56
4.3.1 Sources of Error………………………………………………………..56
4.3.2 Consistency Test……………………………………………………….57
4.3.3 Relation between the Tilt Orientation of the DOE and the Offset
Direction of the Spherical Wave Front………………………………...57
4.3.4 Influence of the Tilt Amount of the DOE in the Presence of a Systematic
Error of the Setup………………………………………........................59
4.3.5 Matching Condition and Quasi Nature of the Procedure……………...60
4.4 Conclusions…………………………………………………………………….62

5 Quasi Absolute Testing of Rotationally Invariant Aspherics and
Toric Surfaces: Experimental Results 65
5.1 Experimental Setup…………………………………………………………….65
5.1.1 Twyman-Green Interferometer………………………………………...65 vi Contents
5.1.2 Combo-DOE…………………………………………………………...68
5.1.3 Specimen Under Test…………………………………………………..68
5.2 Interferometer’s Performance……………………………………………….....69
5.2.1 Interferometer Stability………………………………………………...69
5.2.1.1 Repeatability……………………………………………….....69
5.2.1.2 Reproducibility…………………………………………...…..70
5.2.1.3 Drift Analysis………………………………………………...70
5.2.2 Removal of Misalignment Aberrations………………………………...71
5.3 Quasi Absolute Measurement………………………………………….............73
5.3.1 Measurements with Striped and Superposed DOE…………………….73
5.3.2 Substrate Quality…………………………………………………..…...73
5.3.3 Disturbing Diffraction Orders………………………………………….74
5.3.4 Measurement with Optimized Striped DOEs………………………......75
5.3.5 Consistency Results with Different Striped DOEs………………….....75
5.4 N-Position Test………………………………………………………………...77
5.5 Quasi Absolute Test for Toric Surfaces………………………………………..79
5.5.1 Representation of the Toric Surface Under Test……………………....79
5.5.2 Measurement Techniques……………………………………………...80
5.5.2.1 Quasi Absolute Test by using Combo-DOE……………….....80
5.5.2.2 bination of a DOE and
Spherical Condenser………………………………….………81
5.5.3 Experimental Results…………………………………………………..82
5.5.3.1 Using Combo-DOE…………………………………………..82
5.5.3.2 bination of a DOE and Spherical Condenser……..83
5.6 Conclusions…………………………………………………….………………84

6 Conclusions and Future Scope 87
A Laser Lithography System 89

References 91

List ofFigures . 97

List of Tables 101


Zusammenfassung

Diese Dissertation ist das Ergebnis von Forschungsarbeiten, die bei der „Central
Scientific Instruments Organisation (CSIO)“, Chandigarh, Indien, und am Institut für
Optik, Information und Photonik (IOIP), Max-Planck-Forschungsgruppe, Universität
Erlangen, Deutschland, durchgeführt wurden. Ziel der Forschungsarbeiten war die
hochgenaue Fabrikation und Charakterisierung asphärischer Flächen. Asphärische
Flächen werden in optischen Systemen verwendet, um die Korrektur von Aberrationen zu
verbessern, oftmals sogar ohne zusätzliches Gewicht einzubringen oder die Abmessungen
des Systems zu vergrößern. Bedeutendes Hindernis für den Einsatz dieser Flächen sind
jedoch die schwierige Herstellung und die präzise Prüfung. Die vorliegende Arbeit
diskutiert die beiden folgenden haupts&