Note: Descriptions are shown in the official language in which they were submitted.
Description
Fiber Optic Strain Sensor
Technical Field
This device relates generally to optical wave-
guide sensor, and more particularly, to an optical
waveguide having at least two cores particularly
shaped and positioned in a common cladding so that
the light is coupled, or cross-talks, between the
adjacent cores as a function of strain or hydro-
static pressure only thereby causing the opticalwaveguide to act as a strain or hydrostatic pressure
sensor.
Background Art
Optical waveguides have been known for many
years and, with the advent of low loss glasses,
devices incorporating optical waveguides have been
employed in ever-increasing numbers, in many differ-
ent fields such as communications and monitors. An
optical waveguide typically consists of a dielectric `-
core fabricated from a glass, or the like, having a
certain refractive index, and this core is surrounded
by a second material, also normally glass or the like,
having a lower refractive index. This surrounding
material is generally known as the cladding. A beam
of light is guided by this composite structure so
long as the refractive index of the material comprising
the core exceeds the refractive index of the material
forming the cladding. A light beam within the core
is guided generally along the core axis by reflection
of the boundary between the core and the cladding.
A number of different designs for optical wave-
guides have been proposed including the multimode
step index profile, the single mode profile, and the
multimode graded index profile. Where a single mode
R-2~j8A
q~
--2--
is desired, the single mode optical waveguide is
used. In such a waveguide, the diameter of the core
is typically less than 10 ~m and the difference
between the refractive indices of the cores and
the cladding is on the order of 10 3. As a result,
only the lowest order mode will be supported in such
a waveguide.
Optical cables have also been fabricated which
include multiple cores disposed in numerous different
arrays and positioned within a common cladding. One
such disclosure is contained in U.S. Patent No.
4,148,560 issued April 10, 1979 to D. Margolis for
OPTICAL GUIDES. This disclosure is directed toward
an assembly including a plurality of fibers embedded
in an encapsulating material. This particular patent
shows an optical bundle positioned between two rein-
forcing wires and embedded in a protective sheath
of plastic material.
The phenomena known as "cross-talk" between
cores in a common cladding occurs when the light
energy propagating along one core is coupled to an
adjacent core. This occurs because, as is known,
the light energy is not totally confined by the
boundary between the core and cladding but, in
fact, it penetrates to a small degree into the
cladding.
It has been recognized that the cross-talk
phenomena in a waveguide having at least two cores
will vary to some extent as a function of tempera-
ture. For example, in a treatise entitled OPTICALWAVEGUIDES by N. S. Kapany and J. J. Burke published
in 1972, it was recognized that in two closely spaced
glass fiber cores positioned in a cladding experienced
an optical beat phenomena. Beginning on page 255,
there is an experiment described in which the optical
beat phenomena of the aforementioned optical wave-
guide varies in response to changes in the ambient
temperature.
A temperature sensor employing an optical wave-
guide is described in U.S. Patent No. 4,151,747 issued
May 1, 1979 to M. Gottlieb et al for MONITORING
ARRANGEMENT UTILIZING FIBER OPTICS. A temperature
sensor consists of an optical waveguide. A light
source is positioned at one end of the waveguide and a
detector is located at the other end. Temperature
changes are then perceived by variations in the light
received at the detector. Another embodiment in-
cludes two optical fibers positioned adjacent each
other in a common cladding. Input light is conducted
along the length of one fiber and passes out of the
wall of that fiber in an amount which varies with the
temperature of the fiber. The second fiber is in
sufficiently close proximity to the first fiber for
capturing at least some of the light passing out of
the first fiber. By monitoring the light received
in the second fiber, a determination can be made as to the
amount of temperature variation.
0f interest is U.S. Patent No. 4,278,794, FIBER
OPTIC HOT SPOT DETECTOR, issued November 3, 1981, by the
same parties as the applicants herein, which describes an
optical fiber that can be embedded in a cable, or the like,
to detect hot spots. A plurality of cores in the common
cladding are particularly shaped and spaced from each
other so that cross-talk initially occurs at the point
where the temperature exceeds a predetermined level. The
wavelength of the light propagating along the fiber can
30 be changed so that the precise point of the hot spot along
the cable can be identified.
