Optical pulse test method and optical pulse test equipment
An object of the present invention is to propose a design method of a minimum value N of the number of multiplexed frequencies that is necessary for measuring an object vibrational frequency according to DAS-P while taking into consideration a trade-off between a measurement distance and an upper limit of a measurable vibrational frequency. When a phase change of an arbitrary section of a measured optical fiber is represented by A×sin(2πfvt), N=4Zfv/ν is satisfied when A is smaller than π/2 but N=2Zfv/(ν·Arcsin (π/2A)) is satisfied when A is equal to or larger than π/2, where fv represents vibrational frequency, t represents time, Z represents a length of the measured optical fiber (a measurement distance), and ν represents the speed of light inside the measured optical fiber.
1. An optical pulse test method comprising:
inputting an optical pulse sequence of which the number of wavelength multiplexes is N and in which optical pulses with different optical frequencies are arranged at temporally regular intervals to one end of a measured optical fiber;
receiving scattered light of each wavelength having returned to the one end of the measured optical fiber;
observing a vibration of the measured optical fiber as a time variation of a phase component of the scattered light; and
determining the number of wavelength multiplexes N as a minimum value satisfying Math. C1 as follows
[
Math
.
C1
]
When
F
υ
(
t
)
<
π
(
C1
)
N
≥
4
Zf
υ
max
v
when
F
υ
(
t
)
≥
π
N
>
2
Z
vC
max
-
1
(
π
)
where
t represents time,
Z represents a length of the measured optical fiber (measurement distance),
ν represents the speed of light inside the measured optical fiber,
F ν (t) represents a time waveform of a phase change in an arbitrary section of the measured optical fiber,
{tilde over (F)} ν (ƒ ν ) represents a function obtained by a Fourier transform of F ν (t),
ƒ ν max represents a maximum value of a frequency range occupied by {tilde over (F)} ν (ƒ ν ),
C(t) represents an absolute value of a phase change between a time point t and a time point t+T N ,
C max (T N ) represents a maximum value of C(t) when arbitrarily changing the time point t,
C max −1 (F ν ) represents an inverse function of C max (T N ),
F ν represents a difference between a maximum value and a minimum value of F ν (t),
T N represents intervals of optical pulses in the optical pulse sequence, and
C max −1 (Π) represents the intervals T N of the optical pulses when an absolute value of a magnitude of phase change is Π.
2. The optical pulse test method according to claim 1 , comprising:
forming the optical pulse by arranging M-number of minute optical pulses with different optical frequencies at shorter intervals than optical pulse intervals of the optical pulse sequence; and
setting the number M of the minute optical pulses so that 1/√M times a noise level is equal to or lower than a predetermined value.
3. The optical pulse test method according to claim 2 , comprising:
inputting, before inputting the optical pulse sequence to the one end of the measured optical fiber, a correction optical pulse sequence in which optical pulse pairs in which optical pulses with different optical frequencies are arranged at shorter intervals than optical pulse intervals of the optical pulse sequence are arranged to the one end of the measured optical fiber; and
calculating a correction value of the phase component of the scattered light by Math. C2,
[
Math
.
C2
]
ϕ
(
i
(
m
′
)
,
i
(
m
)
)
=
arg
[
1
P
∑
p
=
1
P
R
[
arg
{
r
i
(
m
)
(
z
,
t
p
+
2
z
/
υ
)
}
]
r
i
(
m
′
)
(
z
,
t
p
+
2
z
/
υ
)
]
(
C2
)
where Φ(i(m′), i(m)) represents an angle difference between two of the optical pulses with different optical frequencies,
P represents the number of the optical pulse pairs included in the correction optical pulse sequence,
p represents a number (an integer from 1 to P) of the optical pulse pair,
t p represents a time at which the p-th optical pulse pair is input to the one end of the measured optical fiber,
z represents a distance from the one end of the measured optical fiber,
r i(m) (z, t p +2z/v) and r i(m′) (z, t p +2z/v) represent complex vectors of scattered light from the distance z,
an arg function represents a function which calculates a deflection angle of a complex vector of an argument within a range from −π to π and which outputs a real number, and
R(*) represents an operator which rotates a complex vector r clockwise by an angle * on a complex plane.
