Laser Doppler vibrometry is currently the method that offers the best displacement and velocity resolution and is used in many fields of basic science. It enables femtometer amplitude resolution and is linear and therefore has a consistent amplitude right up to the very high frequency ranges – reaching more than 1 GHz at present. These properties are independent of the measuring distance, so this principle is used both in microscopic operations and over very large distances. Light as a sensor does not influence the sample, making it non-invasive and therefore enabling measurements to be carried out on extremely small and extremely lightweight structures. Since this procedure offers such unbeatable properties, Polytec has made it robust and fit for use in both the laboratory and outdoors.
If a wave is reflected by a moving object and detected by an instrument (as is the case with the LDV), the measured frequency shift of the wave can be described as:
fD = 2· v/λ
where v is the object’s velocity and λ is the wavelength of the emitted wave. To be able to conversely determine the velocity of an object, the (Doppler) frequency shift has to be measured at a known wavelength. This is done in the LDV by using a laser interferometer.
The laser doppler vibrometer works on the basis of optical interference, whereby essentially two coherent light beams, with their respective light intensities I1 and I2, are required to overlap. The total intensity of both beams is not just the sum of the single intensities, but is modulated according to the formula:
Itot = I1 + I2 + 2 √(I1 I2) cos [2π(r1 - r2)/λ]
with a so-called “interference” term. This interference term relates to the path length difference between both beams. If this difference is an integer multiple of the light wavelength, the total intensity is four times a single intensity.
The image above shows how this physical law is exploited technically in the LDV.
The beam of a laser is split by a beam splitter (BS 1) into a reference beam and a measurement beam. After passing through a second beam splitter (BS 2), the measurement beam is focused onto the sample, which reflects it. This reflected beam is now deflected downwards by BS 2 (see figure), and is then merged with the reference beam onto the detector.
As the optical path of the reference beam is constant over time (r2 = const.) (with the exception of negligible thermal effects on the interferometer), a movement of the sample (r1 = r(t)) generates a light / dark pattern, typical of interferometry, on the detector. One complete light / dark cycle on the detector corresponds to an object displacement of exactly half of the wavelength of the light used. In the case of the helium neon laser often used for vibrometers, this corresponds to a displacement of 316 nm.
Changing the optical path length per unit of time manifests itself as the measurement beam’s Doppler frequency shift. In metrological terms, this means that the modulation frequency of the interferometer pattern determined is directly proportional to the velocity of the sample. As object movement away from the interferometer generates the same modulation pattern (and modulation frequencies) as object movement towards the interferometer, this set-up alone cannot unambiguously determine the direction the object is moving in. For this purpose, an acousto-optic modulator (Bragg cell) that typically shifts the light frequency by 40 MHz is placed in the reference beam (for comparison purposes, the laser light’s frequency is 4.74 · 1014 Hz). This generates a typical interference pattern modulation frequency of 40 MHz when the sample is at a standstill. If the object then moves towards the interferometer, this modulation frequency is increased, and if it moves away from the interferometer, the detector receives a frequency less than 40 MHz. This means that it is now possible to not only clearly detect the path length, but also the direction of movement too.
In principle, it is possible to directly measure displacements as well as velocities with the LDV. In this case, the Doppler frequency is not transformed into a voltage proportional to velocity; instead, the LDV counts the light / dark fringes on the detector. Using suitable interpolation techniques, Polytec’s vibrometers can thus attain a resolution of 2 nm, and with digital demodulation techniques this can even be extended as far down as the pm range. Displacement demodulation is better suited to low frequency measurements (in the sub Hz range), while velocity demodulation is better for higher frequencies, since the maximum amplitudes of harmonic vibrations can be expressed as follows:
v = 2π • f • s
As its frequency increases, a vibration generates a relatively high velocity at a very low displacement amplitude.
Stroboscopic video microscopy
Stroboscopic video microscopy (SVM) makes use of the fact that high-frequency vibrations at component level can be visualized with normal video cameras when rapid movements are visually frozen using short flashes of light.
The system’s temporal resolution capacity is determined by means of the LED strobe’s flash pulse width, as the camera isn’t quick enough to clearly record very fast events. If the strobe light is switched off, the CCD sensor cannot capture any images, and this is precisely why light is only recorded during selected movement phases when the strobe light is switched on and why events can be recorded over a period of time shorter than the camera’s shortest possible exposure time. The excitation signal that causes the sample to vibrate, the LED strobe flashes and the camera exposure time must all be exactly coordinated to one another as regards time. The image below shows the time diagram for synchronizing the PMA software, taking the example of two camera shots during two different phases of periodic sample excitation.
Combination with laser doppler vibrometry
You can use a combined SVM and LDV system to identify the mechanical resonances of structures that move in all three spatial directions.
The laser beam of a laser doppler vibrometer and the strobe light are coupled into the integrated microscope lens’ beam path using beam splitter units. Working in conjunction with the signal generator and the vibrometer controller, the computer controls the laser beam’s movement (scanning LDV), the strobe lighting, processing of the interferometric signals and the camera image, and (if necessary) the sample excitation too. The measurements are ultimately evaluated and graphically represented using the high-performance system software.
The combined method is particularly significant with respect to characterizing micromechanical components (MEMS).
Single point vibrometers measure an object’s vibrations in the direction of the laser beam. If the system is aligned perpendicularly to the surface, it is also referred to as an “out-of-plane” vibrometer. This general LDV sensor situation is used in microscopic applications and in measurements over large distances. Single-point sensors provide amplitudes and transfer functions. Non-contact operational deflection shape measurements can also be carried out by combining single-point sensors to build a multipoint vibrometer. Scanning methods are used for stationary processes (see separate section).
Differential vibrometry describes vibration measurement at two points that vibrate relative to one another. Two methods are commonly used:
The difference is generated directly in the optical path (the interferometer’s reference beam is guided to the object). The benefit lies in the fact that absolute phase fidelity is guaranteed during subtraction – which is why this method is suitable for high frequencies.
The difference is calculated electronically with two independent interferometers. This method is more flexible to set up.
In-plane vibrometry describes vibration and movement measurements perpendicular to the measurement axis. In-plane vibrometry contactlessly detects the stroke movements of pistons, valve shafts or tools, for example, and is used for highly dynamic strain measurements.
Rotational methods describe the measurement of the angular velocity and angular displacement of rotational vibrations on any shape of rotating structure. This is how the rotational dynamics on drivetrains, gas turbines, electrical generators, printers and copiers, for example, are analyzed.
Microscopic vibrometry describes the measurement of vibrations on small components and microsystems using microscope lenses. Scanning laser Doppler vibrometry is used in full-field applications either stand-alone or together with stroboscopic video microscopy.
Scanning vibrometry describes vibration measurement whereby the laser beam sequentially scans the sample’s surface using a range of single-point measurements. This results in transfer functions for each and every measurement location. In the frequency domain, these transfer functions are represented as an operating deflection shape. The areal simultaneous motion sequence of the structure under examination can be animated in the time domain.
When deflection shapes of dynamic or transient events need to be detected, a synchronous measurement of various vibration sensors is key. In contrast to scanning vibrometry, all optical channels measure at the very same moment of time. This multisensor approach allows the analysis of the full-field vibrations in both the time and frequency domain.
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