What is dithienylethene used for?

Progress reports VDI Dipl.-Ing. (FH) Robert Kowarsch, Clausthal-Zellerfeld No. 1270 Measurement, control and regulation technology series 8 Heterodyne laser interferometry using phase-coupled semiconductor lasers and absorption modulation nanoscopy for Gigahertz vibration measurement technology K ow ar sc h V ib ro m et er -M ik ro sk op for GH z- M ik ro sy st em e V ib ro m et er -Micro sk op r GH z- M ik ro sy st em e series 88 · N o. 1 27 0 12 70 T he series of progress reports VDI: 1 Construction technology / machine elements 2 Production technology 3 Process technology 4 Civil engineering 5 Basic materials / plastics 6 Energy technology 7 Flow technology 8 Measurement, control and regulation technology 9 Electronics / micro and nanotechnology 10 Computer science / communication 11 Vibration technology 12 Transport technology / vehicle technology 13 Conveyor technology / logistics 14 Agricultural technology / food technology 15 Environmental technology 16 Technology and economy 17 Biotechnology / medical technology 18 Mechanics / fracture mechanics 19 Heat technology / refrigeration technology 20 Computer-aided processes (CAD, CAM, CAE CAQ, CIM.... .) 21 Electrical engineering 22 Human-machine systems 23 Technical building equipment ISBN 978-3-18-527008-6 Cyan Magenta Black Preflight Lx3 on January 18, 2021 | 15:04:28 | 350 mm x 250 mm L_ 21 00 48 _R ei he _0 8_ 12 70 _U m sc hl ag .p df · P age 1 L_210048_Reihe_08_1270_Umschlag.pdf · Page 1 1 1 More opinion. More orientation. Learn more. Essential information on new technologies and markets. This is what VDI nachrichten, Germany's opinion-forming weekly newspaper on technology, business and society, offers engineers. Subscribe and read immediately. Thursday evenings as an e-paper or Friday as a newspaper. Subscribe now: Reader Service VDI nachrichten, 65341 Eltville Phone: +49 6123 9238-201, Fax: +49 6123 9238-244, [email protected] Engineers always want to know everything exactly. How about an e-paper or newspaper subscription? www.vdi-nachrichten.com/abo Cyan Magenta Yellow Black Preflight Lx3 on January 18, 2021 | 15:04:29 | 350 mm x 250 mm L_ 21 00 48 _R ei he _0 8_ 12 70 _U m sc hl ag .p df · P age 2 L_210048_Reihe_08_1270_Umschlag.pdf · Page 2 2 2 Heterodyne laser interferometry using phase-coupled semiconductor lasers and absorption modulation nanoscopy for the Gigahertz-Schwingungsmesstechnik Dissertation to obtain the doctoral degree in engineering presented by Dipl.-Ing. (FH) Robert Kowarsch from Ellwangen an der Jagst approved by the Faculty of Mathematics / Computer Science and Mechanical Engineering at Clausthal University of Technology Oral Examination Day August 27, 2020 D 104 Dean: Prof. Dr.-Ing. Volker Wesling Chairman of the doctoral committee: Prof. Dr. rer. nat. Alfred Weber Supervisor: Prof. Dr.-Ing. Christian Rembe Reviewer: Prof. Dr.-Ing. habil. Andreas Fischer L_210048_Reihe_08_1270_Innentitel.indd 1 18.01.2021 15:04:41 Heterodyne laser interferometry using phase-coupled semiconductor lasers and absorption modulation nanoscopy for Gigahertz vibration measurement technology Dipl.-Ing. (FH) Robert Kowarsch, Clausthal-Zellerfeld Measurement, Control and Regulation Technology No. 1270 Series 8 Progress Reports VDI Black Preflight Lx3 on January 18, 2021 | 15:05:18 | 148 mm x 210 mm L_ 21 00 48 _R ei he _0 8_ 12 70 _I nn en tit el .p df · S ei te 1 L_210048_Reihe_08_1270_Innentitel.pdf · Page 1 1 1 L_210048_Reihe_08_1270_Innentitel.indd 2 18.01.2021 ©. 15:04:41 VDI Verlag GmbH · Düsseldorf 2021 All rights reserved, including those of partial reprinting, partial or complete reproduction (photocopy, microcopy), storage in data processing systems, on the Internet and translation. Printed as a manuscript. Printed in Germany. ISSN 0178-9546 ISBN 978-3-18-527008-6 Kowarsch, Robert Heterodyne laser interferometry by means of phase-coupled semiconductor lasers and absorption modulation nanoscopy for Gigahertz vibration measurement technology Fortschr.-Ber. VDI series 08 No. 1270. Düsseldorf: VDI Verlag 2021. 200 pages, 76 pictures, 18 tables. ISBN 978-3-18-527008-6 ISSN 0178-9546, € 71.00 / VDI member price € 63.90. For documentation: Optical measurement technology - laser measurement technology - laser interferometry - vibrometry - vibration measurement technology - optical phase-locked loop - heterodyne method - superresolution microscopy - nanoscopy - absorbance modulation This dissertation is aimed at engineers and scientists in the field of optical vibration measurement technology and high-resolution microscopy (nanoscopy). It deals with the modeling and simulation of two central challenges in the device technology of heterodyne laser interferometry for vibration measurement on microsystems up to 6 GHz. On the one hand, the effect of the gigahertz carrier generation by means of phase-coupled lasers in an optoelectronic phase-locked loop on the resolution for oscillation amplitudes in the sub-picometer range is theoretically investigated and demonstrated