Technical Papers

» Non-contact fiber optic vibrometer

Pepe Davis and Jeff Bush
Optiphase Inc.
7652 Haskell Ave.
Van Nuys, CA 91406

Abstract

A novel fiber optic vibrometer has been built and characterized. The vibrometer’s optical design is based on the Sagnac interferometer. Due to the nature of the Sagnac’s optical configuration, the optical phase shift induced by the surface being probed is differentiated, and therefore results in a measured optical phase shift that is directly proportional to the velocity of surface. The path matched Sagnac design eliminates the need for a coherent light source used in laser doppler vibrometers and offers great design flexibility for tuning the vibrometer’s frequency response and dynamic range to specific applications. The vibrometer’s dynamic measurement capabilities span as much as 8 decades (1 Hz noise band), where the maximum range may extend as high as 100 m/s. A fiber optic Sagnac vibrometer was built and evaluated. Experimental results demonstrating the vibrometers performance are presented.

Keywords: Fiber Optic, Vibration, Velocity Sensor, Sagnac

1. INTRODUCTION

Vibrometers are important tools for assessing the operating condition of mechanical equipment as well as studying the properties of mechanical systems. As equipment monitors, they can be used to measure vibrational spectra of motors or pumps in order to determine bearing wear or motor balance. Typically electronic accelerometers are used for monitoring vibrations. These devices are available with various sensitivities and dynamic ranges and can be fairly inexpensive. However, they must be attached to the vibrating surface and because of their size and mass can change the characteristics of the vibrations. Furthermore, they require an electrical connection with signal conditioning electronics which can be awkward and dangerous in some applications. For example, when studying the dynamics of hard disks, the mass of an accelerometer would significantly perturb the system. In addition, a means for passing the electrical signal from the rotating disk to a stationary laboratory apparatus would have to be found. Certainly, a non-contacting and therefore non-perturbative diagnostic is needed. In fact, even in the case of monitoring large equipment, a non-contact vibrometer has some merit. The non-contact vibrometer can directly monitor locations that an accelerometer could not, such as a rotating shaft. In addition, since mounting is not required, the time required to make a measurement is shortened, and furthermore the mechanical interface between the vibrometer and the device under test does not have to be considered unlike with accelerometers.

Optical vibration monitoring techniques, such as laser Doppler vibrometers, offer a non-contact solution for vibration monitoring. As a non-contact diagnostic, these devices do not perturb the vibrating surface and can be used in situations where electrical connections to the surface are not possible. They can be used to monitor rotation and feed fluctuations for machining equipment, conveyance velocity fluctuations of processed materials and flow measurements of both liquids or gasses in medical or industrial applications. Many non-contact vibrometers already exist on the market. Most employ solid state lasers and expensive electronics to achieve accurate measurements of the doppler shift of light as it is reflected by the target. These vibrometers are usually large (occupying an equipment rack), power hungry (require wall power) and typically cost $20,000 to $100,000. The high price, lack of portability, and non-trivial setup keep these vibrometers mainly in the R&D arena and out of production environments.

The Sagnac vibrometer promises to provide an economical and portable solution to non-contact vibration monitoring. Its performance can match that of laser Doppler vibrometers at a fraction of the cost. An all fiber optic construction enables flexible and small volume packaging formats. In addition, the optical probe can be remotely deployed on a single optical fiber. The probe can be attached with standard optical connectors so that the base interrogation unit can be used with multiple probes that are permanently deployed. The Sagnac Vibrometer is constructed primarily of low cost components. The expected manufacturing costs will enable end user instrument pricing in the $5,000 to $10,000 range, well below the cost of laser Doppler vibrometers available on the market today.

2. ANALYTIC MODEL OF THE SAGNAC VIBROMETER

The basic optical configuration of the Sagnac vibrometer is shown in Figure 1. An incoherent optical source (ELED/SLD or Erbium ASE source) feeds a 2x2 coupler that splits the light into two fibers. One fiber contains a fiber optic phase modulator and delay coil. The light from both fibers is then combined onto the target surface such that return light is coupled back into the opposite fiber, thereby closing the Sagnac loop. An incoherent light source is used so that only the counter propagating waves in the Sagnac loop interfere (all other optical paths are different in length by more than the coherence length of the source). The counter propagating waves are recombined at the coupler and an optical receiver is used to measure the interferometric intensity at the optical port that is complementary to the optical source fiber.

