U.S. patent application number 13/973495 was filed with the patent office on 2014-02-27 for free space single-mode fibers and fiber components for fiber sensor applications.
This patent application is currently assigned to National Cheng Kung University. The applicant listed for this patent is National Applied Research Laboratories, National Cheng Kung University. Invention is credited to Yi-Fan Chung, Ren-Young Liu, Yu-Lung Lo, Chih-Chung Yen.
Application Number | 20140055786 13/973495 |
Document ID | / |
Family ID | 46490545 |
Filed Date | 2014-02-27 |
United States Patent
Application |
20140055786 |
Kind Code |
A1 |
Lo; Yu-Lung ; et
al. |
February 27, 2014 |
FREE SPACE SINGLE-MODE FIBERS AND FIBER COMPONENTS FOR FIBER SENSOR
APPLICATIONS
Abstract
This invention relates to a near real time optical compensation
verification system for verifying a fiber or fiber component
through internal or external compensation to achieve equivalently
free space propagation of a broadband light when coupled into
fiber. Preferably, no component is added to the fiber or fiber
component, and the compensation method is realized through real
time fiber bending, twisting or other means at either or both ends
of a fiber or fiber component. The output optical characteristics
of the compensated fiber or fiber component are measured by a
polarimeter through changing the input light properties. The
required multi-variable compensation to achieve Unitary Matrix free
space condition is computed in near real time, and as the feedback
to formulate the required compensation. The disclosed invention not
only enhances yield in the fiber and fiber component, but also
accelerates the optimization of optical fiber sensors employed free
space fiber coil.
Inventors: |
Lo; Yu-Lung; (Tainan City,
TW) ; Liu; Ren-Young; (HsinChu, TW) ; Yen;
Chih-Chung; (Tainan City, TW) ; Chung; Yi-Fan;
(Taipei City, TW) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
National Cheng Kung University
National Applied Research Laboratories |
Tainan City
Taipei |
|
TW
TW |
|
|
Assignee: |
National Cheng Kung
University
Tainan City
TW
National Applied Research Laboratories
Taipei
TW
|
Family ID: |
46490545 |
Appl. No.: |
13/973495 |
Filed: |
August 22, 2013 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
13149208 |
May 31, 2011 |
|
|
|
13973495 |
|
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Current U.S.
Class: |
356/364 |
Current CPC
Class: |
G01C 19/72 20130101;
G01J 4/04 20130101; G01J 4/00 20130101; G02B 6/2793 20130101 |
Class at
Publication: |
356/364 |
International
Class: |
G01J 4/00 20060101
G01J004/00 |
Foreign Application Data
Date |
Code |
Application Number |
Jan 19, 2011 |
TW |
100102012 |
Claims
1. An optical verification system for verifying an optical
compensation of an equivalent free space via an optical system,
comprising: a broadband light source for emitting a light, an
optical circuit having an optical fiber or fiber coil is used to
input the light and output the light, wherein the optical circuit
has optical characteristics of an equivalent free space via
internal or external optical compensation; a sample optical
component having a given optical parameter, coupled to the optical
circuit; and a polarimeter for measuring an optical parameter of
the output light, wherein the optical parameter is compared with
the given optical parameter to verify the compensation of an
equivalent free space for the optical circuit.
2. The system as claimed in claim 1, wherein the sample optical
component is an optical component for changing an optical
polarization state.
Description
CROSS REFERENCE TO RELATED APPLICATION(S)
[0001] This application is a division of U.S. patent application
Ser. No. 13/149,208, filed May 31, 2011, claiming foreign priority
as well to TW-100102012, filed on Jan. 19, 2011, which is/are
incorporated by reference as if fully set forth.
FIELD OF THE INVENTION
[0002] The invention relates to a compensation method for a fiber
or a fiber component. More particularly this invention is to
compensate the changes of optical characteristics for the light in
a fiber or a fiber component such as a fiber coil of the optical
fiber sensor (for example, the fiber optic gyros). The compensation
method not only makes the optical characteristics of each fiber or
fiber component like as the free space but also greatly accelerate
the design simulation for optical circuit optimization of optical
fiber sensors.
BACKGROUND OF THE INVENTION
[0003] In our daily life, the role of optical fiber technology is
getting more and more important. The sensitivity, stability and
reproducibility of fiber components are more important when they
are applied in the navigation, orientation and platform stability
technologies. Because the manufacture process of fiber components
(e.g. fiber coil) causes fiber's optical property change and loss,
it will make the function of fiber components reduce and
degrade.