Disclosure of Invention
It is an object of the present invention to pro-
vide an optical waveguide which is particularly well
A
suited to measure changes in hydrostatic pressure or
strain independent of any temperature change.
According to the present invention, an optical
waveguide having two or more cores is fabricated in
a manner so as to optimize the response to variation
in strain or hydrostatic pressure.
In accordance with a particu'ar embodiment of the
invention, a strain monitor comprises: strain responsive means
including an optical fiber positionable where strain is to be
measured, said optical fiber having a plurality of cores which
are spaced apart from each other in a cladding, said cladding
and each of said plurality of cores being sized and fabricated
from such materials as to support only the lowest order pro-
pagation mode, thereby allowing cross-talk to occur between
said cores' source means for generating light to be coupled
into one of said cores, said light being cross-talked to adja-
cent cores in a manner related to strain acting on said optical
fiber, detector means for receiving light energy emerging from
each of said plurality of cores, and for providing an
electrical signal related to the intensity of said emerging
light, and whereby a strain acting on said optical fiber causes
a change in the dimensions and refractive indices of said
plurality of cores and said cladding such that mode interference
between the modes of propagating light energy within said
plurality of cores produces a change in the intensity of light
emerging from said cores which is uniquely related to such
strain acting on said optical fiber.
According to a feature of the present invention,
an optical waveguide has a plurality of cores which are
fabricated from selected materials and formed in such a
manner that cross-talk between adjacent cores is primarily
a function of strain or hydrostatic pressure, and is
relatively unresponsive to changes in temperature. As light
energy propagates along one core in the optical fiber, changes
in strain or in hydrostatic pressure cause a change in the
relative energy that is cross-coupled between the cores.
- 4a -
A significant feature of the present invention is
that an optical waveguide having multiple cores can be so
fabricated that cross-talk between adjacent cores is a function
of hydrostatic pressure or strain independent of any variation
in temperature. Light energy propagating along one core then
is coupled, or cross-talk, to adjacent cores only as a function
of hydrostatic pressure or of strain thereby optimizing the
optical waveguide as a strain sensor.
The foregoing and other objects, features and
advantages of the present invention will become more
apparent from the following description of preferred embodiments
and accompanying drawings.
Brief Description of Drawings
Fig. 1 is an enlarged schematic illustration de-
picting a pressure measuring system incorporating an
optical fiber according to the present invention which
has been optimized to sense changes in hydrostatic pressure
.
Fig. 2 is an end view of the optical fiber
according to the present inven~ion depicted in Fig. l;
Figs. 3A-3D are schematic illustrations of
possible modes that can exist in the optical fiber
according to the present invention depicted in
Fig. l;~ -
Fig. 4 is an end view of a second embodiment of
an optical fiber according to the present invention
which includes a second cladding; -
Fig. 5 is an end view of a third embodiment of
an optical fiber according to the present invention
which includes a second cladding and a third cladding;
Fig. 6 is a fourth embodiment of an optical
fiber according to the p-esent invention having
multiple cores for providing an unambiguous response
to a wide range of hydrostatic pressure changes;
Fig. 7 is a graph depicting the relative light -
intensity as a function of beat phase of light energy
propagating along a five-core fiber;
Fig. 8 is a strain sensor which includes an
optical fiber according to the present invention
that has been attached to a deflectable substrate
for measuring deformation of such a substrate; and
Fig. 9 is a cross-sectional view of the optical
fiber depicted in Fig. 7.
Best Mode for Carrying Out the Invention
Referring initially to Fig. 1, there is an
optical waveguide 10 according to the present inven-
tion which has been optimized to respond to changesin strain or hydrostatic pressure along its length,
independent of any changes in temperature. The
optical fiber includes at least two cores 12 and 14
which are ideally arranged in an array across the
--6--
diameter and extend along the entire length of the
optical cable 10. A cladding 16 is provided and
totally surrounds each of the cores 12 and 14
throughout the length of the cableO Both the cores
12 and 14 and the cladding 16 are typically fabri-
cated from a glass material, or the like, and the
selection of the precise material from which the
core and cladding are fabricated, the size of the
cores, the exact spacing separating the cores, the
number of cores, etc., are critical and form a
significant part of the present invention, as will
be more apparent hereinafter.