There are two primary benefits of using a Sagnac vibrometer over a laser Doppler vibrometer. First, the Sagnac vibrometer operates with an incoherent light source. This reduces the systematic errors produced by stray light reflections and facilitates an all fiber optic implementation. In addition, incoherent light sources are generally less expensive and more stable that coherent light sources. Secondly, the Sagnac vibrometer sensitivity and frequency response can be changed by adjusting the optical delay loop. This provides a simple means of tailoring the vibrometer performance to fit a particular application. A simple derivation of the Sagnac vibrometer sensitivity is given below.

Using the optical configuration in Figure 1 as our model, we can mathematically derive the relationship between the target velocity and the optical phase of the two counter propagating beams in the Sagnac loop. The generalized expression for the interferometric signal amplitude of a modulated Sagnac Interferometer is shown in equation 1:

 

where,
b is the modulation depth in peak radians;
ω_mis the modulation (radian) frequency;
θ_S(t) = Interferometric Phase

Given that we have a Sagnac Interferometer, a more appropriate way to represent its phase, θ_S(t), is to write it as an expression of the difference of the CW and CCW waves, or θ_S(t) = ф_S(t) - ф_S(t-τ). Hence, equation 1 can be rewritten as:

 

where,
τ= the Sagnac Loop delay time (seconds) = the group index of refraction of the fiber multiplied by the length of the Sagnac

Loop (in meters) divided by the speed of light (m/s).;
ф_S(t) = optical phase from the vibrating target (cw beam);
ф_S(t-τ) = phase from the vibrating target (ccw beam); (note that ф_S(t)andф_S(t-τ) represent target displacement and not velocity)

To add some physical meaning to ф_S(t) for the case of the Sagnac Vibrometer, we let this signal represent the linear displacement of the vibrating element expressed as an optical phase. Thus, in terms of surface displacement, ф_S(t) = (2)2p/λx(t) where λis the optical wavelength in air and where the factor of 2 in parenthesis is due to a reduction in Sagnac loop length of twice the surface displacement (double pass).

If we further assume the displacement signals vary sinusoidally in time, such that ф_S(t) = Acos(ω_vt) and ф_S(t-τ) = Acos[ ω_v(t-τ)], where ω_v is the (radian) frequency of the vibration signal and A is its amplitude (radians), the expression for ф_S(t) may be rewritten in equation 3 as follows.

 

where trigonometric identities yield

We can further reduce K using more trigonometric identities (or power series) to yield K = 2 sin (ω_vτ / 2). If we constrain ourselves to conditions where ω_vτ < 0.5, we can invoke the small angle approximation and result in

 

 

Using equation 4, we can rewrite equation 3 as:

 

It is important to note that when ω_vτ< 0.5, θ_S(t) appears as the derivative ofф_S(t), scaled by τ the Sagnac loop delay time. Therefore,

 

from the relationship between ф_S(t) and x(t) defined above. Therefore the optical phase change measured at the output of the Sagnac interferometer is directly proportional to the velocity of the target surface.

The performance characteristics of the Sagnac vibrometer incorporating an Optiphase, Inc. OPD-200 digital demodulator¹ were investigated as a function of modulation frequency and delay loop length. The optical wavelength assumed in the calculations was 1.5µm and the coherence length was assumed to be 100 µm (matching that of the Erbium ASE source used for most of the measurements). The limitations imposed by the OPD-200 are as follows: noise floor of 5 µradians/rt-Hz, a slew rate limit of p radians/modulation period, and a vibration frequency below the modulation frequency. At low frequencies an additional limitation occurred when the optical phase difference exceeded the coherence length of the source. The Sagnac vibrometer performance range is depicted in Figure 2 as the region between the coherence and slew rate limits and the noise floor.

