Lateral resolution limit of laser Doppler vibrometer microscopes for the measurement of surface acoustic waves

Abstract 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 f...

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Autores principales:	Robert Kowarsch, Christian Rembe
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/c9cd1bdb49f84c189b163314fb6432ec
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spelling	oai:doaj.org-article:c9cd1bdb49f84c189b163314fb6432ec2021-12-02T19:12:27ZLateral resolution limit of laser Doppler vibrometer microscopes for the measurement of surface acoustic waves10.1038/s41598-021-96684-y2045-2322https://doaj.org/article/c9cd1bdb49f84c189b163314fb6432ec2021-09-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-96684-yhttps://doaj.org/toc/2045-2322Abstract 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 $$433\,{\mathrm {MHz}}$$ 433 MHz 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.Robert KowarschChristian RembeNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-9 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Robert Kowarsch Christian Rembe Lateral resolution limit of laser Doppler vibrometer microscopes for the measurement of surface acoustic waves
description	Abstract 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 $$433\,{\mathrm {MHz}}$$ 433 MHz 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.
format	article
author	Robert Kowarsch Christian Rembe
author_facet	Robert Kowarsch Christian Rembe
author_sort	Robert Kowarsch
title	Lateral resolution limit of laser Doppler vibrometer microscopes for the measurement of surface acoustic waves
title_short	Lateral resolution limit of laser Doppler vibrometer microscopes for the measurement of surface acoustic waves
title_full	Lateral resolution limit of laser Doppler vibrometer microscopes for the measurement of surface acoustic waves
title_fullStr	Lateral resolution limit of laser Doppler vibrometer microscopes for the measurement of surface acoustic waves
title_full_unstemmed	Lateral resolution limit of laser Doppler vibrometer microscopes for the measurement of surface acoustic waves
title_sort	lateral resolution limit of laser doppler vibrometer microscopes for the measurement of surface acoustic waves
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/c9cd1bdb49f84c189b163314fb6432ec
work_keys_str_mv	AT robertkowarsch lateralresolutionlimitoflaserdopplervibrometermicroscopesforthemeasurementofsurfaceacousticwaves AT christianrembe lateralresolutionlimitoflaserdopplervibrometermicroscopesforthemeasurementofsurfaceacousticwaves
_version_	1718377063212122112

Lateral resolution limit of laser Doppler vibrometer microscopes for the measurement of surface acoustic waves

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