Optical fiber microbend horizontal accelerometer

A highly sensitive microbend horizontal fiber-optic accelerometer has been conceived, particularly useful in seismological research where minute accelerations must be detected. The device uses a cantilever beam and the compliance of an optical fiber mounted between deforming teeth to act as the springs in the accelerometer's spring-mass system. Acceleration is detected by sensing the changes in the intensity of light propagating through the deformed fiber due to the motion of the mass relative to the case. Accelerations as small as 5 .mu.g at 1 Hz can be detected with a dynamic range of 100 dB.

BACKGROUND OF THE INVENTION 
The microbending of an optical fiber has been considered a simple and 
rugged design approach for a highly sensitive motion detector. The 
components required for such a device are simple, inexpensive and easily 
obtained. All that is required is one optical fiber, a light source (such 
as an LED) and detector with associated control electronics, and a means 
of modulating the bends in the fiber. In order to take advantage of the 
sensitivity of the microbend approach, mechanical designs that take full 
advantage of the large dynamic range and the minute displacements involved 
must be considered. At the same time, the mechanical and optical 
limitations of the sensing mechanism must be dealt with. 
Sensors employing microbend technology are known in the art and reference 
is made to the Macedo et al U.S. Pat. No. 4,342,907. 
Fiber optic accelerometers are also known and the Davis et al Pat. No. 
4,322,829 is an example, as is the Nissl Pat. No. 4,226,120. 
SUMMARY OF THE INVENTION 
The fiber optic microbend accelerometer of the invention may be generally 
defined as including a rigid housing, a beam connected at one end to the 
housing, and a mass connected at the other end of the beam, the connected 
mass being free to move within the housing upon application of force to 
the housing in a direction normal to the plane of the beam. A pair of 
fiber deforming teeth sets mounted in opposed relation, one to the mass 
and the other to the housing, and an optical fiber positioned between the 
pair of teeth sets and in contact with the teeth.