in experiments. On the other hand, by means of reversibly optically switchable absorbance in a photochromic thin film, a method for local high resolution beyond the diffraction limit is investigated for reflection microscopy. Based on the findings, approximation formulas and instructions for use are given. Bibliographic information from the Deutsche Bibliothek The Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliographie; detailed bibliographical data are available on the Internet at www.dnb.de. Bibliographic information published by the Deutsche Bibliothek (German National Library) The Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliographie (German National Bibliography); detailed bibliographic data is available via Internet at www.dnb.de. D 104 Black Preflight Lx3 on January 18, 2021 | 15:05:19 | 148 mm x 210 mm L_ 21 00 48 _R ei he _0 8_ 12 70 _I nn en tit el .p df · S ei te 2 L_210048_Reihe_08_1270_Innentitel.pdf · Page 2 2 2 Acknowledgments This dissertation was written while I was working as a research assistant at Metrology Chair at the Institute for Electrical Information Technology at Clausthal University of Technology. During this time, I had the honor and pleasure of working with a large number of excellent researchers and people, without their inspiration, their enthusiasm for discussion and friendship, the doctoral project would have been far less pleasant and goal-oriented. Special thanks go to the institute director and professor of measurement technology, Prof. Dr.-Ing. Christian Rembe for giving me the opportunity and the confidence to become part of his working group. He has looked after my work through his extensive experience with valuable impulses and constant new inspiration, while always giving me the freedom to develop myself personally and professionally. I also thank Prof. Dr.-Ing. habil. Andreas Fischer from the University of Bremen for taking over the lecture. Only the discourse and the cooperation with many scientists allowed this interdisciplinary work to mature. I would like to thank Dr. Claudia Geisler and Prof. Dr. Alexander Egner from the Institute for Nanophotonics Göttingen. For the deep insights into photochemistry and physics, I thank Prof. Dr. Andreas Schmidt from the Institute for Organic Chemistry and Prof. Dr. Jörg Adams from the Institute for Physical Chemistry and for the discussions about coating technology Prof. Dr. Wolfgang Maus-Friedrichs and Prof. Dr. Sebastian Dahle. My thanks for the measurements on oscillating quartz microbalances go to the working group led by Prof. Dr. Diethelm Johannsmann, especially Frederick Meyer. Another big thank you goes to Prof. Dr. Hyuck Choo and Dr. Hyunjun Cho from Caltech, whom I was able to support with measurements on his energy harvester for voice stimulation, also for the hospitality during my visit to Pasadena. I would like to thank all scientists at the Institute for Electrical Information Technology, especially Dr.-Ing. Georg Bauer and fellow campaigners from the very beginning Xiaodong Cao and Laura Mignanelli. Furthermore, I would like to thank the institute workshops for the uncomplicated cooperation in the creation of mechanics and electrical circuits. The scope of the present work would not have been possible without the eager cooperation of some intelligent students in the context of their thesis, project work or their research internship. Last but not least, I would like to thank my entire family for supporting my doctoral project, especially my wife Franziska for her love and the daily mental and emotional support and my two wonderful children, Charlotte and Johannes, who enrich my life with their joy and energy . III If you can not measure it, you can not improve it. (Lord Kelvin, 1824 - 1907) IV Contents List of Symbols IX Abstract XIX 1 Introduction 1 1.1 Motivation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Approach to Gigahertz Carrier Generation. . . . . . . . . . . . . . . . . . 6 1.3 Nanoscopy approach for technical surfaces. . . . . . . . . . . . . . 7 1.4 Scientific hypotheses. . . . . . . . . . . . . . . . . . . . . . . 10 1.5 Structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2 State of the art 13 2.1 Laser interferometry for high-frequency vibration measurement. . . . . . 13 2.1.1 Acousto-optical carrier generation. . . . . . . . . . . . . . . . . . 14 2.1.2 Extension of the measurement bandwidth. . . . . . . . . . . . . . . . . . 16 2.1.3 Electro-optical carrier generation. . . . . . . . . . . . . . . . . 17 2.1.4 Carrier generation using a two-wavelength laser. . . . . . . . 17 2.1.5 Carrier generation by means of frequency difference control. . . . . . . 18 2.1.6 Models for differential phase noise in the interferometer. . . . 18 2.1.7 Conclusion on the state of the art in carrier production. . . . . 19 2.2 Nanoscopy using absorbance modulation. . . . . . . . . . . . . . . . . 19 2.2.1 Realizable photochromic concentrations and layer thicknesses. 20 2.2.2 Models and studies on absorbance modulation. . . . . . . . . 