[0004] In the prior art, several different strategies (US
2003/0007751A1-US 2005/0226563A1) are used to solve the problem in
optical property change or loss in optical fiber elements. For
example, the polarization-maintaining (PM) fiber can be applied to
keep the polarization state of light, but the cost of PM fiber is
high. Furthermore, the PM fiber ring around the coil is required to
maintain the polarization extinction ratio, and this parameter is
not easy to maintain. Thus it will increase the cost and difficulty
in the manufacture process. Also, the quality of fiber coil is
easily affected easily by fiber quality, stress and strain in the
winding process, and the rubber filled in the fiber coil. As a
result, every fiber coil may produce different levels of optical
properties such as linear birefringence (LB), linear diattenuation
(LD) and circular birefringence (CB) characteristics or their
combination.
[0005] For a long time, the high-quality fiber coil winding process
in fiber gyroscopes is a high-tech process. It requires not only
the combination of special optical fiber and automatic tension
control machines, but also the machine under a highly experienced
mechanic operation in order to control the quality of fiber coil in
an acceptable rage. Thus the high-tech process in fiber coil causes
the production costs extremely high. If the quality of fiber coil
(from different production dates or different plants) is
uncontrollable, the fiber coil winding process needs additional
time-consuming tests by re-adjusting fiber coil within the scope of
the best quality. If you bypass this adjusting in fiber coil, the
poor fiber coils are forced to the lower level in business. Thus
the yield of high-quality fiber coil will be substantially
reduced.
[0006] According to the present invention, applicants have departed
from the conventional wisdom, and had conceived and implemented the
free space single-mode fibers for fiber sensor, which is relative
to that of compensating the fiber or fiber component such that the
fiber or fiber component plus the compensated optical circuit act
as if an Unitary Matrix free space condition. The disclosed free
space single-mode fiber invention not only greatly enhances
repeatability in the fiber and fiber component production line, it
also can be employed to accelerate the design simulation for
optical circuit optimization of optical fiber sensors. Such a fast
simulation and the compensated optical circuit nearly acted as if a
free space are unprecedented in open literature. The invention is
briefly described as follows.
SUMMARY OF THE INVENTION
[0007] In the prior act, the equivalent parameters represented the
optical circuit can be obtained by the Mueller-Stokes Matrix
(Characterization on five effective parameters of anisotropic
optical material using Stokes parameters-Demonstration by a
fiber-type polarimeter, Optics Express, Vol. 18, Issue 9, pp.
9133-9150, April 2010). Please refer to FIG. 1, which shows the
experiment environment in the prior art. The polarized light
provided by the laser 100 passes through the quarter-wave plate 101
and the polarizer 102 in order to generate four linear polarized
lights (0.degree., 45.degree., 90.degree. and 135.degree.) and two
circuit polarized lights (left spin and right spin), and then the
six polarized lights are input into the sample fiber 103. After
that, the six polarized lights output from the sample fiber 103 and
input the Mueller Stokes Matrix polarimeter 104 for measuring the
polarization states of the six polarized light.
[0008] Then, the five equivalent parameters represented the sample
fiber 103, a principal axis angle (.alpha.), a phase retardation
(.beta.), a diattenuation axis angle (.theta..sub.d), a
diattenuation (D) and the optical rotation angle (.gamma.), are
obtained by inverting the polarization states of the six polarized
light measured from the Mueller Stokes Matrix polarimeter 104. The
dynamic range for the five parameters a, .beta., .theta..sub.d, D
and .gamma. is measured in 0.degree..about.180.degree.,
0.degree..about.180.degree., 0.degree..about.180.degree., 0.about.1
and 0.degree..about.180.degree., respectively.
[0009] The Stokes vectors are used to represent the polarization
state of the light as follows:
S = [ S 0 S 1 S 2 S 3 ] = [ I x + y I x - I y I 45 .degree. - I -
45 .degree. I RHC - I LHC ] ( 1.1 ) ##EQU00001##
[0010] where I.sub.x and I.sub.y is the intensity of the horizontal
and vertical polarized light, respectively, I.sub.45.sup.0 and
I.sub.-45.sup.0 is the intensity of the 45.degree. and -45.degree.
polarized light, respectively, I.sub.RIIC and I.sub.LIIC is the
intensity of the left spin and right spin polarized light,
respectively, S.sub.0 is the total intensity of the light, S .sub.1
is the difference of the intensity of the horizontal and vertical
polarized light, S.sub.2 is the difference of the intensity of the
45.degree. and -45.degree. polarized light and S.sub.3 is the
difference of the intensity of the left spin and right spin
polarized light. The Mueller Stokes Matrix polarimeter 104 can
measure the polarization state of the light, i.e., four Stokes
parameters.