The optical waveguide of the present invention
is optimized to respond to strain or hydrostatic
pressure and, as such, is particularly well suited
to functioning in a system which is to measure either
strain or hydrostatic pressure at some remote point.
Such a system would include a source 18 located to
couple a beam of light energy into one of the two
cores, such as core 12. The optical fiber 10 leads
from the location of the light source 18 to a second
location, such as in a container 20 where a physical
parameter, such as hydrostatic pressure, is to be
measured. From the second location, the optical
fiber leads to another location where the emerging
light from both the cores 12 and 14 is presented
to the intensity of light energy incident thereon.
Referring to Fig. 2 in addition to Fig. 1, as
is known so long as the refractive index of the
cladding 16 is less than the refractive index of each
of the cores 12 and 14, light energy entering either
core will be substantially passed by the optical
fiber 10. The number of distinct modes that will
exist in the cores 12 and 14 is a function of the
refractive indices of both the core material and
the cladding material, the dimension of each core,
J~
--7
and the wavelength of light propagating through the
waveguide. For a circular cross section for the
core, the nun~er of modes that can exist is deter-
mined by the V parameter, which is given by the
relationship:
V = 2~ (a/~) ~ (1)
where a is the radius of the core, ~ is the light
wavel~ngth, nl is the refractive index of the core,
and n2 is the refractive index of the cladding.
For the preferred elliptical cross section of the
present in~ention, it is sufficient to take Equation
(1) for the V parameter but with the value of a now
given as the geometric average of the semi-major and
semi-minor axis of the elliptical core dimensions.
If V is less than 2.405 (the first zero of the
Bessel function, J0) then only the lowest order mode,
known as the HEll mode, can be supported. For values
of V that are much larger than 2.405, this occurring
when the average diameter 2a of each core 12 is much
larger or the difference between the refractive
index of the core and that of the cladding is greater,
then many modes will be supported by the waveguide.
As briefly mentioned heretofore, a significant
feature of the present invention is the strain or
hydrostatic pressure dependence and temperature
independence of cross-talk between the individual
cores in a multicore waveguide, this characteristic
allowing strain or hydrostatic pressure along the
length of the fiber to be measured. In such a wave-
guide, the materials from which the core and thecladding are carefully selected and would have
refracti~e indices for the cores and cladding of n
and n2, respectively. The spacing separating each
core is relatively small while the outer diameter of
the cladding is large so that interactions at the
boundary formed by the outer wall of the cladding
does not affect the light distribution within the
cores. It is also necessary that the light propagate
in each core in only the lowest order mode, the
HEll mode, in accordance with the aforementioned
Equation (1).
Referring still to Figs. 1 and 2, as mentioned,
the light source 18 emits a beam of light energy
which is incident on only one of the two cores of
the array, such as core 12. The light is preferably
polarized in the same direction as the shortest axis
of the elliptical core. As the light propagates down
the fiber, cross-talk occurs to the core 14 as a
function of hydrostatic pressure or strain. Thus,
the distribution of light Il, I2 from the exit face
of the fiber is a function of the strain or hydro-
static pressure acting on the fiber. The detectors
22 contain polarization analyzers so as to respond
only to the same polarization as was incident on
core 12. It has been found that in some cases
elliptical cores oriented with their long axis
parallel to each other and perpendicular to the line
joining the core centers provide stronger coupling
between cores for the same core area and center-to-
center spacing than is the case for cores of circularcross section.
A significant aspect of the present invention
relates to the change in the distribution of light
energy between the cores 12 and 14 as a function of
change in strain or hydrostatic pressure on the
optical fiber 10. The following may be helpful in
understanding this phenomena. The four normal modes
which can be guided are plain polarized with the
transverse E-fields aligned parallel or perpendicular
to a line connecting the center of the cores.
Referring additionally to Fig. 3, the four modes
that can be supported comprise two orthogonally
1;~
g
polarized pairs, a symmetric pair, Fig. 3A and Fig.
3B, and an anti-symmetric pair, Fig. 3C and Fig. 3D.
