Shape measurement system and shape measurement method
A shape measurement system and method for a three-dimensional shape of a linear object over a long distance with high resolution. The shape measurement system comprises: a multicore optical fiber having a center core positioned in the center of the cross section thereof and three or more outer peripheral cores positioned at equal intervals concentrically with respect to and outside of the center core; a measurement device for measuring the backward Brillouin scattered light distribution in the propagation direction of each core of the multicore optical fiber; and an analysis device for calculating position coordinates, in three-dimensional space, of a linear structure having an unknown three-dimensional shape from the backward Brillouin scattered light distributions of a multicore optical fiber positioned along the linear structure having an unknown three-dimensional shape and a multicore optical fiber positioned along a linear structure having a known three-dimensional shape.
1. A shape measurement system comprising:
a multi-core optical fiber including a center core arranged in a center of a cross section of the multi-core optical fiber and three or more outer peripheral cores arranged at equal intervals on an outside of the center core and in a concentric manner;
a measuring device that measures a backward Brillouin scattering light distribution in a propagation direction of each core of the multi-core optical fiber; and
an analysis device that computes positional coordinates in a three-dimensional space of a linear structural object having an unknown three-dimensional shape from the backward Brillouin scattering light distribution of the multi-core optical fiber arranged along the linear structural object having the unknown three-dimensional shape and the multi-core optical fiber arranged along a linear structural object having an already-known three-dimensional shape.
2. The shape measurement system according to claim 1 , wherein
when a position in a longitudinal direction of the multi-core optical fiber is defined as z,
the analysis device performs:
calculating a difference in strain at the position z as a difference between a strain amount at the position z of each core of the multi-core optical fiber obtained from the backward Brillouin scattering light distribution when the multi-core optical fiber is arranged along the linear structural object having the unknown three-dimensional shape and a strain amount at the position z of each core of the multi-core optical fiber obtained from the backward Brillouin scattering light distribution when the multi-core optical fiber is arranged along the linear structural object having the already-known three-dimensional shape;
calculating a bending strain ε of each of the outer peripheral cores by subtracting the difference in strain of the center core from the difference in strain of each of the outer peripheral cores;
calculating a curvature κ and a bending angle β at the position z of the multi-core optical fiber from the bending strain ε of each of the outer peripheral cores using a relational expression (1); and
computing positional coordinates in the three-dimensional space of the linear structural object having the unknown three-dimensional shape from the curvature κ and the bending angle β at the position z using Frenet-Serret formulas;
ε= r· κ·cos(α−β) [Relational Expression (1)]
where r is a center-to-center distance between the center core and the outer peripheral cores, and α is an angle representing a position of the outer peripheral core on a cross section of the multi-core optical fiber.
3. The shape measurement system according to claim 1 , wherein
the multi-core optical fiber is provided with an already-known twist, and
when the positional coordinates are computed, the analysis device estimates an unintended twist generated when the multi-core optical fiber is arranged along the linear structural object having the unknown three-dimensional shape, based on a twisting strain generated in the multi-core optical fiber and a strain by the already-known twist, and removes an influence by the unintended twist.
4. The shape measurement system according to claim 3 , wherein
when a position in a longitudinal direction of the multi-core optical fiber is defined as z,
the analysis device performs:
calculating a difference in strain at the position z as a difference between a strain amount at the position z of each core of the multi-core optical fiber obtained from the backward Brillouin scattering light distribution when the multi-core optical fiber is arranged along the linear structural object having the unknown three-dimensional shape and a strain amount at the position z of each core of the multi-core optical fiber obtained from the backward Brillouin scattering light distribution when the multi-core optical fiber is arranged along the linear structural object having the already-known three-dimensional shape;
calculating a bending strain ε bending,i of each of the outer peripheral cores by subtracting the difference in strain of the center core from the difference in strain of each of the outer peripheral cores;
calculating a curvature κ and a bending angle β at the position z of the multi-core optical fiber from the bending strain ε bending,i of each of the outer peripheral cores using a relational expression (2) of removing an influence by the unintended twist; and
computing positional coordinates in the three-dimensional space of the linear structural object having the unknown three-dimensional shape from the curvature κ and the bending angle β at the position z using Frenet-Serret formulas;
ε bending,i =k 1 κr cos(ω i −β) [Relational Expression (2)]
where r is a center-to-center distance between the center core and the outer peripheral cores, k 1 is a correction coefficient of a twist expressed by Formula (3), v is a Poisson's ratio of the multi-core optical fiber, a i is an initial angle of a core i, ω i is an angle representing a position of the outer peripheral cores on a cross section at the position z of the multi-core optical fiber expressed by Formula (4), p is a spin rate of the outer peripheral cores, ε twisting is a twisting strain generated at the position z of the multi-core optical fiber, φ(z) is a specific angle of twist at the position z of the multi-core optical fiber expressed by Formula (5), and k 2 is a correction coefficient of a twist expressed by Formula (6)
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5. The shape measurement system according to claim 4 , wherein
the analysis device computes a spin rate p of the outer peripheral cores from a cyclic fluctuation of the bending strain ε bending,i of each of the outer peripheral cores.
6. The measurement system according to claim 1 , wherein
in the multi-core optical fiber, a count of the outer peripheral cores is three, and a cladding diameter is 375 μm or more.
7. The measurement system according to claim 1 , wherein
in the multi-core optical fiber, a center-to-center distance between the center core and the outer peripheral cores is 120 μm or more.