21 2.2.3 Conclusion on the state of the art in high resolution using absorbance modulation. . . . . . . . . . . . . . . . . . . 22 3 Heterodyne interferometry using frequency difference control 23 3.1 Laser interferometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.1.1 Heterodyne method and bandwidth requirements. . . . . . . 25 3.1.2 Effect of non-linearity on the bandwidth requirement. 28 3.1.3 Phase noise and line width of the laser source. . . . . . . . 31 3.1.4 Signal processing. . . . . . . . . . . . . . . . . . . . . . . . . 33 V Contents 3.2 Frequency difference control for carrier generation. . . . . . . . . . . . . 33 3.2.1 Nonlinear modeling. . . . . . . . . . . . . . . . . . . . . 34 3.2.2 Small-signal modeling in the operating point. . . . . . . . . . . . 36 3.2.3 Stability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.2.4 Stop and catch area. . . . . . . . . . . . . . . . . . . . . . . 38 3.2.5 Flexible and dynamic choice of the carrier frequency. . . . . . . . 39 4 Amplitude resolution of an interferometer with phase-coupled lasers 40 4.1 Noise-equivalent amplitude resolution. . . . . . . . . . . . . . . . . 40 4.2 Model of the differential phase noise. . . . . . . . . . . . . . . . . . 43 4.2.1 Correlation of noise between differential phase and interference signal. . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.2.2 Variance of the differential phase noise. . . . . . . . . . . . . . 45 4.3 Model validation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 4.3.1 Two free-running lasers in the interferometer. . . . . . . . . . . . . 47 4.3.2 Two ideally coupled lasers in the interferometer. . . . . . . . . . 47 4.4 Differential phase noise from phase-locked lasers. . . . . . . . 48 4.5 Numerical simulations with discussion. . . . . . . . . . . . . . . . . 49 4.5.1 Ideal OPLL with a finite control bandwidth. . . . . . . . . . . 50 4.5.2 OPLL with finite gain. . . . . . . . . . . . . . . . . 51 4.5.3 Beam collapse. . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.5.4 Transition to shot noise-limited detection. . . . . . . . . 52 4.5.5 Transition to intensity noise-limited detection. . . . . . . 54 5 Spatial resolution of microscopy and absorbance modulation 56 5.1 Diffraction-limited spatial resolution. . . . . . . . . . . . . . . . . . . . . 56 5.1.1 Spatial resolution of optical microscopy. . . . . . . . . . . . . 56 5.1.2 Spatial resolving power of an LDV microscope. . . . . . . . . 58 5.2 Modeling a reflection nanoscope by means of absorbance modulation 64 5.2.1 Photophysical parameters of the photochrome BTE-I. . . . . 65 5.2.2 Rate equation for photokinetics. . . . . . . . . . . . . . . . . 66 5.2.3 Absorption and absorbance. . . . . . . . . . . . . . . . . . . . . 67 5.2.4 Analytical approximation to photokinetics. . . . . . . . . . . . . . 68 5.2.5 Interface reflection at the AML. . . . . . . . . . . . . . . . . 69 5.3 Evaluation criteria for AMI nanoscopy. . . . . . . . . . . . . . . . . 71 5.3.1 Transmission contrast. . . . . . . . . . . . . . . . . . . . . . . 71 5.3.2 Thickness of the absorbance modulation layer. . . . . . . . . . . . . 71 5.3.3 Reflection contrast by AMI. . . . . . . . . . . . . . . . . . . 73 5.3.4 Relationship between signal and interference. . . . . . . . . . . . . . . . . 75 VI Contents 6 Simulation of a reflection nanoscope by means of absorbance modulation 76 6.1 Implementation of the simulation model. . . . . . . . . . . . . . . . . 76 6.1.1 Photo stationaryity and termination criterion. . . . . . . . . . . . 78 6.1.2 Post-processing of the simulation data. . . . . . . . . . . . . . 80 6.2 Findings from optical radiation simulation. . . . . . . . . . . . . . 80 6.2.1 Absorbance distribution and resulting AMI point spread. . . . . 81 6.2.2 Increasing the spatial resolution. . . . . . . . . . . . . . . . . . . 82 6.2.3 Overall transmission and background interference. . . . . . 87 6.2.4 Photokinetics in the AML. . . . . . . . . . . . . . . . . . . . . 88 6.3 Wave-optical expansion of the model. . . . . . . . . . . . . . . . . 91 6.4 Simulation results of the parameter study. . . . . . . . . . . . . . . . 93 6.5 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 6.6 Use of absorbance modulation in laser Doppler vibrometry 100 6.6.1 Special requirements for AML. . . . . . . . . . . . . . 100 6.6.2 Mass coverage of the vibrating component by AML. . . . 100 6.6.3 Energy input into the AML. . . . . . . . . . . . . . . . . . . . . 102 7 Experimental setup of the laser Doppler vibrometer microscope 104 7.1 Optical setup of the LDV microscope. . . . . . . . . . . . . . . . . . 104 7.1.1 Structure of the laser Doppler vibrometer. . . . . . . . . . . . . . 104 7.1.2 Photo detectors. . . . . . . . . . . . . . . . . . . . . . . . . . 107 7.1.3 Structure of the microscope. . . . . . . . . . . . . . . . . . . . . . . 110 7.1.4 Coupling in a commercial LDV. . . . . . . . . . . . . . 112 7.2 Optoelectronic phase locked loop. . . . . . . . . . . . . . . . . . . 