Digital Holographic Methods: Low Coherent Microscopy and Optical Trapping in Nano-Optics and Biomedi

1 Introduction 1

2 Theory 7

2.1 Basicprinciplesofholography....................... 7

2.1.1 Classicholography ......................... 8

2.1.2 Fourierholography ......................... 10

2.1.3 Digitalholography ......................... 12

2.1.4 Computergeneratedholograms .................. 12

2.1.5 Numerical reconstruction of digital holograms . . . . . . . . . . 14

2.2 Phasesshiftingreconstructionmethods . . . . . . . . . . . . . . . . . . 15

2.2.1 Temporalphaseshiftingmethod. . . . . . . . . . . . . . . . . . 16

2.2.2 Spatialphaseshiftingtechniques . . . . . . . . . . . . . . . . . 18

2.3 Numeric propagation of the complex object wave . . . . . . . . . . . . 20

2.3.1 Digitalholographicmicroscopy . . . . . . . . . . . . . . . . . . 21

2.4 Benefits of the Partially Spatial Coherence for DHM . . . . . . . . . . . 23

2.4.1 SpatialFrequencyFiltering .................... 23

2.4.2 MultipleRe ectionRemoval.................... 27

2.5 Typesofspatiallightmodulators ..................... 29

2.5.1 Di erentmethodsofaddressing . . . . . . . . . . . . . . . . . . 29

2.5.2 Digital micromirror devices and liquid crystal SLMs . . . . . . . 30

2.5.3 Light modulators as holographic elements . . . . . . . . . . . . 32

2.6 Micromanipulationwithlight ....................... 34

2.6.1 Observationofthemomentum................... 35

2.6.2 Geometric optical explanation -Mie regime . . . . . . . . . . . 37

2.6.3 Wave optical analysis -Rayleigh regime . . . . . . . . . . . . . . 39

2.6.4 Features and in uences of optical traps . . . . . . . . . . . . . . 39

2.6.5 Algorithms for generating optical trap patterns in Fourier plane 42

2.6.6 Calibrationofthetrapforces ................... 43

2.7 Dynamic holography for optical micromanipulation . . . . . . . . . . . 44

2.8 Applicationsofopticaltweezers ...................... 46

2.9 Di ractive and non-di ractive beam types . . . . . . . . . . . . . . . . 46

2.9.1 Gaussianbeams........................... 47

2.9.2 Besselbeams ............................ 48

2.9.3 Superpositionofbesselbeams................... 51

2.9.4 Laguerre............................... 56

2.9.5 Mathieubeams ........................... 57

2.9.6 Airybeams ............................. 59

2.10 Direct laser writing with two-photon polymerization . . . . . . . . . . . 60

3 State of the art                                                                                                                    63

3.1    Systemsforopticaltraps.......................... 63

3.2    Imaging by means of digital holographic quantitative phase contrast methods................................... 64

3.3    Directlaserwritinglithography ...................... 65

3.4    Multifunctional combined microscopy systems . . . . . . . . . . . . . . 67

3.5    OverviewofHOT-systemsinresearch................... 67

4 Experimental investigations                                                                                                  69

4.0.1     Introduction -Objectives and Justifications . . . . . . . . . . . 69

4.1    Subsequent digital holographic focussing . . . . . . . . . . . . . . . . . 70

4.1.1     Autofocus strategies and application to phase distributions . . . 70

4.1.2     Haltonsampling .......................... 74

4.1.3     Experimentalinvestigations .................... 76

4.2    Digital Holographic Microscopy with partially coherent light sources . . 78

4.2.1     Optical Setups and Digital Holographic Reconstruction . . . . . 79

4.2.2     CoherentNoiseRemoval...................... 80

4.2.3     Experimental Demonstrations and Applications . . . . . . . . . 81 BiomedicalApplications ...................... 81 StudyofCellCultures ....................... 81

4.2.4     Adaptionofreconstructionmethods. . . . . . . . . . . . . . . . 82 Reconstruction with consideration of spectrum . . . . . . . . . . 83 Experimentalinvestigations .................... 85

4.2.5     Tayloringofcoherencelength ................... 88<

4.3    Application of atomic force microscopy in NMM-1 as reference system . 93

4.3.1     Introduction............................. 94

4.3.2     Propertiesofapplieddevices.................... 95 Nanopositioning and nanomeasuring machine . . . . . . . . . . 95 Integration of AFM-sensor into the NMM-1 . . . . . . . . . . . 96

4.3.3     Calibration ............................. 97
Demands .............................. 97
Nano-andmicroroughness..................... 98
Measurementstrategy ....................... 99
Correctionofverticaldrift..................... 99

4.3.4     Experimentalresults ........................103 Measurements on calibration gratings . . . . . . . . . . . . . . . 103 Applicationonopticalsurfaces ..................105

4.4    SimulationanddesignofHOTsetups...................107

4.4.1     SystemRequirements........................107

4.4.2     Considerationsonopticaldesign. . . . . . . . . . . . . . . . . . 108

4.4.3     Investigations on experimental optical system . . . . . . . . . . 110 Moduleforopticaltweezers ....................111 Digital holographic phase contrast microscopy . . . . . . . . . . 115 Overallsystem ...........................115