8. A shape measurement method comprising:
arranging a multi-core optical fiber having a center core arranged in a center of a cross section of the multi-core optical fiber and three or more outer peripheral cores arranged at equal intervals on an outside of the center core and in a concentric manner along a linear structural object;
measuring a backward Brillouin scattering light distribution in a propagation direction of each core of the multi-core optical fiber; and
computing positional coordinates in a three-dimensional space of a linear structural object having an unknown three-dimensional shape from the backward Brillouin scattering light distribution of the multi-core optical fiber arranged along the linear structural object having the unknown three-dimensional shape and the multi-core optical fiber arranged along a linear structural object having an already-known three-dimensional shape.
9. The shape measurement method according to claim 8 , comprising:
defining a position in a longitudinal direction of the multi-core optical fiber as z when computing positional coordinates in a three-dimensional space of the linear structural object having the unknown three-dimensional shape;
calculating a difference in strain at the position z as a difference between a strain amount at the position z of each core of the multi-core optical fiber obtained from the backward Brillouin scattering light distribution when the multi-core optical fiber is arranged along the linear structural object having the unknown three-dimensional shape and a strain amount at the position z of each core of the multi-core optical fiber obtained from the backward Brillouin scattering light distribution when the multi-core optical fiber is arranged along the linear structural object having the already-known three-dimensional shape;
calculating a bending strain ε of each of the outer peripheral cores by subtracting the difference in strain of the center core from the difference in strain of each of the outer peripheral cores;
calculating a curvature κ and a bending angle β at the position z of the multi-core optical fiber from the bending strain ε of each of the outer peripheral cores using a relational expression (1); and
computing positional coordinates in the three-dimensional space of the linear structural object having the unknown three-dimensional shape from the curvature κ and the bending angle β at the position z using Frenet-Serret formulas;
ε= r ·κ·cos(α−β) [Relational Expression (1)]
where r is a center-to-center distance between the center core and the outer peripheral cores, and α is an angle representing a position of the outer peripheral cores on a cross section of the multi-core optical fiber.
10. The shape measurement method according to claim 8 , wherein
the multi-core optical fiber is provided with an already-known twist, and
when the positional coordinates are computed, an unintended twist generated when the multi-core optical fiber is arranged along the linear structural object having the unknown three-dimensional shape is estimated, based on a twisting strain generated in the multi-core optical fiber and a strain by the already-known twist, and an influence by the unintended twist is removed.
11. The shape measurement method according to claim 10 , comprising:
defining a position in a longitudinal direction of the multi-core optical fiber as z when computing positional coordinates in a three-dimensional space of the linear structural object having the unknown three-dimensional shape;
calculating a difference in strain at the position z as a difference between a strain amount at the position z of each core of the multi-core optical fiber obtained from the backward Brillouin scattering light distribution when the multi-core optical fiber is arranged along the linear structural object having the unknown three-dimensional shape and a strain amount at the position z of each core of the multi-core optical fiber obtained from the backward Brillouin scattering light distribution when the multi-core optical fiber is arranged along the linear structural object having the already-known three-dimensional shape;
calculating a bending strain ε bending,i of each of the outer peripheral cores by subtracting the difference in strain of the center core from the difference in strain of each of the outer peripheral cores;
calculating a curvature κ and a bending angle β at the position z of the multi-core optical fiber from the bending strain ε bending,i of each of the outer peripheral cores using a relational expression (2) of removing an influence by the unintended twist; and
computing positional coordinates in the three-dimensional space of the linear structural object having the unknown three-dimensional shape from the curvature κ and the bending angle β at the position z using Frenet-Serret formulas;
ε bending,i =k 1 κr cos(ω i −β) [Relational Expression (2)]
where r is a center-to-center distance between the center core and the outer peripheral cores, k 1 is a correction coefficient of a twist expressed by Formula (3), v is a Poisson's ratio of the multi-core optical fiber, a i is an initial angle of a core i, ω i is an angle representing a position of the outer peripheral cores on a cross section at the position z of the multi-core optical fiber expressed by Formula (4), p is a spin rate of the outer peripheral cores, ε twisting is a twisting strain generated at the position z of the multi-core optical fiber, φ(z) is a specific angle of twist at the position z of the multi-core optical fiber expressed by Formula (5), and k 2 is a correction coefficient of a twist expressed by Formula (6)
[
Math
.
3
]
k
1
=
1
-
v
(
2
π
pr
)
2
(
2
π
pr
)
2
+
1
(
3
)
[
Math
.
4
]
ω
i
=
a
i
+
∫
0
S
(
2
π
p
+
ϕ
(
z
)
)
dz
(
4
)
[
Math
.
5
]
ϕ
(
z
)
=
ε
twisting
k
2
r
(
5
)
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Math
.
6
]
k
2
=
2
π
pr
(
2
π
pr
)
2
+
1
.
(
6
)
12. The shape measurement method according to claim 11 , wherein
a spin rate p of the outer peripheral cores is computed from a cyclic fluctuation of the bending strain ε bending,i of each of the outer peripheral cores.
13. The shape measurement method according to claim 8 , wherein
in the multi-core optical fiber, a count of the outer peripheral cores is three, and a cladding diameter is 375 μm or more.
14. The shape measurement method according to claim 8 , wherein
in the multi-core optical fiber, a center-to-center distance between the center core and the outer peripheral cores is 120 μm or more.