4. The optical pulse test method according to claim 1 , comprising:
inputting, before inputting the optical pulse sequence to the one end of the measured optical fiber, a correction optical pulse sequence in which optical pulse pairs in which optical pulses with different optical frequencies are arranged at shorter intervals than optical pulse intervals of the optical pulse sequence are arranged to the one end of the measured optical fiber; and
calculating a correction value of the phase component of the scattered light by Math. C2,
[
Math
.
C2
]
ϕ
(
i
(
m
′
)
,
i
(
m
)
)
=
arg
[
1
P
∑
p
=
1
P
R
[
arg
{
r
i
(
m
)
(
z
,
t
p
+
2
z
/
υ
)
}
]
r
i
(
m
′
)
(
z
,
t
p
+
2
z
/
υ
)
]
(
C2
)
where Φ(i(m′), i(m)) represents an angle difference between two of the optical pulses with different optical frequencies,
P represents the number of the optical pulse pairs included in the correction optical pulse sequence,
p represents a number (an integer from 1 to P) of the optical pulse pair,
t p represents a time at which the p-th optical pulse pair is input to the one end of the measured optical fiber,
z represents a distance from the one end of the measured optical fiber,
r i(m) (z, t p +2z/v) and r i(m′) (z, t p +2z/v) represent complex vectors of scattered light from the distance z,
an arg function represents a function which calculates a deflection angle of a complex vector of an argument within a range from −π to π and which outputs a real number, and
R(*) represents an operator which rotates a complex vector r clockwise by an angle * on a complex plane.
5. An optical pulse test method comprising:
forming M-number of groups in which N×M+1-number (where N and M are natural numbers) of minute optical pulses with different optical frequencies are arranged;
arranging the M-number of groups and segmenting M-numbers of the minute optical pulses from the top group of the groups to form N×M+1-number of optical pulse pairs;
inputting an optical pulse sequence in which the N×M+1-number of optical pulse pairs are arranged at temporally regular intervals to one end of a measured optical fiber;
receiving scattered light of each wavelength having returned to the one end of the measured optical fiber;
observing a vibration of the measured optical fiber as a time variation of a phase component of the scattered light;
determining the number of wavelength multiplexes N as a minimum value satisfying Math. C1; and
setting the number of wavelength multiplexes M so that 1/√M times a noise level is equal to or lower than a predetermined value where Math. C1 is as follows
[
Math
.
C1
]
When
F
υ
(
t
)
<
π
(
C1
)
N
≥
4
Zf
υ
max
v
when
F
υ
(
t
)
≥
π
N
>
2
Z
vC
max
-
1
(
π
)
where
t represents time,
Z represents a length of the measured optical fiber (measurement distance),
ν represents the speed of light inside the measured optical fiber,
F ν (t) represents a time waveform of a phase change in an arbitrary section of the measured optical fiber,
{tilde over (F)} ν (ƒ ν ) represents a function obtained by a Fourier transform of F ν (t),
ƒ ν max represents a maximum value of a frequency range occupied by {tilde over (F)} ν (ƒ ν ),
C(t) represents an absolute value of a phase change between a time point t and a time point t+T N ,
C max (T N ) represents a maximum value of C(t) when arbitrarily changing the time point t,
C max −1 (F ν ) represents an inverse function of C max (T N ),
F ν represents a difference between a maximum value and a minimum value of F ν (t),
T N represents intervals of optical pulses in the optical pulse sequence, and
C max −1 (Π) represents the intervals T N of the optical pulses when an absolute value of a magnitude of phase change is Π.
6. The optical pulse test method according to claim 5 , comprising:
inputting, before inputting the optical pulse sequence to the one end of the measured optical fiber, a correction optical pulse sequence in which optical pulse pairs in which optical pulses with different optical frequencies are arranged at shorter intervals than optical pulse intervals of the optical pulse sequence are arranged to the one end of the measured optical fiber; and
calculating a correction value of the phase component of the scattered light by Math. C2,
[
Math
.