These graphs show that for frequencies below 100 Hz the Sagnac vibrometer has a dynamic range of 10⁸ and can measure velocities from 1 micron/s to beyond 10 m/s. For frequencies above 100 Hz, the vibrometer performance is limited by the slew rate and therefore the modulation frequency used as the carrier for the digital demodulation process. Currently, the OPD-200 is limited to a modulation frequency of 100 kHz, however, a 1 MHz design could be implemented with current DSP processing technology and will be developed in the future.

3. EXPERIMENTAL SETUP

Based on modeling described above, a 1 km delay coil was chosen for the experimental demonstration in order to maximize sensitivity without sacrificing linearity up to 10 kHz. The Sagnac vibrometer was constructed using a dual wavelength coupler and phase modulator so that the system could be evaluated with both 1300 nm and 1530 nm light. However, only the 1530 nm Erbium source was used for all the testing because the high powered (> 1 mW) 1300 nm SLDs were not delivered in time for implementation in the breadboard testing. The 10 mW Erbium source was de-rated to < 3 mW in order to simulate a signal to noise equivalent to using a high powered SLD light source.

The experimental setup for the vibration measurements is depicted schematically in Figure 3. The SRS SR780 Network Analyzer was used as the signal generator for both fixed frequency and swept sine vibration measurements. Its output was amplified by the Labworks Inc. PA-138-1 Power Amplifier in order to drive the Labworks Inc. ET-126A electrodynamic shaker. A PCB 352C66 Accelerometer was mounted to the shaker so that the vibrometer output could be compared with a

calibrated accelerometer. The accelerometer signals were integrated to provide velocity data that could then be compared directly to the vibrometer measurements since the vibrometer output is directly proportional to velocity. Both the vibrometer and accelerometer signals were simultaneously recorded with the SR780 Network Analyzer and the Tektronics TDS420A Oscilloscope. The network analyzer recorded spectral data while the oscilloscope recorded time data during fixed frequency operation. The optical phase was measured with the Optiphase Inc. OPD-200 demodulator which produced an analog output proportional to phase and therefore proportional to velocity of the target surface. A picture of the experimental setup is shown in Figure 4.

There are three factors which limit the shaker table vibration amplitude: displacement, voltage, and current. The maximum armature displacement for this shaker is 0.75 inches. This limit is only approached at low frequencies (< 100 Hz) and did not limit the shaker from achieving 150 VdB up to 100 Hz. The voltage and current limits are 20 Vrms and 12 Arms respectively. It was only at frequencies above 1 kHz that shaker could not achieve the 140 VdB level without suffering possible damage due to these voltage and current limits. The shaker vibration limits are plotted in Figure 12 along with the solicitation requirements. Nevertheless, the ET-126A shaker was capable of producing vibration amplitudes from 10 Hz to 10 kHz that covered 95% of the stated solicitation requirement range.

Although the shaker is suppose to provide only linear vibrations, imperfections in the shaker and any imbalance in the fixture load will induce some lateral vibrations which can be particularly evident at frequencies above 2 kHz. An accelerometer that is mounted to the shaker surface will respond to these lateral vibrations since they are manifested by surface rotations (i.e. accelerations of the surface on which the accelerometer is mounted). The vibrometer, on the other hand, only measures vibrations along the line of sight between the shaker surface and the optical probe and therefore will observe a reduction in the vibration amplitude at the high frequencies when the vibration takes on a lateral component. In addition, at frequencies > 4 kHz, vibrational resonances in the shaker and mounting fixture assembly can cause differences in the vibration amplitude and phase at different locations on the mounting fixture surface.

To investigate these discrepancies, measurements were taken with two accelerometers at two locations 120 degrees apart on the shaker fixture (labeled “A” and “B” in Figure 5.) The two accelerometers used were PCB Model #352c66 SN13540 (sensitivity of 97.6 mV/g) and PCB Model #353b16 SN 49900 (sensitivity of 10.52 mV/g). Since we only have one signal amplifier, measurements were not made simultaneously, however, the measurements were repeatable from sweep to sweep to within 0.2 dB for each accelerometer. Vibration spectra were recorded from 1 kHz to 10 kHz with each accelerometer at each position in the fixture. At frequencies below 4 kHz, not only do the two accelerometers agree within 0.5 dB but also the difference was fairly constant, indicating a calibration error of about 0.5 dB. However, at frequencies above 4 kHz, the two accelerometers can disagree by as much as 4 dB.