DESCRIPTION OF PREFERRED EMBODIMENT 
Referring to FIG. 3, 10 generally designates a microbend fiber-optic 
accelerometer which includes a housing 12. From one wall of the housing, 
is attached a cantilevered beam 14 to the free end of which is attached a 
mass 16. The mass is free to move in the direction of the directional 
arrow 18 upon the application of a force F which is normal to the plane of 
the beam 14. Attached to one face 20 of mass 16 is a set of deforming 
teeth 22 and to the wall 24 of the case or housing 12 is mounted a 
complimentary set of deforming teeth 26. Between the teeth 22 and 26 is an 
optical fiber 28, the outer surface of which is in contact with the 
deforming teeth 22 and 26. 
Every optical fiber is sensitive to microbending, some more than others. 
The more sensitive fibers are those that have low cladding-to-core 
thickness ratios (low .delta.). It is also known that for a fiber there is 
an optimal spacing between deformations, 1.sub.c FIG. 1, that will produce 
the greatest change in transmission loss dT for a given depth of 
deformation dZ. For step-index fiber, the critical length that gives the 
greatest dT/dZ is given by the expression: 
EQU 1.sub.c =.sqroot.B2.times..pi. na/NA (1) 
where: 
a = fiber core radius 
n = index of refraction of core 
NA = numerical aperature of the fiber 
The microbend transducer in the accelerometer, FIG. 1, uses step-index 
multimode fiber having a core diameter of 120 .mu.m, with an aluminum 
jacket approximately 10 .mu.m thick. The NA is 0.2 and the refractive 
index of the core is 1.46. The value of 1.sub.c calculated from equation 
(1) is 1.95 mm. This is the spacing to be used in the sensor test. 
While a step-index multimode fiber was used in the test system, the device 
will work with graded index fiber and single mode fiber as well. 
The number of deformations of the fiber affects the mechanical stiffness of 
the sensor. A compromise between the fiber stiffness and the design 
resonance of 300 Hz led to the selection of 5 deformations. Values of 
fiber stiffness vs. the mechanical quiescent (bias) operating point were 
experimentally determined. A 300 Hz resonance was necessary to ensure an 
operational bandwidth of 1 to 100 Hz. The high sensitivity of a microbend 
sensor has been demonstrated in the laboratory using an LED as the light 
source, displacements as small as 0.04A at 800 Hz have been measured with 
a dynamic range of almost 90 dB over minimum detectable. To work as an 
accelerometer, the microbend sensor must be mass loaded with a system 
resonant frequency that is much greater than the bandwidth of interest. 
The equation of motion for a spring-mass system is: 
EQU my=-k(y-x)-c(y31 x) (2) 
where: 
k is the spring constant of the system 
y is the coordinate of the mass 
x is the coordinate of the case 
y,x are the respective velocities 
c is the damping coefficient 
y is the acceleration of the mass. 
If c=0 and .DELTA.Z is the displacement of the mass relative to the case 
(and also the depth of deformation of the fiber, where .DELTA.Z =y-x , 
then solving the equation of motion gives: 
EQU .DELTA.=(.omega./.omega..sub.n).sup.2 .DELTA.X/[1-.omega./.omega..sub.n 
.sup.2 ] (3) 
where: 
.omega.=2.pi.f=angular frequency of excitation 
.omega..sub.n =resonant frequency of the system 
.DELTA.Z=amplitude of the fiber deformation 
.DELTA.x=the accelerometer case displacement 
For the device to work as an accelerometer the excitation frequency .omega. 
must be well below the resonance. For equation (3) becomes: 
EQU .DELTA.Z=.omega..sup.2 .DELTA.x/.omega..sub.n.sup. (4) 
The absolute acceleration of the case is given by: 
EQU A.sub.case =.omega..sup.2 .DELTA.x (5l ) 
Combining equations (4) and (5) gives: 
EQU A.sub.case =.omega..sub.n.sup.2 .DELTA.Z (6l ) 
The minimum detectable acceleration, A.sub.min' for a shot-noise limited 
sensor is: 
EQU A.sub.mion =[2Th.nu..DELTA.f/qW.sub..degree. ].sup.178 
(.DELTA.T/.DELTA.A).sup.-1 (7) 
where 
T = optical transmission coefficient 
h = Planck's Constant 
v = light frequency 
.DELTA.f = detection bandwidth 
q = photodiode quantum efficiency 
W.sub.o T =light power incident on the photodetector .DELTA.T/.DELTA.A can 
be written as: 
EQU .DELTA.T/.DELTA.A =(.DELTA.T/.DELTA.Z)(.DELTA.Z/.DELTA.A) (8) 
where .DELTA.z/.DELTA.A is the fiber deformation resulting from the case 
acceleration A. From equation (6) it can be seen that 
.DELTA.Z/.DELTA.A.sub.case =1/.omega.n.sup.2 
EQU Thus, A.sub.min =[2Th.nu..DELTA.f/qw.sub.20 ].sup.1/2 .omega..sub.n.sup.2 
(.DELTA.T/.DELTA.Z).sup.-1 (9) 
The accelerometer bandwidth of interest was chosen to be 1 to 100 Hz. The 
resonance of the accelerometer was chosen to be at least 3 times the upper 
limit, or 300 Hz. To obtain this resonance frequency, the amount of mass 
and the stiffness of the system must be considered. Because the test 
device must measure horizontal acceleration, the microbend transducer 
cannot use gravity to position the mass on the moving deformers. This 
means that another compliant member must be present in the system to 
position the mass while allowing it to move relative to the case, and 
along only one axis. The resulting system is illustrated in FIG. 2. 
In FIG. 2, K.sub.1 is the spring constant of the fiber, K.sub.2 is the 
spring constant of the locating member, and M is the mass. This mass moves 
between these two springs. If K.sub.1 =K.sub.2 the natural frequency of 
the system is: 
EQU f.sub.n =(2.pi.).sup.-1 (K.sub.1 +K.sub.2)/M (10) 
For 5 deformations of the aluminum-coated fiber at relatively large 
quiescent depths, K.sub.1 has been measured to be 1.3.times.10.sup.9 
dyn/cm. For an easily predictable motion, the locating member is designed 
to have the same spring constant. The type of member chosen was a 
cantilever beam as shown in FIG. 3. This approach has several advantages. 
First, cantilever beam theory is well developed. It is a simple task to 
determine design dimensions that give the beam the required stiffness. 
Second, the beam positions the mass independently from the fiber so the 
initial quiescent can be set and reset easily by sliding the entire 
spring-mass assembly towards the deformers. Third, the cantilever can be 
designed to have its significant movement along only one axis, thereby 
reducing cross-axis sensitivity. By making the beam wider than it is 
thick, the beam has its highest compliance perpendicular to the beam's 
length. 
Several experiments were performed to investigate the performance of the 
accelerometer. Included in the tests were measurements of the device's 
frequency response, minimum detectable acceleration, and dynamic range. 
Shown in FIG. 4 is a block diagram of an experimental set-up. A calibrated 
PZT stack of known displacement (60.ANG./V) was used to excite the 
accelerometer. A Hewlett-Packard 3582A spectrum analyzer was used to 
record the results. 
Some results of the experiments are shown in FIGS. 5 and 6. The response of 
the device versus frequency for a constant acceleration is shown in FIG. 
5. As can be seen, the response is flat to within +1dB over the recorded 
frequency range. In FIG. 6, the output of the device for a 20 .mu.g 
acceleration at 8.8 Hz is shown. Also shown is the output of the device 
with no drive signal. As can be seen, the signal-to-noise is near 14 dB 
and thus the minimum acceleration measured at 8.8 Hz is near 4.mu.gs. 
Referring now to FIG. 7, the microbend sensor utilizes very simple and 
common electronics to power the unit and provide an output voltage 
proportional to the change in received light at the photodetector 40. 
The circuitry consists of three different sections, the first being a 
current source section 42 that powers the LED 44. Since the accelerometer 
is to be used as an AC device, low frequency (i.e. 0.5 Hz) in light level 
fluctuations are filtered from the signal, so a simple current regulator 
46 is all that is needed for the LED 44. 
The second section is a current-to-voltage converter 48 which has its input 
from the photodiode 40. This is a common device that uses an OP-AMP and a 
feedback resistor to gain the output of the photodiode and provide a 
voltage input to the filtering section 50. 
This third filtering section uses three filters in line to give the 
accelerometer the desired output characteristics. The first is a high pass 
with a roll-off frequency at 0.5 Hz. This eliminates the low frequency 
fluctuations in signal due to the LED output varying. Next, the signal is 
passed through a 100 Hz low pass filter to give the accelerometer the 
required operating bandwidth of 1 to 100Hz. The final filter is a 
notch-type used to defeat the signal at the mechanical system's resonant 
frequency of 320 Hz. The output of this filter is the output of the sensor 
.