113 7.2.1 Tunable slave laser. . . . . . . . . . . . . . . . . . . 113 7.2.2 Master laser. . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 7.2.3 Phase detection. . . . . . . . . . . . . . . . . . . . . . . . . . 118 7.2.4 Loop filter. . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 7.2.5 Procedure for locking the phase control. . . . . . . . . . . 122 7.3 Software for automated LDV measurement. . . . . . . . . . . . . . . 123 7.4 Signal acquisition and processing. . . . . . . . . . . . . . . . . . . . . 125 7.4.1 Full modulation on the analog-digital converter. . . . . . . . . . . 125 7.4.2 Demodulation and reconstruction of the waveform. . . . . . . 125 7.5 Amplitude resolution of the configurations of the experimental setup. . 127 7.5.1 LDV amplitude resolution through quantization noise. . . . 128 7.5.2 Optimizing the reference performance. . . . . . . . . . . . . . . . . 128 7.5.3 Data volume and measurement time. . . . . . . . . . . . . . . . . . . . 129 VII Contents 8 Experiments 133 8.1 Demonstration of a Vibration Measurement. . . . . . . . . . . . . . . . 133 8.2 Vibration measurement on a SAW filter. . . . . . . . . . . . . . . . 135 8.2.1 Measurement on 600MHz carriers with Si photodetectors. . . . . . 136 8.2.2 Measurement on 2.4 GHz carriers with GaAs photodetectors. . . . 137 8.2.3 Grid measurement of the surface wave. . . . . . . . . . . . . . . 140 8.2.4 Measurement of electromechanical properties. . . . . . . . . . . 143 8.3 Flexural vibrations on quartz oscillating microbalances. . . . . . . . . . . . 145 8.3.1 Grid measurement of the deflection shapes for the harmonics. . . . 146 8.3.2 Grid measurement of the anharmonic sidebands. . . . . . . . 149 9 Summary and Outlook 151 9.1 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 9.2 Outlook. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 Appendix 158 A Details on Absorbance Modulation Microscopy 158 A.1 Modeling the diffraction-limited foci. . . . . . . . . . . . . . 158 A.1.1 Approximation using Laguerre-Gaussian modes. . . . . . . . . . . . . 158 A.1.2 Parabolic approximations in the center. . . . . . . . . . . . . . . 161 A.2 Estimation of the switching cycles. . . . . . . . . . . . . . . . . . . . . . . 161 B Details on the experimental setup 163 B.1 Measurement volume. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 B.2 Common-mode rejection in the interferometer. . . . . . . . . . . . . . . 164 B.2.1 Balanced photodetector. . . . . . . . . . . . . . . . . . . 164 B.2.2 Quality of the power division at the beam splitter. . . . . . . . . . . . 165 B.2.3 Alignment of the gallium arsenide photodetectors. . . . . . . . 166 B.3 Detailed component lists. . . . . . . . . . . . . . . . . . . . . . . . . . 167 Bibliography 169 VIII List of Symbols Constants? 0 Electric field constant. . . . . . . . . . . . 8.8541878128 · 10−12As / (Vm)? 0 Magnetic field constant. . . . . . . . . . . . . 1.25663706212 · 10−6N / A2 j Imaginary unit. . . . . . . . . . . . . . . . . . . . . . . . . . . . j = √ −1? 0 speed of light in a vacuum. . . . . . . . . . . . . 2.99792458 · 108m / s? Elemental charge. . . . . . . . . . . . . . . . . . . . . . 1.602176634 · 10−19C ℎ Planck’s quantum of action. . . . . . . . . . . . . . 6.62607015 1034 J s? B Boltzmann constant. . . . . . . . . . . . . . . . . . . 1.380649 10−23 J / K? A Avogadro's constant. . . . . . . . . . . . . . . . . . 6.02214076 · 1023mol − 1 Latin symbols and formula signs? Absorbance (definition in (5.27)). . . . . . . . . . . . . . . . . . . . . . . . . -? Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m2? (?) Amplitude response? ? Absorption coefficient at wavelength? . . . . . . . . . . . . . . . . m − 1? ? Coefficient? -th order of a polynomial? Bandwidth of a resonance. . . . . . . . . . . . . . . . . . . . . . . . . . . Hz CNR Carrier-to-Noise Ratio. . . . . . . . . . . . - CSR carrier-to-sideband ratio. . . . . . . - CT transmission contrast (definition in (5.35))'Transmission Contrast'). . . . . . . . . . . . . . . . . . . . . . . . . . -? I concentration of photochromes in state I. . . . . . . . . . . . . . . m − 3? tot total concentration of the (active) photochromes. . . . . . . . . . . . . . m − 3? amb speed of light of the (surrounding) medium. . . . . . . . . . . . . . m / s? Layer thickness of the AML. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m? Electric field strength. . . . . . . . . . . . . . . . . . . . . . . . . . . . V / m IX List of symbols? Frequency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hz? (?) Transfer function of the loop filter? 0 constant transfer factor? See also sampling rate. . . . . . . . . . . . . . . . . . . . . . . . . s − 1? B detector bandwidth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hz? L control bandwidth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hz? (?) Transfer function of the open control loop? (?) Transfer function of the control loop? Intensity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . W / m2? Electrical current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A? ,? ,? ,? ,? Index, numerator, order (whole number). . . . . . . . . . . . . . . . . . . . . . . -? Complex compliance. . . . . . . . . . . . . . . . . . . . . . . . . . . m / N? Stationary transfer factor, constant, gain? Number of quantization levels. . . . . . . . . . . . . . . . . . . . . . . Bit? Wavenumber. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m − 1? B Rate of thermal decay from state B. . . . . . . . . . . . . . s − 1 ℓcoh coherence length of a laser source (definition in (3.24)). . . . . . . . . . . . m? Length, distance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m? Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kg? vib modulation index of the phase modulation due to the laser Doppler effect (definition in (3.9)). . . . . . . . . . . . . . . . . -? PhC Molar mass of the photochrome. . . . . . . . . . . . . . . . . . . . . . kg / mol NA Numerical aperture of the microscope objective. . . . . . . . . . . . . . . . . - NEP ′ spectral density of the noise-equivalent (optical) radiated power (“Noise-Equivalent Power”). . . . . . . . . . W / √ Hz NF Noise Figure. . . . . . . . . . . . . . . . . . . . . . . . -? (Sample) number. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -? see also memory depth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -? amb refractive index of the (surrounding) medium. . . . . . . . . . . . . . . . . . - OPD optical path difference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m PR power ratio. . . . . . . . . . . . . . . . . . . . - X List of symbols PRsat Characteristic saturation power ratio of an AMI nanoscope (definition in (6.15)). . . . . . . . . . . . . . . . . . . -? Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . W? ? Partial autocorrelation function of size? RBW resolution bandwidth. . . . . . . . . . . . Hz RIN ′ Spectral power density of the relative intensity noise (definition in (7.2)). . . . . . . . . . . Hz − 1 r position vector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m? Reflectance (definition in (5.34)). . . . . . . . . . . . . . . . . . . . . . . -? Radius or radial coordinate. . . . . . . . . . . . . . . . . . . . . . . . . m? ,? ,? Cylindrical coordinates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m? ? Size autocorrelation function? ? ? ? Cross-correlation function of the quantities? and ? ? (Current) sensitivity of the photodetector. . . . . . . . . . . . . . . . A / W SBR Signal-to-Background Ratio (definition in (5.43)). . . . . . . . . . . . . . . . . . . . . . - SNR signal-to-noise ratio. . . . . . . . . . . . - SR splitting ratio of the optical power at a beam splitter (splitting ratio). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -? Complex frequency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . s − 1? Path or path length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m? ? Spectral (auto) power density of size? . . . . . . . . . . . . . . [? ] 2 / Hz? 11 Input reflection factor of a two-port. . . . . . . . . . . . . . . . . . . . -? 21 Forward transmission factor of a two-port. . . . . . . . . . . . . . . . . . -? ? ? Cross spectral power density of sizes? and ? . . . . . . . . . . [? ] [? ] / Hz? Absolute temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K? Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . s? AML transmittance of the AML at the measurement wavelength? m. . . . . . . . . . . -? Constant duration or period. . . . . . . . . . . . . . . . . . . . . . . . . . s? LDV interferometer delay. . . . . . . . . . . . . . . . . . . . . . . . . . . . s? L loop delay. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . s? stat photostationary duration. . . . . . . . . . . . . . . . . . . . . . . . . . . . s XI symbol directory? Electric voltage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V? Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m3? Speed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m / s? Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J? Radius of a laser beam. . . . . . . . . . . . . . . . . . . . . . . . . . . . m? PhC mass fraction of the photochrome. . . . . . . . . . . . . . . . . . . . . . . . . . -? ,? ,? Cartesian space coordinates. . . . . . . . . . . . . . . . . . . . . . . . . m? (?) Electrical time signal at the entrance? (?) Electrical time signal at output Z? Zernike moment of the OSA / ANSI index '? . . . . . . . . . . . . . . . . . . . . -? Electrical impedance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ω? acoustical impedance. . . . . . . . . . . . . . . . . . . . . . . . . . . . Ns / m Greek symbols and formula signs? Relative measurement error. . . . . . . . . . . . . . . . . . . . . . . . . . . . . -? eff Effectiveness of the performance ratio over the AML thickness (definition in (6.11)). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -? Reproduction scale. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -? AB Concentration ratio of the photochromes in state A to B (definition in (6.8)). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - Γ Adjustment factor for the theoretical saturation power ratio PRsat to the simulation results (definition in (6.15)). . . . . . . . . . . -? Optimization factor of the product of the concentration and atomic absorption cross-sections of a target photochrome for AMI related to BTE-I (definition in (5.37)). . . . . . . . . . . . . . . . . . . . . . . . . - Δ? Laser line width. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hz Δ? Difference phase. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . rad Δ? Half width of a point spread. . . . . . . . . . . . . . . . . . . . . . . . m Δ? R depth of field. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m? ? I atomic absorption cross-section at the wavelength? for state I. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m2? Propagation angle to the surface normal. . . . . . . . . . . . . . . . rad XII symbol directory? I → J transition probability from state I to state J. . . . . . . . -? Polar angle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . wheel? Temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ∘C? Factor of the increase in spatial resolution in relation to the diffraction limit (definition in (6.4)). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - Λ Acoustic wavelength. . . . . . . . . . . . . . . . . . . . . . . . . . . . . m? Wavelength of the optical radiation. . . . . . . . . . . . . . . . . . . . . . m? Frequency of a source. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hz? P Poisson's number. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -? Factor of the additional noise of an avalanche photodetection. . . . . . . . . . -? Phase argument. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . wheel? (Mass) density. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kg / m3? Reflection factor of the amplitude (definition in (5.32)). . . . . . . . . . . . . -? ? I → J interaction cross-section at the wavelength? for the transition between states I and J. . . . . . . . . . . . . . . . . . . . . . . . m2? ? Standard deviation of size? ? Delay or postponement. . . . . . . . . . . . . . . . . . . . . . . . . s? Time constant of the process. . . . . . . . . . . . . . . . . . . . . . . . . . . s Φ auxiliary variable (difference between the accumulated difference phases). . . . . . . . . . wheel? Photon flux density. . . . . . . . . . . . . . . . . . . . . . . . . . . . m − 2 s − 1? Phase. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . wheel? Interference efficiency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -? Angular frequency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . s − 1 Indices A The basic state of the photochrome pertaining to a The activation beam pertaining to Airy Des Airy disc acoustically amb pertaining to the environment AMI The absorbance modulation imaging pertaining to XIII List of symbols AML The absorbance modulation layer pertaining to B The state of the Photochromes after the photoreaction pertaining to bal When using balanced photodetectors BB In the baseband c Pertaining to the carrier D At the location of the photodetector det The detection process pertaining to effective Effective single When using a single photodetector el Electrical est Estimated exc Excited for Free-running hold In the holding area of ​​the phase-locked loop I First order in incoming kin (Photo-) kinetic L The control loop regarding LDV The laser Doppler vibrometer concerning LO The local oscillator concerning lock In the regulated / steady state m the measuring st rahl concerning M the master laser concerning max maxmalwert mes the measuring process concerning min minimum value mix the mixing process concerning mod the modulation input of the slave laser concerning ne noise equivalent (engl. 'Noise Equivalent') P A pole of the transfer function relating to XIV list of symbols Ph Related to photons PhC The photochromic relating to PN Phase noise r The reference beam relating to ref Reference relax The relaxation oscillation relating to RINlim Intensity noise-limited (Intensity -Noise limited ') S Concerning the slave laser sa Concerning sampling sat Saturated SN Shot noise SNlim Shot noise limited stat Im photostationary equilibrium, static, stationary str disturbance or parasitic sub The substrate regarding T transversal th thermal TIV transimpedance amplifier tot total, total tw traveling acoustic wave vib The oscillation concerning Z concerning a zero point of the transfer function (engl . 'Zero') Abbreviations A Stable ground state of the photochrome (open ring structure of a BTE) B State of the photochrome after the Pho toreaktion (closed ring structure of a BTE) S0 ground state of a fluorophore S1 excited state of a fluorophore? Acoustic longitudinal mode? Acoustic shear mode XV Symbol index AB Aperture diaphragm AC Alternating current ADU Analog-digital converter or converter AMI Absorbance-Modulation Imaging AML Absorbance-Modulation Layer (Eng. 'Absorbance-Modulation Layer') AMOL Eng. 