It was also evident from these measurements that the vibration spectra at position “A” is different from that at position “B” despite efforts to design a rigid mounting fixture. Vibrational spectra were also measured with the same accelerometer mounted at both location “A” and location “B”. Again, at frequencies below 4 kHz, the vibration spectra agree to within 0.2

dB indicating that the fixture is rigid up to 4 kHz such that the entire fixture surface moves with the same velocity. However, at higher frequencies, the vibration amplitudes again differed by up to 4 dB from position "A" to position "B". Also noted was that the difference between position "A" and "B" was nearly identical for both accelerometers, SN13540 and SN49900, thereby confirming that the difference is not related to the accelerometers. Such a large difference can only be explained by actual differences in the vibrations at the two locations

Since we have found discrepancies in accelerometer measurements as large as 3 dB at the same location and as large as 4 dB at different locations, we must conclude that the accuracy of our measurements is less than 3 dB near resonances. Therefore we can expect similar discrepancies when comparing vibrometer measurements with accelerometer measurements. However, since the vibrometer measurements do not suffer from mounting issues (non-contact measurement) and therefore do not affect in any way the surface being measured, the vibrometer measurement will most accurately represent the linear vibrational velocity of the surface.

4. EXPERIMENTAL RESULTS

Before making vibration measurements, the noise floor of the accelerometer and the vibrometer were measured. These measurements for both the accelerometer and the vibrometer are graphed in Figure 6 along with the theoretical vibrometer performance limits. As expected, the vibrometer noise floor is basically flat for frequencies > 100 Hz in velocity-frequency space. At frequencies between 7 and 100 Hz the vibrometer signal tracks with the accelerometer signal and is probably an accurate measurement of the environmental vibrations of the shaker test stand, particularly the broad peak which occurs around 30 Hz. Below 7 Hz few data points were taken, however, the graph indicates that the vibrometer noise floor is decreasing towards the theoretical minimum while the accelerometer noise floor is increasing due to its natural response. Note that due to the derivative relationship between velocity and acceleration, the noise floor of the accelerometer in VdB-frequency space decreases with increasing frequencies.

1. Fixed Frequency Measurements

Initial vibration measurements were made at 7 frequencies (10 Hz, 50 Hz, 100 Hz, 500 Hz, 1 kHz, 5 kHz and 10 kHz) and at two amplitude levels for each frequency. The high amplitude level was chosen to be about a factor of 2 below the shaker table limit and the low amplitude level set about 50-100 times below the high level. These measurements are plotted in Figure 7 along with the shaker limits and the theoretical vibrometer performance limits. Excellent correlation was observed between the vibrometer and accelerometer measurements. The measurements from 10 Hz to 1 kHz agreed to better than 0.5 dB while the measurements at 5 kHz and 10 kHz matched to within 5 dB (within the expected margin for error due positional differences in the probe locations on the shaker). We believe the differences at the higher frequency were due either to the mounting problems with the accelerometer or to the positional vibration differences of vibrational modes at high frequencies also discussed above. For large drive amplitudes at 10 Hz, both the vibrometer and accelerometer signals resulted in distorted sine waves. Although the harmonic content was slightly different, the fundamental frequency component agreed within 0.5 dB as indicated in Figure 7. At these low frequencies, the long displacements traversed by the shaker armature are likely to produce rotations of the surface which accounts for the difference between vibrometer and accelerometer measurements.

2. Swept Sine Measurements

Vibration spectra were recorded simultaneously using the vibrometer and the accelerometers mounted in positions "A" and "B". The vibrometer probe beam was focused directly on the machine finished shaker mounting fixture without the need for any special surface preparation. The relative positions of the accelerometers and the vibrometer probe spot were shown above in Figure 6. As with the accelerometer spectra, the vibrometer spectra were reproducible to within 0.5 dB from sweep to sweep. The vibrometer spectra are presented along with the accelerometer measurements in Figure 8.

