expended to create the optical analogs of present electrical sensors, thereby allowing for development of electrically passive fiber-optic sensor systems. To date, fiber-optic sensors have been developed that sense acoustic waves,1-6
rotation rates,7 linear displacements,8 fluid flow,8 temperature,9 magnetic fields,10 etc. These may be roughly divided into two groups: those based on single-mode fiber-optic technology and those based upon multimode fiber-optic technology. In this Letter, a multimode fiber-optic acceierometer is described. It is based upon the phenomenon of photoelasticity and represents a general technique for constructing a variety of fiber-optic sensors. Use of this technique for a single-mode acoustic sensor has been described previously in the literature.6 The present approach has the advantage that it uses commercially available multimode fiber-optic technology and is compatible with electrically passive fiber-optic multiplexing approaches already reported.11,12
For the photoelastic sensor configuration shown in Fig. 1, the optical power reaching the detector is13
where t is the optical path length through the birefringent material, ƒ is the material fringe value, and S is applied stress. If S0 is the amount of stress required to make the detected optical power go from a minimum to a maximum, the material fringe value can be determined from
Since the stress applied to the active element is simply (ma)/A, where a is the acceleration, m is the mass of the birefringent material between the optical beam and the attached mass plus the attached mass itself, and A is the cross-sectional area of the birefringent material, the response of this sensor to acceleration is given by
Fig. 1. Schematic diagram of photoelastic acceierometer.
The partial derivative of Eq. (3) with respect to a may be calculated as
where α = (πtm)/(ƒA). Then
At the α = 0 point, this expression may be rewritten as
If ΔI is equated with the minimum detectable optical power and I with the optical power for α = 0, the minimum detectable acceleration Δa may be determined:
Alternately, the output of the optical detector may be analyzed by a spectrum analyzer. In that case, for an acceleration as at some given frequency, the signal at the input of the spectrum analyzer may be written
or
For sufficiently small αa.
Since the spectrum analyzer is only concerned with the signal at the frequency of interest, the static component may be ignored with the result
Similarly if the acceleration is turned off, a noise equivalent acceleration may be found from the noise voltage at the frequency of interest, i.e.,
This noise equivalent acceleration aN may then be found from the spectrum analyzer determined signal-to-noise ratio R:
Equations (7) and (13) then determine the minimum detectable accelerations in the static and dynamic cases. The minimum detectable static acceleration can be equated with the peak minimum detectable dynamic acceleration or, since aN is an rms value,
The basic device configuration is shown in Fig. 1. Light was injected into a Dupont PiFax S120 type 30 200-μm core plastic clad fiber from an RCA C86007E pigtailed laser diode. The light at 0.82 μm passed from the fiber into a quarter pitch graded-index rod (GRINrod). This lens, bonded to the fiber with clear epoxy, served to collimate the light which then passed through a polarizer oriented at 45° to the normal and then through a ¼ wave plate to provide circular polarization. The light then passed through the active birefringent element, a 0.6- × 0.6- × 1.2-cm prism of Pyrex glass, which was rigidly bonded to the sensor housing with its long dimension parallel to the normal. A 16-g mass was bonded to the top of the prism
Fig. 2. Optical power throughput as a function of applied stress for photoelastic accelerometer.
which had a mass of 1.5 g. About two-thirds of the mass of the birefringent element contributed to the stress seen by the optical beam. The light was then captured by a second GRINrod and injected into the output fiber. The light leaving the output fiber was detected by an RCA C30808 photodiode with a 200-kΩ load resistor. The optical power level at the detector for no acceleration was 0.6 μW. The optical power level at the detector with the polarizer—¼ wave plate—birefringent element analyzer removed was 4 μW.