Because only core 12 is excited by light eneryy from
the source with its polarization parallel to the
line connecting the centers of the core, the sym-
metric composite mode, Fig. 3B, and the anti-
symmetric composite mode, Fig. 3D, are launched with
equal intensities. As the light energy propagates
down the core, cross-talk occurs and the phase rela-
tionship of the modes are such that light energy istransferred between adjacent cores. As light propa-
gates along the waveguide, modal interference causes
a beat phenomena producing spatial interference that
can be analyzed as an energy flow between adjacent
cores. As stated above, the normal modes of the twin-
core fiber are linear combinations of the lowest
order HEll single core excitations. A normal mode
is a field distribution which propagates along the
fiber axis without change in its cross-sectional
intensity pattern. The z (fiber axis) and time
dependencies of a normal mode are given by a simple
harmonic function Re [exp {i(~t ~ ~iZ)]' where
Re [...] denotes the real part of the quantity in
brackets and the propagation constant ~i has a sub-
script i to designate the various possible HEllcombinations, Figs. 3A-3D. There are four distinct
field distributions which constitute the possible
normal modes of the twin-core fiber. They consist
of two orthogonally polarized, symmetric and anti-
symmetric pairs (see Fig. 3). Let ~i' i = 1, 2, 3,4, designate the amplitudes of the four normal modes.
Illumination o~ a single core is equivalent to excita-
tion of a pair of modes; namely, a symmetric and anti-
symmetric combination having the same polarization.
If ~2 and ~4 are taken as the propagation constants
for the symmetric mode, Fig. 3B, and the anti-
symmetriF mode, Fig. 3D, the division of energy
--10--
between the two cores is a function of the difference
2~ 2-~4 and the distance along the fiber. At a
distance Zl = ~/(2~), the two composite modes, Fig.
3B and Fig. 3D, are exactly 180 out of phase and all
the light is in the right core. Fo~ a distance less
than Zl some of the light is in both cores, and simi-
larly for greater distances where the phase difference
between modes continues to increase. At a distance
Z2 ~ 2zl, the composite modes are exactly in phase,
as they were at the entrance face; and the light
returns to the left core. As the light propagates
along the twin-core fiber, mode interference causes
a beat phenomena producing spatial interference that
can be thought of as energy interchange between cores.
The beat wavelength ~b is ~ . For two circular
cores of radius a with a center-to-center spacing of
d, the beat wavelength is given by:
~an,
b NA F(V,dJa) ( )
where
F = (U /V3) K0(Wd/a)/Kl (W) (3)
- ~ = tv2_u2) (4)
4 ~
U = (1+~2)V/[1+(4+V ) ] (5)
The Ro and Kl are the modified Hankel functions of
order ~ero and one, respectively, and d is the center-
to-center separation between cores.
A change in hydrostatic pressure or strain in
general causes a change in ~b and an expansion or
contrac.ion of the fiber length L. The net effect
is a corresponding varia,ion in the beat phase
~ -L at the end of the fiber of initial length L.
For complete cross-talk, i.e., total power transfer
from the first to the second core, it is necessary
that the phase velocities for the propagation in
the two cores have the same size and indices o~
refraction. However, it is also possible to have
two cores of different glasses with different
reractive indices, and correspondingly different
sizes, with the same phase velocities at the wave-
length of operation of the fiber. For two circular
cores in a common cladding, the rate of change of
beat phase with temperature is given by:
d~ ~ L V ddv (a+~) (6?
where a and ~ are, respectivel~, the the-mal coeffi-
cients of linear expansion and of the inaex of
refraction (n 1 dn/dT) for hoth core and cladding,
i.e., these material properties have been assumed
to be the same for the core and cladding in this
~.
-12-
ex~mple of the present invention. For a cha~ge in
temperature, there will be a change ir. dimensions
of the fiber and a change in indices of refraction
for cores and cladding. In general, both the thermal -
5 expansion coefficients and thermal coefficients ofrefractive indices for core and cladding materials
are different; however, to simplify the present dis-
cussion the core and cladding thermal material proper-
~ies have been assumed to be alike.
