Multiple Reflection Assisted Laser Doppler Vibrometer Setup for High

Research Article 1 Multiple reflection assisted Laser Doppler Vibrometer setup for high resolution displacement measurement ∗ ∗ NIKHIL KUMAR PACHISIA1,†, ,K AJAL TIWARI1,‡, , AND RITWICK DAS1,§ 1School of Physical Sciences, National Institute of Science Education and Research, HBNI, Jatni-752050, India ∗N. K. Pachisia and K. Tiwari contributed equally to this work †[email protected] ‡[email protected] §[email protected] December 12, 2019 Non-intrusive displacement measurement technique has a distinct edge over displacement sensors working in contact mode. Laser Doppler Vibrometry based schemes (LDV) offer such an advantage. However, the measurements are limited up to l/4, where l is the wavelength of optical source. An experimental design of high resolution non-intrusive displacement sensor working on the principle of basic LDV is being presented here. Resolution enhancement has been achieved through phase multiplication using multiple reflections within a high-Q cavity created by a vibrating surface and a high reflection mirror kept parallel to each other. Displacement of 72 nm has been measured with an error range of ±14 nm through direct counting of characteristic peaks in “half cycle” of the interferogram. The experimental design offers a straightforward route to measure displacement and the measurement resolution is mainly limited by the reflectivity and physical dimension of moving source. 1. INTRODUCTION devices and several sensing configurations have been proposed which are essentially derived from the principle Vibration measurements essentially comprise frequency, of Laser Doppler effect. The impact of a ‘vibrating’ object instantaneous velocity, acceleration and displacement on laser interferometry is employed for analyzing its measurements, which provide crucial information about durability and quality. This technique is widely deployed the robustness of the design, resilience to vibrations testing of foot-over bridges and elevated pathways [4, 5], and structural defects of the object under evaluation monitoring the health of dynamic machine parts such as [1]. However, most of the schemes developed so far automotive components [6], turbo machines [7], damage for modal parameter estimations, have one basic disad- detection and bio-medical applications such as study of vantage; they primarily work in contact-mode which vibration in tympanic membranes, sensing mechanical could be unfeasible and possibly, erroneous in a few cardiovascular activity, diagnostic tool for patients with situations. Mass-loading introduces errors and may cause abdominal aortic aneurysms [8–10]. arXiv:1912.05030v1 [physics.ins-det] 9 Dec 2019 substantial damage especially when testing delicate or small structures or highly damped non-linear materials [2]. Additionally, component positioning and orientation Laser Doppler Vibrometer (LDV) has been extensively restricts contact methods. Non-intrusive interferometric used for small displacement measurement over a decade techniques for vibration measurements offers an attractive [11]. As the name suggests, LDV utilizes Doppler-shift route to overcome the bottlenecks imposed by contact which occurs due to scattering of light from moving sur- measurements. Laser interferometric techniques utilizing face. It is a single point ‘axial’ vibrometer as it measures Doppler effect for measurement of fluid velocity was only the component of the velocity along the laser line-of- first reported by Yeh and Cummins [3] at Columbia sight. LDV technique allows the data acquisition at differ- University in 1964. Since then, crucial developments ent points by straightforward adjustments of optical parts have taken place in the field of laser interferometry-based and thereby, provides additional degrees of freedom to Research Article 2 Fig. 1. A mirror moving at a constant velocity v towards Fig. 2. (a) A retro-reflecting mirror mounted on a piezo- right. electric crystal undergoing oscillatory motion in the direction of propagating laser beam. (b) An equivalent configuration of “(a)”, as angle between incident beam and reflected beam is 180o, implying a = 0 (refer Fig.1). enhance the measurement resolution. In addition, it facili- tates remote measurements which may not be physically accessible. LDV based systems extend measurement capa- interferometry, and is capable of implementing non- bilities with respect to the classical transducers (such as ac- contact measurements of frequency, single-point veloc- celerometers [12], strain gauges, inductive, capacitive elec- ity and maximum displacement of vibrating objects. The trical sensors, Linear Variable Displacement transformer present scheme elucidates the improvements in the ba- [13]) through accurate measurement of modal parameters. sic design, methodology and strategy for measuring Such characteristics are brought about by remote, non- nanoscopic displacement range with high precision using intrusive, high-spatial resolution measurements with re- phase