'Absorbance-Modulation Optical Lithography' APP Anamorphic pair of prisms AU In relation to the diameter of the Airy disk ('Airy Unit') BAW Bulk Acoustic Wave ') BPF bandpass filter BTE 1,2-bis (thienyl) ethene BTE-I 1,2-bis (5,5'-dimethyl-2,2'-bithiophen-yl) perfluorocyclopent-1-ene CCO current-controlled oscillator ( 'Current-Controlled Oscillator') DBR 'Distributed Bragg Reflector' DC Direct Current DSO Digital Storage Oscilloscope EM Electromagnetic FI Faraday Isolator FK Fiber Collimator HF High Frequency HWP Half-wave plate I / Q In-phase / Quadrature IDT Interdigital Transducer Ir Iris Kon Condenso r L lens LB pinhole LD laser diode LDV laser Doppler vibrometer LED light emitting diode (engl. 'Light-Emitting Diode') XVI List of symbols LO Local oscillator LP Long pass MEMS Microelectromechanical system, NCO Numerically-controlled oscillator NF Low frequency OPLL Optoelectronic phase-locked loop Optical phase-lock loop ') PD photodetector PE Peltier element PIN' Positive Intrinsic Negative 'PM-SMF Polarization-maintaining singlemode fiber PMT Photomultiplier (' Photomultiplier Tube ') PP Plane-parallel plate PSD Spectral power density (English' Power Spectral Density ') PSF point spread function (point spread function) PST polarizing beam splitter QCM quartz crystal micro balance RK directional coupler SAW surface acoustic wave SF Beam trap Sp Mirror ST Non-polarizing beam splitter STED Engl. 'Stimulated-Emission Depletion' TEM Transversal-electromagnetic mode TIV Tr ansimpedance amplifier TL tube lens TPF low-pass filter UV spectral range of ultraviolet electromagnetic radiation VNA vector network analyzer VWP quarter-wave plate XVII List of symbols Mathematical operations and functions Δ (·) Width, fluctuation, change, discretization ˙ (·) Partial derivative according to time dd? d differential ⟨(·)⟩? Arming mean ⟨(·)⟩? Time mean (·) mean (·) * complex conjugate (·)? Transposition of the vector (̂ ·) amplitude ℑ (·) imaginary part ℜ (·) real part x vector H? (·) Struve function of order? J? (·) Bessel function of the first kind and order? δ (·) Delta distribution ℱ {·} (?) Fourier transformation according to the variable? (·) ′ Spectral density of the size related to 1 Hz resolution bandwidth (︀??) ︀ Binomial coefficient max {·} Maximum value of size XVIII Abstract Heterodyne interferometry or laser Doppler vibrometry has proven to be a contactless, sensitive and precise vibration measurement technology for the Microsystem technology established in industry and research. Due to current developments, particularly in communications technology, there is a need to measure microacoustic oscillations up to 6 GHz at subnanometer amplitudes. Conventional interferometry equipment reaches its limits with regard to the advantageous carrier or heterodyne method. For unrestricted measurement capability up to 6GHz, device technology is required that can generate carrier frequencies of at least 6GHz. The conventional technology for carrier generation limits the interferometers of the state of the art and measurement capability is only achieved at the expense of immunity to non-linearities and uniqueness. The unrestricted measuring ability of an interferometer also requires a sufficient spatial resolution of the deflection shapes on the microsystem. As the oscillation frequency increases, the acoustic wavelength decreases, so that the measuring laser beam has to be focused with a microscope lens. The diffraction limits the minimum size of the laser focus and thus the spatial resolution, which also limits the ability of an interferometer to measure vibration frequencies in the gigahertz range. In this work, the carrier generation by means of phase-coupled lasers in an optoelectronic phase-locked loop was investigated theoretically and experimentally in order to achieve a measurement capability of heterodyne interferometers for mechanical vibrations up to 6 GHz. In addition, the increase in spatial resolution beyond the diffraction limit through absorption modulation nanoscopy in reflection was analyzed theoretically. Using the system-theoretical description of the optoelectronic phase-locked loop, requirements for the properties of suitable lasers and the other components were formulated. The control bandwidth must be larger than the summed line width of the laser. As an important property of the interferometer, the achievable oscillation amplitude resolution depending on the interferometer structure, the phase-coupled lasers and the phase-locked loop was modeled and numerical simulations were carried out.It has been shown that the influence of the phase noise of the phase-coupled lasers disappears with increasing oscillation frequency and therefore other noise contributions, such as shot noise, can limit the oscillation amplitude resolution. Furthermore, the collapse of the usable carrier was described analytically, which results from the loss of mutual coherence in the case of large path differences in the interferometer structure. Theoretical modeling thus simplifies