The vibrometer measurement spectrum differs from that of the accelerometer by less than 3 dB. This is well within the measurement errors postulated above from either accelerometer mounting or positional differences due to the relative locations of the optical probe spot and the accelerometer. The only general trend which seems to indicate some real discrepancy between the vibrometer and the accelerometers is the slow increase in the velocity amplitude difference between the accelerometers and vibrometer in the 1 kHz - 10 kHz frequency range. At 10 kHz, the vibrometer appears to measure approximately 1 dB lower amplitude than the accelerometer. Neither the Sagnac frequency response nor the Optiphase Inc. demodulator can cause this rolloff. As described in Section 2, as long as ω_vτ< 0.5, the optical phase will track linearly with the velocity to within 1% (0.1 dB). Even at 10 kHz, ω_vτ = 0.3 and therefore cannot explain the > 1 dB rolloff observed. Likewise, with the demodulator operating at 100 kHz, the demodulator rolloff is less than 3% (0.2 dB) and also does not account for the observed rolloff. Therefore, this rolloff can only be explained by a real difference in the measurements due to differences in the measurement techniques. As stated above, the vibrometer will measure only linear vibrations along the line of sight between the optical probe and the surface. An accelerometer, however, is susceptible to rotations and lateral vibrations since it is mounted directed to the surface. As demonstrated above with two accelerometers, at frequencies > 4 kHz, different positions on the vibrating surface experience different velocities. Therefore, rotations and lateral translations of the surface do occur. The velocities in the lateral directions are not observed by the vibrometer and therefore the amplitude measured by the vibrometer will be lower than that of the accelerometer. This explains the reason for the apparent vibrometer rolloff which is actually an accurate measurement of the linear velocity.

Overall, the vibration spectra correlate extremely well between the vibrometer and the accelerometers. Below 4 kHz vibrometer and accelerometer measurements agree to within 0.2 dB (2%). Even the maximum deviation of 2 dB (25%)

between the vibrometer and accelerometer measurement is less than the maximum difference of 3 dB observed between the two vibrometers and therefore within the measurement errors of our testbed.

5. HAND HELD VIBROMETER IMPLEMENTATION

To demonstrate the potential of the Sagnac vibrometer as a hand held measuring device, we implemented a vibrometer design using components that are scaleable to a hand held design and can be battery operated. Hand held vibrational spectra were then measured using this design.

1. Hand Held Probe Design

The first step towards the development of a hand held vibrometer was the design of a hand held optical probe. Using the basic vibrometer design, a single fiber tether can be used to connect the Sagnac optics with a hand held probe which contains a single focusing lens to focus to and collect light from the vibrating surface. With this optical probe, alignment is achieved by simple displacement and tilt of the optical probe. In addition, the focal spot position can be adjusted from 4" to 18" from the microscope lens. With this probe, we have been able to achieve excellent signal to noise from unpolished metal surfaces and painted surfaces.

As shown roughly to scale in Figure 9, the optical probe is also compact and easily hand held. A single connectorized fiber links the probe with the optical system. Therefore, the bulk of the optics and electronics could be carried in either a backpack or shoulder bag and only the optical probe would be hand carried. In addition, since the probe size is quite small and the optical tether easily manipulated, the probe can be easily positioned in tight spaces.

Our testing has shown that the reflected signals from unpolished metal or painted surfaces can vary dramatically across the surface (> factors of 10 ). However, with the excellent reflected signal sensitivity we achieved with this probe and the inherent insensitivity to optical signal level of the Optiphase Inc. demodulation scheme, we have been able to perform hand held vibration measurements despite these large variations in signal level.

2. Compact Demodulation Electronics

Just as with the optical packaging, the electronics must also be miniaturized. The demodulator used in the preceding measurements was a labtop model OPD-200 Optiphase Inc. demodulator. At its core is a 4" x 9" electronics board. Although this size is already manageable, Optiphase Inc. has recently developed an OEM demodulator that is both smaller in size and consumes less power than the labtop model. This demodulator consists of two electronics boards which are sandwiched together to form a 2" x 3" x 1" package. A picture of the demodulator is shown in Figure 11. This demodulator can be implemented in a portable, battery operated design.