[0011] The 4.times.4 Mueller Matrix is used to represent the
optical component which changes the polarization state of the
light. According to FIG. 1, the polarization state (s) of the
outputting light are obtained by multiplying the polarization state
(S) of the inputting light by the matrix of the equivalent optical
parameters (M) of the fiber component, as follows:
S = [ S 0 S 1 S 2 S 3 ] = ( m 11 m 12 m 13 m 14 m 21 m 22 m 23 m 24
m 31 m 32 m 33 m 34 m 41 m 42 m 43 m 44 ) ( S ^ 0 S ^ 1 S ^ 2 S ^ 3
) = M S ^ ( 1.2 ) ##EQU00002##
and the Mueller Matrix M is:
[0012] M = ( m 11 m 12 m 13 m 14 m 21 m 22 m 23 m 24 m 31 m 32 m 33
m 34 m 41 m 42 m 43 m 44 ) ( 1.3 ) ##EQU00003##
[0013] where m.sub.ij, i, j=1, 2, 3 and 4, is the equivalent
optical parameters of the fiber component.
[0014] The Jones Matrix (U) of the optical component is:
U = [ u 11 u 12 u 21 u 22 ] ( 1.4 ) ##EQU00004##
[0015] where u.sub.ij, i, j=1 and 2 is the equivalent optical
parameters of the fiber component.
[0016] The Mueller Matrix represented the optical component is
obtained via the following transformation formula:
M=T(U{circle around (.times.)} U*)T.sup.-1S (1.5)
[0017] where U is the Jones Matrix, S is the polarization state (S)
of the inputting light, T is a matrix described as follows:
T = ( 1 0 0 1 1 0 0 - 1 0 1 1 0 0 - 0 ) ( 1.6 ) ##EQU00005##
[0018] and the matrix U{circle around (.times.)}U* is described as
follows:
U U * = ( u 11 u 11 * u 11 u 12 * u 12 u 11 * u 12 u 12 * u 11 u 21
* u 11 u 22 * u 12 u 21 * u 12 u 22 * u 21 u 11 * u 21 u 12 * u 22
u 11 * u 22 u 12 * u 21 u 21 * u 21 u 22 * u 22 u 21 * u 22 u 22 *
) ( 1.7 ) ##EQU00006##
[0019] In the present invention, the fiber is assumed to have the
linear birefringence, linear diattenuation and circular
birefringence. Firstly, in the case of the fiber having the linear
birefringence of the principal axis angle (.alpha.) and retardance
(.beta.), whose Jones Matrix U.sub.b is described as follows:
U b = [ cos ( .alpha. ) - sin ( .alpha. ) sin ( .alpha. ) cos (
.alpha. ) ] [ exp ( - .beta. 2 ) 0 0 exp ( .beta. 2 ) ] [ cos (
.alpha. ) sin ( .alpha. ) - sin ( .alpha. ) cos ( .alpha. ) ] = [
cos ( .beta. 2 ) - cos ( 2 .alpha. ) sin ( .beta. 2 ) - sin ( 2
.alpha. ) sin ( .beta. 2 ) - sin ( 2 .alpha. ) sin ( .beta. 2 ) cos
( .beta. 2 ) + cos ( 2 .alpha. ) sin ( .beta. 2 ) ] ( 1.8 )
##EQU00007##
[0020] So, the Mueller Stokes Matrix of the fiber having the linear
birefringence is described as the following equation (1.9):
M lb = ( 1 0 0 0 0 cos ( 4 .alpha. ) sin 2 ( .beta. / 2 ) + cos 2 (
.beta. / 2 ) sin ( 4 .alpha. ) sin 2 ( .beta. / 2 ) sin ( 2 .alpha.
