Modern broadband telecommunications require microelectromechanical filters which mechanically vibrate at ultra-high frequencies up to several gigahertz. Heterodyne interferometers, so-called laser-Doppler vibrometers (LDVs), provide a sensitive and contactless measurement technique for vibrations in such filters, but are limited in GHz heterodyning by the efficiency drop of acousto-optic frequency shifters. Heterodyning by frequency-offset locking of two lasers in an optoelectronic phase-locked loop (OPLL) overcomes this limitation. This is demonstrated with our LDV setup with heterodyning up to 1.4 G H z via offset locking of two semiconductor lasers at visible wavelength. The experiments show a vibration-amplitude resolution of less than 1 p m per H z for frequencies higher than 50 M H z up to 700 M H z . The bandwidth is only limited by our photodetectors. This amplitude resolution already qualifies our LDV for vibration measurement of microelectromechanical filters at ultra-high frequencies. We present a comprehensive model for the vibration-amplitude resolution of a LDV with this technique including the laser linewidths, the OPLL transfer function, and interferometer delays. The experiments with our LDV validate the model predictions from numerical simulations. Finally, we discuss the collapse of the heterodyne carrier at vanishing mutual coherence due to interferometer delays, the transition to shot-noise-limited detection, and provide design recommendations.

The lateral or transverse resolution of single-point interferometers for vibration measurement is especially critical for microelectromechanical systems (MEMS) vibrating up to the gigahertz range. In this regime, the acoustic wavelengths are typically in the range of the size of the laser focus. Thus, a successful vibration measurement requires distinct knowledge about the lateral resolution limit and its dependencies with instrumentation parameters. In this paper, we derive an analytic approximation formula, which allows for estimation of the systematic measurement deviation of the vibration amplitude and, thus, a definition of the lateral resolution limit of single-point interferometers for vibration measurement. Further, a compensation and an optimum numerical aperture are proposed the reduce the measurement deviation. For this, the model includes a laser-interferometer microscope of Mach-Zehnder type with Gaussian laser beams considering the Gouy effect and wavefront curvature. As a measurement scenario, an unidirectional surface acoustic wave (SAW) is regarded. The theoretic findings have been validated in the experiment with a representative vibration measurement on a SAW filter at $$433\,{\mathrm {MHz}}$$433MHz with our heterodyne laser-Doppler interferometer with offset-locked semiconductor lasers. The provided formulas help instrument designers and users to choose suitable instrument parameters, especially the numerical aperture of the utilized microscope objective.

Absorbance modulation enables lateral superresolution in optical lithography and transmission microscopy by generating a dynamic aperture within a photochromic absorbance-modulation layer (AML) coated on a substrate or a specimen. The applicability of this concept to reflection microscopy has not been addressed so far, although reflection imaging exhibits the important ability to image a wide range of samples, transparent or opaque, dielectric or metallic. In this paper, a simulation model for absorbance-modulation imaging (AMI) in confocal reflection microscopy is presented and it is shown that imaging well beyond the diffraction limit is feasible. In addition, we derive analytical design equations and estimate the dependence of the achievable resolution and pixel dwell time on relevant parameters, such as the AML properties and the applied light powers. We prove the validity of these equations through a comparison with the simulation results and we show that a resolution enhancement down to 1/5 of the diffraction limit is possible.

The operation of the quartz crystal microbalance (QCM) in liquids is plagued by small flexural admixtures to the thickness-shear deformation. The resonator surface moves not only in the transverse direction, but also along the surface normal, thereby emitting compressional waves into the liquid. Using a simple analytical model and laser Doppler vibrometry, we show that the flexural admixtures are stronger on the fundamental mode than on the overtones. The normal amplitude of motion amounts to about 1% of the transverse motion on the fundamental mode. This ratio drops by a factor of two on the overtones. A similar dependence on overtone order is observed in experiments, where the resonator is immersed in a liquid and faces an opposite planar wall, the distance of which varies. Standing compressional waves occur at certain distances. The amplitudes of these are smaller on the overtones than on the fundamental mode. The findings can be rationalized with the tensor form of the small-load approximation.

The generation of a heterodyne carrier frequency for coherent detection via offset-locking in an optical phase-locked loop was demonstrated in communication, spectroscopy and other fields. In state-of-the-art laser-Doppler vibrometers (LDV), common acoustooptic devices (Bragg cells) allow efficient heterodyning with a static frequency. Moving mechanical parts vibrate in many technical applications, e.g. moving cars, trains, robots, ect.. In such applications, a large laser-Doppler-shift generated by the movement impairs the measurement of the relevant vibrations. A variation of the frequency offset of the interfering laser beams can suppress the Doppler effect of high-speed movements with slow speed variations and adjusts the signal spectrum to the optimal value. Thus, the electronic bandwidth can be set to an optimal value within the modulation bandwidth of the relevant vibrations. However, Bragg cells are not well applicable to shift laser frequencies without affecting the interferometer adjustment. In this paper, we propose offset locking of two independent lasers with an optical phase-locked loop to exploit the possibility of flexible heterodyne-carrier generation for laser-Doppler vibrometry. We demonstrate a LDV setup with offset locked visible DBR semiconductor lasers for a flexible heterodyning up to 200MHz and present first measurements.

Zusammenfassung: Heterodyne Interferometer messen Schwingungsamplituden bei Frequenzen > 100MHz mit definierter Messunsicherheit im Gegensatz zu homodynen Verfahren. Die geringe Effizienz von Bragg-Zellen als Frequenzschieber bei Frequenzen > 409MHz limitieren den Einsatz von heterodynen Interferometern im Gigahertz- Bereich. In diesem Beitrag stellen wir ein heterodynes Laser-Doppler-Vibrometer-Mikroskop vor, in dem eine optoelektronische Phasenregelschleife zwei Diodenlaser auf eine Frequenzdifferenz regelt und die Trägerfrequenz erzeugt. Unser Messsystem bietet eine Auflösung von Schwingungsamplituden im Pikometer-Bereich bei Schwingungsfrequenzen von 10MHz bis 700MHz. Die Messfähigkeit der Betragsamplitude und Phase der Schwingung wird am Messbeispiel eines Oberflächenwellen-Filters demonstriert.