In addition to the implementation of the OEM demodulator, a dedicated data acquisition system should be implemented. We believe that the DSP processing power of the Optiphase Inc. demodulator could be used for both data acquisition and data processing. Ultimately, the demodulator could control the start and stop of the data acquisition and perform FFTs and averaging of the data as desired. The demodulator could still provide a digital output and the user would choose whether to display time or frequency data. We hope to incorporate these additional features in the future.

3. Optical Source Development

Until recently, broadband sources were only available with powers < 1.0 mW and the cost of these sources was high (in the thousands of dollars range). Fiberon Inc. has recently released a > 3 mW SLD light sources with 30 nm optical bandwith. We have recently acquired a few of these sources will test them in the near future.

Unfortunately, the high powered SLD source was not available for the hand held demonstration measurements and a high power (> 10 mW) Erbium source was used for all of the vibration measurements. An optical attenuator was employed to reduce the Erbium source power from 10 mW to 3 mW in order to simulate the optical power of the high power SLD. Although the cost of a 10 mW Erbium source currently runs about $10k-15k in single quantities, in production, we expect that a 1-3 mW Erbium source would cost < $5k. As the production of Erbuim fiber matures, we expect that this cost will be further reduced. Although the Erbium source costs are much higher than that of the SLD source, like the SLD source, it is a solid state design and compatible with both the ruggedness requirement and power efficiency requirement of a hand held vibrometer. Additionally, in multiple vibrometer installations, a single Erbium source could be used to power multiple Saganc vibrometers.

4. Hand Held Demonstration

To prove the capabilities of this hand held concept, the connectorized optical probe shown in Figure 9 was successfully employed to make hand held vibration measurements. As described above, the optical power of the Erbium source was reduce to 2 mW in order to simulate the likely power levels of a hand held vibrometer with either an SLD source or a low powered Erbium source. Real-time FFTs of the vibrometer and accelerometer outputs were performed by the SRS780 network analyzer although in future implementations, the FFT calculations could be performed by the demodulator DSP. The network analyzer was also used to drive the shaker table with two sinusoidal tones. Due to the response of the shaker table, the two-toned drive signal produced two primary vibration frequencies and a number of smaller amplitude harmonics.

Two hand held measurements were performed. In the first test, the shaker vibration from a 60 Hz and 150 Hz drive was recorded. As shown in Figure 11, At 60 Hz the shaker table was able to generate > 140 VdB of vibration amplitude which was faithfully recorded by both the vibrometer and the accelerometer. In addition, the 150 Hz tone and various other harmonics were also recorded. The second hand held measurement was performed while the shaker was driven with a 600 Hz and 1600 Hz two-toned drive signal. Again, the vibrometer measurements matched those of the accelerometer.

In this hand held demonstration, velocities from 0.3 m/s down to 1 micron/s were measured indicating a dynamic range exceeding 5 orders of magnitude in the 10 Hz to 10 kHz frequency range. Excellent agreement with simultaneous accelerometer measurements also establishes the Sagnac vibrometer as an excellent candidate for a portable vibration monitoring device.

6. CONCLUSIONS

We have demonstrated hand held vibration measurements with a Sagnac vibrometer. The vibrometer capabilities extend from < 1 micron/s velocities up to > 10 m/s velocities in a frequency range from 1 Hz to 10 kHz. Its performance can match that of laser Doppler vibrometers at a fraction of the cost. An all fiber optic construction enables flexible and small volume packaging formats. In addition, the optical probe can be remotely deployed on a single optical fiber. The Sagnac vibrometer promises to provide an economical and portable solution to non-contact vibration monitoring.

ACKNOWLEDGMENTS

The authors wish to acknowledge Mirko Invancevic of Optiphase Inc. for his expert assembly of the fiber optic components, Cory Keitz of Optiphase Inc. for his work integrating the electronic components and fabricating the demodulators

REFERENCES

¹A. Cekorich, "Demodulator for interferometric sensors", Paper Number 3860-50, Proceedings of SPIE Vol. 3860

Reprint Proceedings of SPIE Volume 3860-51 "Non-contact fiber optic vibrometer," December 1999