) sin ( .beta. ) 0 sin ( 4 .alpha. ) sin 2 ( .beta. / 2 ) - cos ( 4
.alpha. ) sin 2 ( .beta. / 2 ) + cos 2 ( .beta. / 2 ) - cos ( 2
.alpha. ) sin ( .beta. ) 0 - sin ( 2 .alpha. ) sin ( .beta. ) cos (
2 .alpha. ) sin ( .beta. ) cos ( .beta. ) ) ##EQU00008##
[0021] Secondly, in the case of the fiber having the linear
diattenuation of the diattenuation axis angle (.theta..sub.d) and
the transmission rates u and v, whose Jones Matrix U.sub.d is
described as follows:
U d = [ cos ( .theta. d ) - sin ( .theta. d ) sin ( .theta. d ) cos
( .theta. d ) ] [ u 0 0 v ] [ cos ( .theta. d ) sin ( .theta. d ) -
sin ( .theta. d ) cos ( .theta. d ) ] = [ u cos 2 ( .theta. d ) + v
sin 2 ( .theta. d ) ( u - v ) cos ( .theta. d ) sin ( .theta. d ) (
u - v ) cos ( .theta. d ) sin ( .theta. d ) u sin 2 ( .theta. d ) +
v cos 2 ( .theta. d ) ] ( 1.10 ) ##EQU00009##
[0022] So, the Mueller Stokes Matrix of the fiber having the linear
diattenuation is described as the following equation (1.11):
M ld = ( ( u + v ) 2 cos ( 2 .theta. d ) ( u , v ) 2 sin ( 2
.theta. d ) ( u - v ) 2 0 cos ( 2 .theta. d ) ( u - v ) 2 ( u + v )
2 4 + cos ( 4 .theta. d ) ( u - v ) 2 4 sin ( 4 .theta. d ) ( u - v
) 2 4 0 sin ( 2 .theta. d ) ( u - v ) 2 sin ( 4 .theta. d ) ( u - v
) 2 4 ( u + v ) 2 4 - cos ( 4 .theta. d ) ( u - v ) 2 4 0 0 0 0 uv
) ##EQU00010##
[0023] The diattenuation D is described as follows:
D = u - v u + v and ( 1.12 ) e = 1 - D 1 + D ( 1.13 )
##EQU00011##
[0024] where e is v/u, so that (1.10) and (1.11) are respectively
described as the following equations (1.14) and (1.15):
U d = [ cos ( .theta. d ) - sin ( .theta. d ) sin ( .theta. d ) cos
( .theta. d ) ] [ 1 0 0 1 - D 1 + D ] [ cos ( .theta. d ) sin (
.theta. d ) - sin ( .theta. d ) cos ( .theta. d ) ] = [ cos 2 (
.theta. d ) + 1 - D 1 + D sin 2 ( .theta. d ) ( 1 - 1 - D 1 + D )
cos ( .theta. d ) sin ( .theta. d ) ( 1 - 1 - D 1 + D ) cos (
.theta. d ) sin ( .theta. d ) sin 2 ( .theta. d ) + 1 - D 1 + D cos
2 ( .theta. d ) ] ( 1.14 ) ##EQU00012##
[0025] and equation (1.15):
M ld = ( ( 1 + 1 - D 1 + D ) 2 cos ( 2 .theta. d ) ( 1 - 1 - D 1 +
D ) 2 sin ( 2 .theta. d ) ( 1 - 1 - D 1 + D ) 2 0 cos ( 2 .theta. d
) ( 1 - 1 - D 1 + D ) 2 ( 1 + 1 - D 1 + D ) 2 4 + cos ( 4 .theta. d
) ( 1 - 1 - D 1 + D ) 2 4 sin ( 4 .theta. d ) ( 1 - 1 - D 1 + D ) 2
4 0 sin ( 2 .theta. d ) ( 1 - 1 - D 1 + D ) 2 sin ( 4 .theta. d ) (
1 - 1 - D 1 + D ) 2 4 ( 1 + 1 - D 1 + D ) 2 4 - cos ( 4 .theta. d )
( 1 - 1 - D 1 + D ) 2 4 0 0 0 0 1 - D 1 + D ) ##EQU00013##
[0026] Finally, in the case of the fiber having the circular
birefringence of the optical rotation angle (.gamma.), whose Jones
Matrix U.sub.cb is described as follows:
U cb = [ cos ( .gamma. ) sin ( .gamma. ) - sin ( .gamma. ) cos (
.gamma. ) ] ( 1.16 ) ##EQU00014##
[0027] So, the Mueller Stokes Matrix of the fiber having the
circular birefringence is described as follows:
M cb = ( 1 0 0 0 0 cos ( 2 .gamma. ) sin ( 2 .gamma. ) 0 0 - sin (
2 .gamma. ) cos ( 2 .gamma. ) 0 0 0 0 1 ) ( 1.17 ) ##EQU00015##
[0028] According to the above description, the equivalent
parameters represented the optical circuit of the single-mode fiber
and optical fiber component such as the fiber coil can be
represented by the Mueller Stokes Matrix via the measurement of the
Mueller Stokes Matrix polarimeter.