C2
]
ϕ
(
i
(
m
′
)
,
i
(
m
)
)
=
arg
[
1
P
∑
p
=
1
P
R
[
arg
{
r
i
(
m
)
(
z
,
t
p
+
2
z
/
υ
)
}
]
r
i
(
m
′
)
(
z
,
t
p
+
2
z
/
υ
)
]
(
C2
)
where Φ(i(m′), i(m)) represents an angle difference between two of the optical pulses with different optical frequencies,
P represents the number of the optical pulse pairs included in the correction optical pulse sequence,
p represents a number (an integer from 1 to P) of the optical pulse pair,
t p represents a time at which the p-th optical pulse pair is input to the one end of the measured optical fiber,
z represents a distance from the one end of the measured optical fiber,
r i(m) (z, t p +2z/v) and r i(m′) (z, t p +2z/v) represent complex vectors of scattered light from the distance z,
an arg function represents a function which calculates a deflection angle of a complex vector of an argument within a range from −π to π and which outputs a real number, and
R(*) represents an operator which rotates a complex vector r clockwise by an angle * on a complex plane.
7. An optical pulse test method comprising:
forming N+1-number of groups in which N×M-number (where N and M are natural numbers) of minute optical pulses with different optical frequencies are arranged;
arranging the N+1-number of groups and segmenting M-numbers of the minute optical pulses from the top group of the groups to form N(N+1)-number of optical pulse pairs;
adding an additional minute optical pulse of which an optical frequency differs from the optical frequency of any of the minute optical pulses to each N+1-number of optical pulse pairs among the N(N+1)-number of optical pulse pairs;
inputting an optical pulse sequence in which the N(N+1) number of optical pulse pairs including the optical pulse pairs to which the additional minute optical pulse has been added are arranged at temporally regular intervals to one end of a measured optical fiber;
receiving scattered light of each wavelength having returned to the one end of the measured optical fiber;
observing a vibration of the measured optical fiber as a time variation of a phase component of the scattered light;
determining the number of wavelength multiplexes N as a minimum value satisfying Math. C1; and
setting the number of wavelength multiplexes M so that 1/√M times a noise level is equal to or lower than a predetermined value where C1 is as follows
[
Math
.
C1
]
When
F
υ
(
t
)
<
π
(
C1
)
N
≥
4
Zf
υ
max
v
when
F
υ
(
t
)
≥
π
N
>
2
Z
vC
max
-
1
(
π
)
where
t represents time,
Z represents a length of the measured optical fiber (measurement distance),
ν represents the speed of light inside the measured optical fiber,
F ν (t) represents a time waveform of a phase change in an arbitrary section of the measured optical fiber,
{tilde over (F)} ν (ƒ ν ) represents a function obtained by a Fourier transform of F ν (t),
ƒ ν max represents a maximum value of a frequency range occupied by {tilde over (F)} ν (ƒ ν ),
C(t) represents an absolute value of a phase change between a time point t and a time point t+T N ,
C max (T N ) represents a maximum value of C(t) when arbitrarily changing the time point t,
C max −1 (F ν ) represents an inverse function of C max (T N ),
F ν represents a difference between a maximum value and a minimum value of F ν (t),
T N represents intervals of optical pulses in the optical pulse sequence, and
C max −1 (Π) represents the intervals T N of the optical pulses when an absolute value of a magnitude of phase change is Π.
8. The optical pulse test method according to claim 7 , comprising:
inputting, before inputting the optical pulse sequence to the one end of the measured optical fiber, a correction optical pulse sequence in which optical pulse pairs in which optical pulses with different optical frequencies are arranged at shorter intervals than optical pulse intervals of the optical pulse sequence are arranged to the one end of the measured optical fiber; and
calculating a correction value of the phase component of the scattered light by Math. C2,
[
Math
.