o If the assumption is made .hat the material
parametess and ~ are the same for the c~re and
cladding material3, the condition that the beat
- phase ~ be independent of temperature is given by:
dV (7
15 This is the same condition that applies ~or the beat
phase to be independent of uniform hydrostatic pres-
sure. ~ence, a temperature independent pressure
measurement based on observing the change in cross-
t~lk cannot be made with a fiber in which the mate-
20 rials from which the cores and cladding are madehave identical values for a and ~. If c and ~ differ
for the cores and cladding, it is possible to make
be independent of terperature but still depend on
the uniform hydrostatic pressure. Alternatively,
25 a and ~ can be the same for the cores and cladding,
but a second cladding is fused onto the outside of
the fiber as will be described hereinafter. For a
proper choice of material and thickness of the
second cladding and choices for the cores and
30 first cladding mate~ials and their geometries, the
,, r
-13-
beat phase for cross-talk between cores can be made tem-
perature independent but also show a dependence on uni-
form hydrostatic pressure. For the case of stretch
along the fiber axis, the cores with only one cladding,
in which a and ~ are the same for cores and cladding,
can be~made to give a dependence of the beat phase on
the magnitude of the longitudinal stress but be inde-
pendent of both temperature and uniform hydrostatic pres-
sure. Similarly, unidirectional stress applied trans-
verse to the fiber axis can give a change in beat phasefor the light leaving the fiber with the fiber consis-
ting of cores and a single cladding whose ~ and ~ values
for the materials of which they are made are the same
and for which the V value and the d/a ratio are chosen
so as to make the beat phase independent of tempera-
ture and uniform hydrostatic pressure.
Referring still to the single cladding embodiment
of Figs. 1 and 2, there are two identical cores of aver-
age radius a and center-to-center spacing d in a single
uniform cladding. The material parameters for the cores
are nl, ~ and ~1 and the parameters for the cladding n2,
~2 = ~ and ~2' i.e., only the temperature coefficients
for the refractive indices are taken as different for
the refractive indices are taken as different for the
cores and cladding. The condition for temperature in-
dependence for the beat phase is then:
IV dF~ I n2 (~ 2)
~ ~ lo (nl -n2 )~+nl ~1-n2 ~2 (8)
where the vertical line with a zero subscript indicates
temperature independence. In a response to a cylindric-
ally symmetrical elastic deformation, the fractionalchange in be at phase ~ for the light exiting from
the end of the fiber is:
S j~
n22 ~~nl ~n2
Z r n ' n2 ~ 1 n2J
_
V dF ~nl n2 ~nl ~n2~
F dV ~r + nl + 2 2 ~nl ~ n2! (9)
where E and ~ are the longitudinal and radial strains,
which for uniform hydrostatic pressure P and for core
and cladding materials whose Youngs modulus is
El - E2 = E and Poisson's ratio is vl = v2 = v, and
are given by:
,^ = ~ = - (1-2v) P/E. (1~)
In response to an elastic deforma,ion the indices of
refraction change. In general, the index of refrac-
tion for a given state of polarization is a linear
function of the three principal strains. Let the
strain-optic coefficient for the strain parallel to
the polarization be given by P11 and the coefficien,,
for the strain perpendicular to the polarization be
given by P12- Furthermore, although the temperature
dependence of the indices of refraction for core and
cladding materials have been taken to be different, -
i.e., ~ 2~ for simplicity in this discussion the
strain-optic effects in the core and cladding mate-
rials are he.e assumed to be equal. The changes in
indices of refraction in response to the uniform
hydrostatic pressure are then gi~-en by:
hn2 ~,~nl nl Pll 2pl2) (1-2 )P/E (11)
.
.
"~
l~ith equations (lO)and (11) substituted into Equa-
tion (9), the change in beat phase is:
~ F dV [ 2 (Pll P12~ ( 2v)P/ (12)
. .
If the beat phase is made temperature independent,
5 the materials and geometry are chosen so that (V/F)
(dF/dV) is given by the right side of Equation (8);
and the final result for the temperature independent t
beat phase,which however does depend cn uniform L:
hydrostatic pressure,is given by: ,t
0 1 2 ~a+nl ~1~n~2~2 [ 2 (P11+P12¦ (1-2~)P/E
Independent of whether the values for ~ and ~ are the '.
same for core and cladding materials, the beat phase
can be made dependent on uniform hydrostatic pressure
but independent of temperature in a different way.