[0029] The present invention is proposed to measure the equivalent
optical path of optical components or optical fiber such as fiber
coil, and then compensate for it to become a free space unit
matrix. So that the stability and reproducibility of optical
components or optical fiber such as fiber coil in a fiber gyroscope
can be promoted. The theoretical calculation is that Mueller Stokes
polarimeter is applied to analyze the results, and then design and
calculate the compensation for optical fiber or optical components
in order to convert their matrix into the free-space unit
matrix.
[0030] The fiber sensor provided by the present invention is
composed by optically connecting a light source, the optical
components, a fiber or fiber component and a light detector. And
the polarization state of the light passing through the fiber or
fiber components is compensated by a compensation method.
[0031] Preferably, the compensation method is performed by adding a
variable retarder and a half-wave plate and etc, and a polarization
controller can be used to replace the variable retarder and the
half-wave plate.
[0032] Preferably, no component is added, and the compensation
method is realized through fiber bending, twisting or other means
at either or both ends of a fiber or fiber component.
[0033] According to the method provided by the present invention,
the calculated compensation can recover the changes of the optical
characteristics of the light passing through the fiber or fiber
component caused by the environment and the fabrication process.
Compared to the prior art, the invention is performed with adding
the optical component or without adding the optical component to
remain the polarization state of the inputting light. It also can
be employed to greatly accelerate the design simulation for optical
circuit optimization of optical fiber sensors due to the
compensated optical circuit is a free space unit matrix. As a
result, such a fast simulation and the nearly complete recovery of
the optical characteristic (excepting the optic power loss) lead to
that the optical fiber apparatus made by compensation method can be
applied for optical fiber sensors fabricated by fiber and fiber
component such as fiber optic gyros, including navigation,
orientation, platform stabilization and etc.
[0034] In accordance with further aspect of the present invention,
an optical system is provided. The optical system includes an
optical circuit for propagating a light and an optical compensation
assembly placed on the optical circuit to compensate the changes of
optical characteristics of the light after the light passing
through the optical circuit. The compensation is based on a
compensation method of transformation matrix.
[0035] In summary, the present invention has disclosed a
compensation method to make the equivalent optical circuit of the
compensated fiber or fiber component act as if an Unitary Matrix
free space condition after measuring the fiber and fiber component.
Especially, the results obtained from the Mueller Matrix
polarimeter are analyzed theoretically to calculate the
compensation when the equivalent Jones Matrix represented the fiber
or fiber component such as a fiber coil is transformed to the unit
matrix represented the free space. The recovery of optical
characteristics is reached by the compensation method via adding
optical components or no optical components added. And we further
provide an optical verification method to verify the equivalent
optical circuit of the compensated fiber or fiber component.
[0036] The above aspects and advantages of the present invention
will become more readily apparent to those ordinarily skilled in
the art after reviewing the following detailed descriptions and
accompanying drawings, in which:
BRIEF DESCRIPTION OF THE DRAWINGS AND TABLES
[0037] FIG. 1 shows the schematic diagram of simulation
architecture of a Mueller Stoke Matrix in the prior art;
[0038] FIG. 2(a) is a first preferred implementation case schematic
diagram of the present invention, which is used to verify the
accuracy of fiber's five optical parameters;
[0039] FIG. 2(b) is the implementation of the proposed verification
method in the present invention, which is used to verify the
accuracy of fiber's five optical parameters;
[0040] FIG. 2(c) shows the comparison of principal axis angle and
retardance between the known optical parameters of a quarter-wave
plate and optical parameters extracted by using the proposed
verification method;
[0041] FIG. 3(a) shows the schematic diagram of free-space unit
matrix;
[0042] FIG. 3(b) is the comparison of azimuth angles and
ellipticity angles of input/output lights given input lights with
different linear polarization states;
[0043] FIG. 3(c) is the comparison of azimuth angles and
ellipticity angles of input/output lights given input lights with
randomly-chosen right- and left-hand elliptical polarization
states;
[0044] FIG. 3(d) is the comparison of azimuth angles and
ellipticity angles of input/output lights given input lights with
different linear polarization states using a broadband light
source;
[0045] FIG. 3(e) is the comparison of azimuth angles and
ellipticity angles of input/output lights given input lights with
randomly-chosen right- and left-hand elliptical polarization states
using a broadband light source;
[0046] FIGS. 4(a) and (b) are a second and third preferred
implementation case schematic diagrams of the present invention,
respectively, which show the compensated fiber coils;
[0047] TABLE 1. is the comparison of Ellipticity Angles of
Input/Output Lights Given Input Lights with Right- and Left-Hand
Circular Polarization States; and
[0048] TABLE 2. is the comparison of ellipticity angles of
input/output lights given input lights with right- and left-hand
circular polarization state using a broadband light source.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
[0049] The present invention will now be described more
specifically with reference to the following embodiments. It is to
be noted that the following descriptions of preferred embodiments
of this invention are presented herein for the purposes of
illustration and description only it is not intended to be
exhaustive or to be limited to the precise form disclosed.