C2
]
ϕ
(
i
(
m
′
)
,
i
(
m
)
)
=
arg
[
1
P
∑
p
=
1
P
R
[
arg
{
r
i
(
m
)
(
z
,
t
p
+
2
z
/
υ
)
}
]
r
i
(
m
′
)
(
z
,
t
p
+
2
z
/
υ
)
]
(
C2
)
where Φ(i(m′), i(m)) represents an angle difference between two of the optical pulses with different optical frequencies,
P represents the number of the optical pulse pairs included in the correction optical pulse sequence,
p represents a number (an integer from 1 to P) of the optical pulse pair,
t p represents a time at which the p-th optical pulse pair is input to the one end of the measured optical fiber,
z represents a distance from the one end of the measured optical fiber,
r i(m) (z, t p +2z/v) and r i(m′) (z, t p +2z/v) represent complex vectors of scattered light from the distance z,
an arg function represents a function which calculates a deflection angle of a complex vector of an argument within a range from −π to π and which outputs a real number, and
R(*) represents an operator which rotates a complex vector r clockwise by an angle * on a complex plane.
9. An optical pulse test method comprising:
forming (N+1)M+1-number of groups in which N×M+1-number (where N and M are natural numbers) of minute optical pulses with different optical frequencies are arranged;
arranging the (N+1)M+1-numbers of groups and segmenting the minute optical pulses from the top group of the groups so that M+1-number of the minute optical pulses are included in a 1+k(N+1)-th optical pulse pair and M-number of the minute optical pulses are included in the other pulse pairs to form (N×M+1)(N+1)-number of the optical pulse pairs;
inputting an optical pulse sequence in which the (N×M+1)(N+1)-number of optical pulse pairs are arranged at temporally regular intervals to one end of a measured optical fiber;
receiving scattered light of each wavelength having returned to the one end of the measured optical fiber;
observing a vibration of the measured optical fiber as a time variation of a phase component of the scattered light;
determining the number of wavelength multiplexes N as a minimum value satisfying Math. C1; and
setting the number of wavelength multiplexes M so that 1/√M times a noise level is equal to or lower than a predetermined value where Math. C1 is as follows
[
Math
.
C1
]
When
F
υ
(
t
)
<
π
(
C1
)
N
≥
4
Zf
υ
max
v
when
F
υ
(
t
)
≥
π
N
>
2
Z
vC
max
-
1
(
π
)
where
t represents time,
Z represents a length of the measured optical fiber (measurement distance),
ν represents the speed of light inside the measured optical fiber,
F ν (t) represents a time waveform of a phase change in an arbitrary section of the measured optical fiber,
{tilde over (F)} ν (ƒ ν ) represents a function obtained by a Fourier transform of F ν (t),
ƒ ν max represents a maximum value of a frequency range occupied by {tilde over (F)} ν (ƒ ν ),
C(t) represents an absolute value of a phase change between a time point t and a time point t+T N ,
C max (T N ) represents a maximum value of C(t) when arbitrarily changing the time point t,
C max −1 (F ν ) represents an inverse function of C max (T N ),
F ν represents a difference between a maximum value and a minimum value of F ν (t),
T N represents intervals of optical pulses in the optical pulse sequence, and
C max −1 (Π) represents the intervals T N of the optical pulses when an absolute value of a magnitude of phase change is Π.
10. The optical pulse test method according to claim 9 , comprising:
inputting, before inputting the optical pulse sequence to the one end of the measured optical fiber, a correction optical pulse sequence in which optical pulse pairs in which optical pulses with different optical frequencies are arranged at shorter intervals than optical pulse intervals of the optical pulse sequence are arranged to the one end of the measured optical fiber; and
calculating a correction value of the phase component of the scattered light by Math. C2,
[
Math
.