multiplication of multiple reflections [21]. A combi- duced testing time and improved performance. There are nation of retro-reflector corner cube in conjunction with quite a few modified versions (inbuilt designs by Polytec a plane mirror have been employed as reflecting objects Inc., USA) of LDV are now available, which are equipped for displacement and frequency measurements. A low with a video camera and a scanning and tracking system. power (≤ 5 mW) He-Ne laser which is generally used for The scanning laser Doppler vibrometer (SLDV) [14] is an interferometric purposes has been deployed as the source instrument based on laser interferometry that can mea- and vibrations are induced on the surface of reflectors sure high spatial resolution vibration data by sequentially through piezoelectric crystal. positioning the measurement laser beam at discrete po- sitions using two scanning mirrors (for the vertical and horizontal deflection of the beam) [15]. 2. THEORY For nanoscale displacement sensing and estimation, a A. Doppler effect due to moving mirror resolution better than l/2 is required. A plausible alter- We note the frequency shift in a collimated He-Ne laser native is improved version of a ‘self-mixing’ laser having beam reflected from a mirror moving with uniform veloc- an integrated and portable system which could reliably at- ity via Doppler effect [22]. Consider the schematic shown tain the quantum detection regime (in ‘nm’ scale) [16–18]. in Fig.1 where, the frequency of reflected beam is given Sensing and measurement by using the laser relaxation by, oscillation (RO) frequency have been reported, which can 0 1 − v + v2 lead to higher resolution and long range displacement 1 2 c cos a c2 f = fo@ 2 A (1) sensing [19]. However, the measurement range, in their 1 − v technique, is limited by the distance between laser diode c2 and vibrating object. In addition, a high laser diode injec- where, fo is the frequency of incident laser beam, v is the tion current and hence a high laser power is crucial for velocity of mirror, c is the speed of light, a is the angle at improving resolution. An absolute distance measurement which light is incident on the mirror from the direction of using optical combs derived from a femtosecond pulse motion of the mirror (refer Fig.1). laser have been proposed [20]. We consider a case where object is moving towards the In the present work, we present a simple, cost-effective direction of propagation of laser beam. For any arbitrary experimental configuration of an LDV which is based on direction (of movement/vibration), the component of dis- the principle of Laser-Doppler effect and Mach-Zehnder placement in the direction of the beam will be used for Research Article 3 Fig. 5. A typical oscilloscope trace when retro-reflecting Fig. 3. Fringe pattern when the retro-reflecting mirror prism oscillates. at rest position. Assuming center of bright fringe "0" as reference, we mark the distance of each fringe as a multiple of ‘d’ where wavelength (l) is 632.8 nm in case of He-Ne laser. The reflected beam will have a frequency ( fo − D f ). Similarly for the case when the velocity is towards left, the frequency of reflected beam will be ( f0 + D f ) where the value of D f is given by Eq. (2). B. Moving fringes From Section (A), we observe that frequency of laser beam is shifted by ±D f amount after reflection from a mirror moving in −x/+x respectively. When the mirror is not vibrating, a static fringe pattern is observed, refer Fig.3. It should be noted that the translation of one mirrors in a ’Michelson’ interferometer results in movement of the interference fringes in one direction. In other words, the direction of motion could be ascertained through the direction of movement of fringes which primarily dictates the path difference. On a similar note, when the mirror begins to vibrate, the fringes were observed to follow a pattern conforming to the movement of mirror. Fringes Fig. 4. Moving fringes created by two laser beams with move towards the lower frequency beam, with velocity slightly different frequencies (due to Doppler shift). (v f ) given by, v f = d f × D f (3) where, d f is the fringe width between two consecutive analysis due to the axial nature of LDV. Consider a mirror light or dark fringe, D f is frequency shift, given by Eq. moving uniformly in positive x direction (right), then the (2). frequency ( f ) of reflected beam is given by Eq. (1) with From the geometry, it is apparent that the reflected a = 0 (refer Fig.2) which is the case when mirror as well beam frequency will be given as fo − D f for the half cycle as the laser beam are moving in same direction. when the mirror is moving towards the right i.e. in direc- Therefore, f will be given as, tion of incident beam and the reflected beam frequency 0 2 1 will be fo + D f when the mirror is moving towards left 1 − 2 v + v c c2 (towards the incident beam), where f is the emission f = fo@ A o − v2 frequency of incident laser beam.

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