[0050] Please refer to FIG. 2(a), which is the first better
implementation example for this case. It is a schematic diagram in
compensating for fiber 203. FIG. 2(a) illustrates two fiber
coupling devices 202 that is used to connect an optical fiber 203.
The polarizer 206 and the quarter-wave plate 207 is used to produce
linearly polarization light and neutral density filter 205 and
power meter detector 204 is used to ensure that each of the input
lights has an identical intensity. Finally, the polarization state
of input light can be measured by Stokes polarimeter 201.
[0051] In order to measure five effective optical parameters in a
fiber coil, a 1000 m in length of single mode fiber 203 is used for
measurement. FIG. 2(b) illustrates two fiber coupling devices 202
that is used to connect an optical fiber 203. The polarizer 206 and
the quarter-wave plate 207 is used to produce linearly polarization
light and neutral density filter 205 and power meter detector 204
is used to ensure that each of the input lights has an identical
intensity. The single mode fiber 203 is wound on a plastic cylinder
which diameter is 15 cm. And the light source 200 is a broadband
light source such as ASE (1520 nm.about.1570 nm) By the different
combinations of principal angle of polarizer 206 and quarter-wave
plate 207, it can produce four linear polarization lights
(0.degree., 45.degree., 90 .degree., 135.degree.) and two circular
polarization lights (left and right hand). The Stokes polarimeter
201 is applied to measure the Stokes parameters after the different
polarization states of light through optical fiber 203,
respectively. The following method to compute the single model
optical fiber coil's five equivalent parameters is introduced.
[0052] The four linear polarization lights: S.sub.0.degree.=[1, 1,
0, 0], S.sub.45.degree.=[1, 0, 1, 0], S.sub.90.degree.=[1, -1, 0,
0] and S.sub.135.degree.=[1, 0, -1, 0] and two circular
polarization lights: right handed S.sub.RHC=[1, 0, 0, 1] and left
handed S.sub.LHC=[1, 0, 0, -1] are going through the sample,
respectively. In below equations, S.sub.0 is the total light
intensity, S.sub.1 is the intensity difference between the
horizontal and vertical linearly polarized components, S.sub.2 is
the intensity difference between the linearly polarized components
oriented at .+-.45.degree., and S.sub.3 is the intensity difference
between the right- and left-hand circularly polarized
components.
[0053] As a result, the term 2.alpha.+2.gamma. of the sample can be
obtained as
2 .alpha. + 2 .gamma. = tan - 1 ( - S 0 .degree. ( S 3 ) S 45
.degree. ( S 3 ) ) ( 2.19 ) ##EQU00016##
After determining 2.alpha.+2.gamma., the retardance can be obtained
as
.beta. = tan - 1 ( S 45 .smallcircle. ( S 3 ) cos ( 2 .alpha. + 2
.gamma. ) S RH ( S 3 ) ) ( 2.20 ) ##EQU00017## [0054] The
diattenuation axis .theta..sub.d can be expressed as
[0054] 2 .theta. d = tan - 1 ( S 45 .degree. ( S 2 ) + S 135
.degree. ( S 2 ) S 0 .degree. ( S 1 ) + S 90 .degree. ( S 1 ) ) (
2.21 ) ##EQU00018##
The Diattenuation D can be expressed as
D = S 45 .degree. ( S 2 ) + S 135 .degree. ( S 2 ) sin ( 2 .theta.