C2
]
ϕ
(
i
(
m
′
)
,
i
(
m
)
)
=
arg
[
1
P
∑
p
=
1
P
R
[
arg
{
r
i
(
m
)
(
z
,
t
p
+
2
z
/
υ
)
}
]
r
i
(
m
′
)
(
z
,
t
p
+
2
z
/
υ
)
]
(
C2
)
where Φ(i(m′), i(m)) represents an angle difference between two of the optical pulses with different optical frequencies,
P represents the number of the optical pulse pairs included in the correction optical pulse sequence,
p represents a number (an integer from 1 to P) of the optical pulse pair,
t p represents a time at which the p-th optical pulse pair is input to the one end of the measured optical fiber,
z represents a distance from the one end of the measured optical fiber,
r i(m) (z, t p +2z/v) and r i(m′) (z, t p +2z/v) represent complex vectors of scattered light from the distance z,
an arg function represents a function which calculates a deflection angle of a complex vector of an argument within a range from −π to π and which outputs a real number, and
R(*) represents an operator which rotates a complex vector r clockwise by an angle * on a complex plane.
11. An optical pulse test equipment, comprising:
a light source which inputs an optical pulse sequence of which the number of wavelength multiplexes is N and in which optical pulses with different optical frequencies are arranged at temporally regular intervals to one end of a measured optical fiber;
an optical receiver which receives scattered light of each wavelength having returned to the one end of the measured optical fiber;
a signal processing unit which observes a vibration of the measured optical fiber as a time variation of a phase component of the scattered light; and
a calculating unit which determines the number of wavelength multiplexes N as a minimum value satisfying Math. C1 as follows
[
Math
.
C1
]
When
F
υ
(
t
)
<
π
(
C1
)
N
≥
4
Zf
υ
max
v
when
F
υ
(
t
)
≥
π
N
>
2
Z
vC
max
-
1
(
π
)
where
t represents time,
Z represents a length of the measured optical fiber (measurement distance),
ν represents the speed of light inside the measured optical fiber,
F ν (t) represents a time waveform of a phase change in an arbitrary section of the measured optical fiber,
{tilde over (F)} ν (ƒ ν ) represents a function obtained by a Fourier transform of F ν (t),
ƒ ν max represents a maximum value of a frequency range occupied by {tilde over (F)} ν (ƒ ν ),
C(t) represents an absolute value of a phase change between a time point t and a time point t+T N ,
C max (T N ) represents a maximum value of C(t) when arbitrarily changing the time point t,
C max −1 (F ν ) represents an inverse function of C max (T N ),
F ν represents a difference between a maximum value and a minimum value of F ν (t),
T N represents intervals of optical pulses in the optical pulse sequence, and
C max −1 (Π) represents the intervals T N of the optical pulses when an absolute value of a magnitude of phase change is Π.
12. The optical pulse test equipment according to claim 11 , wherein:
the light source inputs, before inputting the optical pulse sequence to the one end of the measured optical fiber, a correction optical pulse sequence in which optical pulse pairs in which optical pulses with different optical frequencies are arranged at shorter intervals than optical pulse intervals of the optical pulse sequence are arranged to the one end of the measured optical fiber; and
the signal processing unit calculates a correction value of the phase component of the scattered light by Math. C2,
[
Math
.
C2
]
ϕ
(
i
(
m
′
)
,
i
(
m
)
)
=
arg
[
1
P
∑
p
=
1
P
R
[
arg
{
r
i
(
m
)
(
z
,
t
p
+
2
z
/
υ
)
}
]
r
i
(
m
′
)
(
z
,
t
p
+
2
z
/
υ
)
]
(
C2
)
where Φ(i(m′), i(m)) represents an angle difference between two of the optical pulses with different optical frequencies,
P represents the number of the optical pulse pairs included in the correction optical pulse sequence,
p represents a number (an integer from 1 to P) of the optical pulse pair,
t p represents a time at which the p-th optical pulse pair is input to the one end of the measured optical fiber,
z represents a distance from the one end of the measured optical fiber,
r i(m) (z, t p +2z/v) and r i(m′) (z, t p +2z/v) represent complex vectors of scattered light from the distance z,
an arg function represents a function which calculates a deflection angle of a complex vector of an argument within a range from −π to π and which outputs a real number, and
R(*) represents an operator which rotates a complex vector r clockwise by an angle * on a complex plane.