15 Referring to Fig. 4, a second cladding of thickness t
is fused onto the outside of the first cladding as
shown. The radius of the first cladding is g and the
radius of the second cladding is h. Although the cores
and first cladding could have thermal expansion coef- E
20 ficients that are different, it is sufficient for this
discussion to assume that al = a2, but that the thermal
expansion coefficient of the second cladding a3 be
different than a2. The Youngs modulus E and the
Poisson's ratio v are each assumed to be the same for
25 all three regions. The condition for temperature in-
dependence of the beat phase is then:
-16 - .
, .
(F d~ +V ) ( C~3 ~ ~ 2 ) ( l-g 2 /q 2
0~2 (1-v)n2 (nl -n2 ) t~l ~2~
X ~(1-3v)(~3-2)(1-g /h ) -1
+2(1-v) [C~2+~1+n2 (nl -n2 ) (~ ;2)~ '-
(14)
This expression can be derived by applying the boundary
conditions for strains resulting from the double clad
configuration.
The change in beat phase due to uniform hydro-
static pressure is given by Equation (9) with:
~n2 ~nl nl2
n2 nl 2 (Pll 2P12)~r r (15)
and
fr = ~z = -(1-2V)P/E , (16) !:
but with (VF 1dF/dV) given by Equation ( 14) . The
second cladding 96 can be of any material whose
expansion coefficient differs from the expansion
coefficient for the first cladding 94. The pre- .
ferred material, because of its stability, is glass;
however, it is possible to use a metal or a plastic
material as well, the key requiremen~ being that
the expansion coefficient for the second cladding 96
be different from the first cladding 94. If glass is
used as the second cladding 95, it may be desirable
to add still another ot third cladding. The glasses
co~monly used for low-loss fibers for telecommunica- -
tions and for sensors frequently involve very
-l7-
high percentages of fused silica. This material has
a low expansion coefficient, so of necessity, in
order to obtain a second cladding with a different
expansion coefficient, it would be necessary to use
a material which has a higher coefficient of thermal
expansion. This is undesirable because it puts the
outer surface under tension in the finished fiber
and thereby creates a potential problem of fiber
fracture. To avoid this problem of the outer sur-
face being under tension, one can add an additionalcladding whose expansion coefficient ~4 is less than
the expansion coefficient a3 for the second cladding.
The thicknesses for the two additional claddings in
relation to the radius for the first cladding would
have to be adjusted so as to give the necessary zero
temperature dependence and still obtain the required
dependence on uniform hydrostatic pressure or on
unidirectional longitudinal or transverse strain.
Figure 5 shows an embodiment of this invention in
which the two cores 100 and 102 are surrounded by
a first cladding 104, a second cladding 106 and a
third cladding 108.
For stretch along the fiber axis, the structure
with one cladding,and with a and ~ values the same
for core and cladding materials, can give a tempera-
ture independent strain measurement. In this case,
Equation (9) applies but with ~nl/nl - ~n2~n2
dV ~ , z = T/E and ~r = -vT/E, where T is the
axial tensile force. The result is:
(~ = (l+v)T/E . (17)
t~
-18-
Referring next to Fig, 6, there is seen another em-
bodiment of an optical fiber according to the present
invention which is well suited to operating in a system
for measuring the strain or hydrostatic pressure
at a locatio~ along the leng~h of the fiber. This
embodiment includes multiple cores and is well --
suited to measuring strain or hydrostatic pressure
~here a wide range of unambiguous readingsare needed.
Ar. optical fiber 50 has a plurality of cores 52 which -
are preferably elliptical-shaped in the same manner
~s described in the dual core case herebefore. A
first cladding 54 totally surrounds each of the
cores 52 throughout the length of the optical fiber
50. A second cladding 56 is positioned along the
entire length of the optical fiber on the first
cladding 54.