a targeted design of the carrier generation using phase-coupled lasers for interferometry. XIX Abstract The theoretical, diffraction-limited spatial resolution of an interferometer was derived from surface acoustic waves. It was shown that the size of the laser measurement spot must be at least 8 times smaller than the acoustic wavelength so that the systematic measurement errors remain negligible. For a spatial resolution beyond the diffraction limit, the absorption modulation nanoscopy was modeled, which generates a reversible, dynamic near-field diaphragm in a thin layer on the measurement surface. The simulation model includes photokinetics, microscopic imaging and diffraction at the dynamic near-field diaphragm. Analytical approximations for a simple design of an absorbance modulation nanoscope were derived from the model. In particular, a formula for increasing the spatial resolution in relation to system parameters is derived, which has an interesting analogy to the known resolution formula of STED microscopy. A parameter study of the numerical simulation shows the potential of an increase in resolution to 1/5 of the diffraction limit at 100 nm layer thickness if an increase in concentration or an improvement in the photophysical properties of the photochrome by a factor of 2 compared to the prior art can be achieved. This study provides the basis for the dimensioning and the experimental proof of the potential of absorbance modulation nanoscopy in reflection. The need for further research on the application in interferometry was discussed. Based on the findings, a heterodyne laser Doppler vibrometer microscope with phase-coupled, monolithic semiconductor lasers in the visible spectral range was designed and implemented. The bandwidth of the data acquisition limits the measurement to vibration frequencies of up to 3GHz. The generation of a carrier frequency is limited to a maximum of 10GHz by the photodetector. The measuring ability of the experimental setup for high-frequency microsystems was demonstrated by means of measurements on a surface acoustic wave filter at 315MHz. The achieved amplitude resolution of ≤ 100 fm / √ Hz for oscillation frequencies> 1 GHz is limited by the intensity noise of the semiconductor laser and the thermal noise of the electronics. Thus, carrier generation by means of phase-coupled semiconductor lasers can enable heterodyne interferometry to measure vibrations up to over 6 GHz if the potential of the absorption modulation to increase the spatial resolution is exhausted. XX 1 Introduction 1.1 Motivation For years there has been a trend in information technology to design and network physical objects ('things') using sensors and actuators 'smart' [149]. The diverse endeavors are summarized under the term “Internet of Things” (“IoT”) and in the industrial environment as “Industrial Internet of Things” (“IIoT”). The envisaged omnipresence of smart technologies demands innovations from the engineering sciences in terms of communication bandwidth, computing capacity, integration density, energy efficiency and manufacturing costs [25, 71, 87]. This need for innovation established microsystem technology as early as the 1960s [146]. The reduction of the structure sizes and the production costs has always benefited from the constant further development in semiconductor technology [64]. In the state of the art, these microsystems1 (“MEMS”) enable the combination of mechanical, electrical, optical, thermal and microfluidic functions in a range of 100 nm to 1000 µm [159]. Such hybrid systems are also known as 'system-on-chip' or 'lab-on-chip' and are characterized by a high functional integration density and energy efficiency. For example, communications engineering uses high numbers of microacoustic radio frequency (HF) filters in highly functional, integrated circuits for selective filtering of communication bands with the aim of efficient use of the available bandwidths [11, 39]. In these microacoustic filters, the electrical signals are converted into surface acoustic waves2 or bulk waves3 in piezoelectric substrates, filtered and converted back again [5]. Since the acoustic wavelength is about a factor of 10,000 smaller than the wavelength of an electromagnetic wave, microacoustic filters can be made more compact, more selective and thus more efficient compared to electrical HF filters4. In the 4G mobile radio standard, these microacoustic filters are used to select communication bands up to 3GHz [5, 29]. The future 5G mobile radio standard5 requires filters for frequencies up to 6GHz (“Sub-6GHz” band) [158]. Suitable microacoustic filters are already available or are currently being developed [5, 158]. In the highly integrated circuits of communications engineering, microelectromechanical systems are also used. 2 In Surface Acoustic Wave (SAW) filters. 3 In 'Bulk Acoustic Wave' (BAW) filters. 4 With comparable filter properties 5 For macro cells. For the planned communication over short distances ('mmWave') with frequencies>