d ) [ S 0 .degree. ( S 0 ) + S 90 .degree. ( S 0 ) ] ( 2.22 )
##EQU00019##
The principal axis 2.alpha. can be expressed as
2 .alpha. = tan - 1 ( C 3 [ S RHC ( S 2 ) - S LHC ( S 2 ) ] - C 2 [
S RHC ( S 3 ) - S LHC ( S 3 ) ] C 2 [ S RHC ( S 2 ) - S LHC ( S 2 )
] - C 1 [ S RHC ( S 3 ) - S LHC ( S 3 ) ] ) ##EQU00020##
where
C 1 = ( ( 1 + 1 - D 1 + D ) 2 4 + cos ( 4 .theta. d ) ( 1 - 1 - D 1
+ D ) 2 4 ) sin ( .beta. ) ( 2.24 ) C 2 = ( sin ( 4 .theta. d ) ( 1
- 1 - D 1 + D ) 2 4 ) sin ( .beta. ) ( 2.25 ) C 3 = ( ( 1 + 1 - D 1
+ D ) 2 4 - cos ( 4 .theta. d ) ( 1 - 1 - D 1 + D ) 2 4 ) sin (
.beta. ) ( 2.26 ) ##EQU00021##
Then, 2.gamma. can be obtained as
2 .gamma. = tan - 1 ( - S 0 .degree. ( S 3 ) S 45 .degree. ( S 3 )
) - 2 .alpha. ( 2.27 ) ##EQU00022##
[0055] Then, we can extract five effective optical parameters of
.alpha., .beta., .theta..sub.d, D, and .gamma. of the SM fiber coil
are 71.92.degree., 144.98.degree., 96.11.degree., 0.041.degree.,
23.67, respectively.
[0056] Please refer to FIG. 2(b), and this is the proposed
verification method of implementation example for this invention.
To verify the accuracy of fiber's five optical parameters, we use
the extracted five effective optical parameters to measure the
known linear birefringence sample. The linear birefringence sample
is a quarter-wave plate 208. The known retardance is 90.degree. and
slow axis of quarter-wave plate 211 in the back of an optical fiber
is rotated in 0.degree., 30.degree., 60.degree., 90.degree.,
120.degree. and 150.degree. for measurement of LB sample in various
angles. If the values of five optical parameters in SM fiber are
correct, the known principal axes and retardance of quarter-wave
plate 208 can be obtained correctly.
[0057] Please refer to FIG. 2(c), and it shows the comparison of
principal axis angle and retardance between the known optical
parameters of a quarter-wave plate 211 and optical parameters
extracted by using the method above. The experimental results show
that the extracted values of the principal axis angle and
retardance of the quarter-wave plate have average absolute error of
.alpha..sub.S=1.42.degree. and .beta..sub.S=4.03.degree.,
respectively. From above results, the extracted five effective
optical parameters can correctly represent the optical properties
of the single-mode fiber coil.
[0058] Please refer to FIG. 3(a), and it shows a variable retarder
(VR) and half-wave plate (HP) are inserted between the power meter
and the fiber coupler used to couple the input polarization light
into the optical fiber (referring to "Design of
Polarization-Insensitive Optical Fiber Probe Based on Effective
Optical Parameters", JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 29, NO.
8, APR. 15, 2011). The VR compensates for the LB property of the
fiber, while the HP compensates for the CB property. Thus, through
an appropriate setting of the principal axis angle and retardance
of the VR, and the optical rotation of the HP, the optical fiber
can be converted into a free-space medium with negligible linear or
circular birefringence. The free-space unit matrix of the
VR/HP/fiber configuration shown in FIG. 3(a) can be formulated as
follows:
[ M Fiber ] [ M HP ] [ M VR ] = ( 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 )
( 2.28 ) ##EQU00023##
[0059] Therefore, it follows that
[M.sub.HP][M.sub.VR]=[M.sub.Fiber].sup.-1 (2.29)
where
[M.sub.Fiber]=[M.sub.ld][M.sub.lb][M.sub.cb].apprxeq.[M.sub.lb][.su-
b.cb] since [M.sub.id].apprxeq.[1], and thus
[M.sub.HP].apprxeq.[M.sub.cb].sup.-1 and
[M.sub.VR].apprxeq.[M.sub.lb].sup.-1. Note that [M.sub.HP] is the
Mueller matrix of the HP , and has one variable parameter,
(.gamma..sub.H). [M.sub.VR] is the Mueller matrix of the VR, and
has two variable parameters, (.alpha..sub.v and .beta..sub.v).