4.4.4     Opticalsimulationwithraytracing . . . . . . . . . . . . . . . . 118

4.4.5     Optical properties of the calculated system . . . . . . . . . . . . 118 Tolerance analysis and sensitivity of optical setup . . . . . . . . 120

4.4.6     Optomechanicalsetup .......................122

4.5 CharacterizationoftheSLM........................124

4.5.1     Calibrationoflinearphaseshift . . . . . . . . . . . . . . . . . . 125

4.5.2     Correction of the system inherent wavefront aberrations . . . . . 127

4.5.3     Addressing and reconstruction of holograms . . . . . . . . . . . 129

4.6 Characterizationoftheoverallsystem . . . . . . . . . . . . . . . . . . . 131

4.6.1     Wavefront based system optimization . . . . . . . . . . . . . . . 131

4.6.2     Generation of variable intensity patterns in the object plane . . 134

4.6.3     Micromanipulation of microspheres . . . . . . . . . . . . . . . . 135

4.6.4     Determinationofthetrapforce . . . . . . . . . . . . . . . . . . 137

4.6.5     Imaging of biological cells using quantitative phase-contrast . . 138

4.6.6     Conclusionsandoutlook......................139

4.7 Integrationinnanopositioningsystem . . . . . . . . . . . . . . . . . . 141

4.7.1     Nano coordinate measuring machine . . . . . . . . . . . . . . . 142

4.7.2     Experimental investigations on sensor integration . . . . . . . . 142

4.8 Realisation and illustration of beam configurations . . . . . . . . . . . . 143

4.8.1     Bessel ................................144

4.8.2     Mathieu...............................145

4.8.3     Laguerre...............................149

4.8.4     Airy .................................150

4.9 Application of trapping patterns and optical torque . . . . . . . . . . . 151

4.10HOT-DHM-combination ..........................153

4.11 Direct laser writing with modified HOT-setup . . . . . . . . . . . . . . 164

4.12 Nanoantennaassistedtrapping . . . . . . . . . . . . . . . . . . . . . . . 167

5 Summary                                                                                                                          171

6 Prospects                                                                                                                         173

Bibliography                                                                                                                        178

Appendix                                                                                                                             204

A.1 Developedsoftware.............................204

A.1.1     ImplementedsoftwareforDHM..................204

A.1.2     ImplementedsoftwareforHOTs . . . . . . . . . . . . . . . . . . 207

A.1.3     OpenGL Code for hologram rendering . . . . . . . . . . . . . . 211

A.1.4     Graphical user interface for complex beam configurations . . . . 212

A.1.5     Extension of HOT-software for multifocal direct laser writing . . 214 Slicer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214

A.2 Technicalinformation............................217

A.2.1     Optic simulation: System data of HOT-module . . . . . . . . . 217

A.2.2     Callibration using a wavefront sensor . . . . . . . . . . . . . . . 217

A.2.3     Interferometrically determined form error of SLM . . . . . . . . 219

A.2.4     Photosofmoduleforopticaltrapping. . . . . . . . . . . . . . . 220

B.1 Specificationsofutilizedsystems ......................221

B.1.1     Supercontinuumlightsource ...................221

B.1.2     SpatialLightModulator(SLM) . . . . . . . . . . . . . . . . . . 225

B.1.3     Spectrometer ............................225

B.1.4     Lightpowermeters.........................225

B.1.5     Technical specifications of applied cameras . . . . . . . . . . . . 226

B.1.6     Piezoactuator ............................227

B.1.7     Resolutiontestchart........................227

B.1.8     Ultra-brightlightemittingdiodes . . . . . . . . . . . . . . . . . 228

B.1.9     Lambertemitters..........................230

B.1.10 CIE-classification of light sources . . . . . . . . . . . . . . . . . 230

B.2 Theoreticalbasics..............................231

B.2.1     Holographythroughoutthetime . . . . . . . . . . . . . . . . . . 231

B.2.2     Maxwellequations .........................233

B.3 WaveOptics.................................233

B.3.1     Fouriertransformandconvolution . . . . . . . . . . . . . . . . . 234

B.3.2     Spatial frequency transfer function and spatial impulse response ofpropagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234

B.3.3     ExamplesofFresneldi raction . . . . . . . . . . . . . . . . . . 236

B.3.4     Fraunhoferdi raction .......................237

B.3.5     Fourier transforming property of ideal lenses . . . . . . . . . . . 240

B.3.6     Synopsis of further holographic reconstruction algorithms . . . . 242

B.3.7     Mathematical approximation of the refractive index . . . . . . . 243

B.3.8     Zernikepolynoms..........................244

B.3.9     ForbesPolynomials.........................247

B.3.10Gaussianoptics . . . . . . . . . . . . . . . . . . . . . . . . . . . 250

List of abbreviations                                                                                                            253

List of Figures                                                                                                                     254

List of Tables                                                                                                                       258