The optical fiber 50 extends through the location --
where the hydrostatic pressure, such as in a con- -
- tainer 58, is to be measured. At the input end of
the optical fiber, a source 60 directs a beam of
light energy toward an end face of one of the cores
52 so that the beam of energy can ~e coupled into
and guided along the axis of the incident core. At
the output end of the fiber the light energy emerges
from each of the cores and is presented to a detector,
such as detectors 62, 64 an~ 66 crea~ing a series of .
electrical signalsthat varies as the distribution of
light energy emerging from the exit face of the
optical fiber in the same fashion as described here-
before. The input light energy is preferably polar-
ized where the primary axis of interest is along tne
short axis of the ellipse and the detectors 62, 64
and 66 include polarizing filters, or equivalent, so
that the electrical signal representing the distribu-
tion of lisht energy emerging from the fiber is prim-
arily related to the light energy along the same axis.
ti~.~, h
--19--
In the same manner as described heretofore, a
significant feature of the present invention is that
the optical fiber 50 can be fabricated so as to be
responsive to strain or hydrostatic pressure and at
the same time be nonresponsive to temperature through
the selection of material for the cores 52 and clad-
dings 54 and 56, size of the cores 52, spacing between
adjacent cores, etc. As a result, light energy propa-
gating through one core will be cross-talked, or
cross-coupled to adjacent cores as a function of
hydrostatic pressure at a predetermined location
along the length of the fiber. This particular multi-
cored embodiment provides, among other things, a larger
unambiguous range for hydrostatic pressure measurements
than can be obtained by using just two cores.
The hereabove discussion of the relationships
in the dual core case can be extended to the multi-
core array by considering the interactions between
adjacent cores. It will be appreciated that the use
of an increasing number of cores 52 increases the
useful range of measurement without decreasing the
sensitivity of the optical fiber 50 to changes in
strain or hydrostatic pressure. Assuming a linear
array of equally spaced cores 52, one core will be
illuminated with light of intensity Io~ The inten-
sity of light I(M, R) emerging from the M'th core
for illumination of the R'th core only for a fiber
of length L is given by:
-20-
2 2 N
I (M, R) = Io (N+1) r~q=l sin [r~R/(N+l)]
x sin [q~R/(N+l)]
x sin [r~M/(N+l)]
x sin [q~M/(N+l)]
x cos [~L/~b (~q ~r)]
(18)
where ~q = 2 cos [q~/(N+l)]
and M, R =-1, 2, ..., N.
For the case of five identical cores with one
of the cores illuminated, the distribution of light
as a function of L might appear as shown in Fig. 7.
The relationship of the distribution of light energy
emerging from the optical fiber 52 as a function of
strain or hydrostatic pressure can be observed from
Fig. 7. It should be noted that the abscissa L/~b
is the same as 1 times the beat phase ~. The dis-
tribution of light energy emerging from the ends of
the core as a function of pressure or strain can be
obtained by noting that the beat phase ~ is a
linear function of hydrostatic pressure or strain,
so that the abscissa is equivalent to the pressure.
For example, at Pl the light distribution from the
cores 52 is shown by the line Pl in Fig. 7. At
pressure P2 the light distribution is shown by the
line P2 and the pressures intermediate between P
and P2 have corresponding distribution of light
energy as appear between the lines Pl and P2.
Numerous embodiments of a strain or hydrostatic
pressure measuring system employing one of the here-
tofore described embodiments of an optical fiber are
possible. For example, referring to Fig. 8, there is
shown an embodiment that is particularly well suited
to responding to a bending strain. An optical fiber
-21-
70 is fixedly attached, by cement or other comparable
adhesive, to one face of a support element 72. The
support element 72 would be rigidly held at one end
(bottom end in the drawing) while the other end
would be free to flex or bend through a predetermined
range (shown in phantom) in response to an applied
force H. The support 42 has its dimension L2 long
compared to the dimension Ll for greater sensitivity
to the force H. A source 74 of light energy is
positioned at the inlet end of the fiber so that light
is coupled into one of the cores. A detector 76 is
positioned at the exit end of the fiber 70 to measure
the light distribution as it emerges from each of
the cores and provides an output electrical signal
which is proportional to such light distribution.
The variation in flex of the support 72 creates
corresponding changes in strain on the optical fiber
70. In turn, as heretofore described, this change
in stress varies the cross-talk between adjacent
cores which is related to the change in intensity
of light emerging from the optical fiber 70.
Although this invention has been shown and
described with respect to a preferred embodiment, it
will be understood by those skilled in this art that
various changes in form and detail thereof may be
made without departing from the spirit and scope of
the claimed invention.