Two types of measurement were carried out. In the first, the response of the device to static loading was measured, as shown in Fig. 2. This allowed determination of the material fringe value ƒ. In the second measurement, both the fiberoptic accelerometer and a Bruel & Kjaer reference accelerometer, type 4371, were rigidly bonded to a Cleveland vibration table, model VP-7-2, and subjected to vertical acceleration with a principal mode at 100 Hz. Measurements were made with a Tektronix 7LS spectrum analyzer to determine signal and noise levels for both devices, as shown in Fig. 3. This allowed determination of the minimum detectable acceleration of the fiber optic accelerometer for the dynamic case.
As shown in Fig. 2, the quantity S0 was determined to be ~21.5 MPa. From Eq. (2) ƒ could then be determined, i.e., ƒ = 0.13 MPa/fringe/m. This value of ƒ determined α, i.e., α = 3.4 × 10 -5 sec2/m. Since the dc optical power level for a = 0 was I = 0.6 μW, the minimum detectable optical power could be determined from standard expressions.14 Carrying out this calculation yielded ΔI = 2.7 × 10 -13 W. Use of these values in Eq. (7) then gave the minimum detectable acceleration, Δa = 6.5 × 10 -3 m/sec2 = 6.5 × 10-4 g.
The second test of the sensor involved subjecting it to a sinusoidal acceleration at 100 Hz and analyzing the results via a spectrum analyzer. Results of this test are shown in Fig. 3. From the signal level of the reference accelerometer, the rms acceleration was found to be as = 0.48 g. From the signal-to-noise ratio obtained from the photoelastic accelerometer (R = 53 dB) the minimum detectable rms acceleration was determined from Eq. (13), i.e., aN = 1.1 × 10 -3 g. The minimum detectable peak acceleration of √2aN = 1.5 × 10-3g was then found to be within a factor of ~2 of the static minimum detectable acceleration Δa = 1.3 × 10 -3 g.
The active glass element in the sensor was then replaced by an element consisting of Thiokol Solithane 113 with dimen-
Fig. 3. Signal (a) and noise (b) characteristics of photoelastic accelerometer and reference accelerometer. Scales are: 10 dB/div vertical, 50 Hz/div horizontal, 0-500-Hz scan, 10-Hz bandwidth; top
of screen is -40 dBV for (a) and -60 dBV for (b).
sions 1.0 × 0.6 × 1.5 cm. The optical path length was 0.6 cm, and the detected optical power for zero acceleration was determined to be 160 nW. The material fringe value for the active element was found to be 104 Pa/fringe/m. The minimum detectable acceleration was then calculated as before, with the results that Δa = 1.6 × 10 -4 m/sec2 = 1.7 × 10 -5 g. The sensor was then subjected to a sinusoidal acceleration of 0.063 g (rms) at 30 Hz, and the SNR was found to be 71 dB, so that the minimum detectable acceleration was 1.8 × 10 -5
g (rms) or 2.5 × 10 -5 g (peak). This experimentally determined value is in reasonable agreement with the calculated value Δa = 1.7 × 10 -5 g.
It should be noted that the sensitivity of the Solithane 113 photoelastic fiber-optic accelerometer was in fact 10 dB greater than the sensitivity of the conventional Bruel & Kjaer accelerometer used as a reference for the present experiment. However, in spite of this very encouraging result, the demonstration of the concept feasibility nature of the present experiment should be emphasized. Indeed careful attention must be given to a host of details, such as structural design and choice of materials, to avoid hysteresis and provide stable response characteristics over normal environmental conditions.
To summarize: a multimode fiber-optic accelerometer has been described that is based upon the photoelastic effect. The device was shown to be able to detect accelerations down to 10 -3 g using glass as an active medium and 2.5 × 10 -5 g using Solithane 113. It is electrically passive and compatible with existing multimode technology and multiplexing techniques. Device sensitivity was shown to be able to be easily changed by changing the active birefringent material. The photoelastic transduction method used is easily transferable to the sensing of phenomena other than acceleration, such as pressure and acoustic waves, and these will be the subject of future papers. Such devices, when combined with the well-known benefits of fiber optics, can be attractive alternatives to available electrical sensors.
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