[M.sub.Fiber] is the Mueller matrix of the optical fiber, and has
three constant parameters, (.alpha., .beta. and .gamma.). Generally
speaking, the values of .alpha..sub.v, .beta..sub.v and
.gamma..sub.H required to compensate for the birefringence
properties of the optical fiber are determined via an experimental
trial-and-error process. However, this process is tedious and
time-consuming Furthermore, it cannot absolutely guarantee the
formation of a free-space condition. Accordingly, in the prior art,
a method is proposed for determining the optimal values of
.alpha..sub.v, .beta..sub.v and .gamma..sub.H for any optical fiber
or fiber configuration using a genetic algorithm.
[0060] According to this implementation example, if a free-space
unit matrix is finally achieved, the input polarization states into
the compensation fiber are exactly same as the output polarization
states. The light traveling in a free-space fiber is just like
light traveling in air. A He--Ne laser (SL 02/2, SIOS Co.) with a
central wavelength of 632.8 nm is uesd to produce linear input
polarization lights.
[0061] Please refer to FIG. 3(b), it is seen that the azimuth angle
of the output light is linearly correlated with the azimuth angle
of the input light for all linear polarization states. Furthermore,
the ellipticity angle of the output light is equal to approximately
zero for all angles of the linear polarized light. FIG. 3(b)
confirm that the azimuth and ellipticity angles of the light
emerging from the VR/HP/fiber structure are virtually identical to
those of the light entering the VR. In other words, a free-space
condition is successfully achieved when using the optimal VR and HP
settings determined by the GA. FIG. 3(b) for linear input
polarization lights, a further series of experiments was performed
to evaluate its feasibility given right-hand and left-hand circular
input polarization lights, respectively. The results presented in
Table 1 confirm that a good agreement exists between the
ellipticity angles of the input and output lights in both
polarization states.
[0062] Please refer to FIG. 3(c), which compares the
azimuth/ellipticity angles of the input/output lights in the
free-space unit matrix media given input lights with various
randomly-selected right- and left-hand elliptical polarization
states, respectively. It can be seen that in every case, the
azimuth angles and ellipticity angles of the output light are in
good agreement with the equivalent angles of the input light. In
other words, the ability of the GA to predict the VR and HP
settings which result in a free-space condition given a random
elliptical polarization state of the input light is confirmed.
[0063] Please refer to FIG. 3(d), which verifies a optical
compensation of a equivalent free space using a broadband light
source such as ASE (1520 nm.about.1570 nm) FIG. 3(d) shows the
linear input polarization lights and the output light. The average
compensation error for azimuth angles and ellipticity angles is
0.75.degree. and 1.52.degree., respectively. A further series of
experiments was performed to evaluate its feasibility given
right-hand and left-hand circular input polarization lights,
respectively. The results presented in Table 2.
[0064] Please refer to FIG. 3(e), which compares the
azimuth/ellipticity angles of the input/output lights in the
free-space unit matrix media given input lights with various
randomly-selected right- and left-hand elliptical polarization
states, respectively. The average compensation error for azimuth
angles and ellipticity angles is 2.1.degree. and 4.7.degree.,
respectively. Thus, a free-space condition is successfully
achieved.
[0065] In addition, the first implementation example is included
but not limited to the five equivalent optical parameters. Any
number of optical parameters sufficient to represent the equivalent
of the optical path may also be implemented in the present
invention.
[0066] Please refer to FIG. 4(a), and it is the second better
implementation example for this case. It is the schematic diagram
in compensating for fiber coil 406 in order to let fiber coil
become a free space unit matrix 407 in a fiber optic gyroscope. It
contains a light source 400, a detector 401, a fiber coupler 402,
IOC 403, and fiber coil 406. At one port of fiber coil, it contains
a variable retarder 404 which is used to compensate for the effect
of the effective property of LB in an optical fiber coil 406, and a
half-wave plate 405 which is used to compensate for the effect of
the effective property of CB in an optical fiber 406. A variable
retarder 404 and half-wave plate 405 also can be replaced by a
polarization controller comprising two quarter waveplates and one
half waveplate. And its configuration position is not limited to
fiber coil 406 outlet but can be arbitrary allocated to the optical
path between IOC 403 and fiber coil 406. All arrangements make the
fiber coil become an equivalent free space. According to this
implementation example, if a free-space unit matrix is finally
achieved, the input polarization states into the compensated fiber
coil are exactly same as the output polarization states. The light
traveling in the fiber coil is just like the light traveling in
air. In addition to the second better implementation example, the
optical components used to compensate for the fiber coil 406 are
not limited in variable retarder 404 and half-wave plate 405 or
polarization controller, and any optical component that can
compensate for fiber coil 406 to achieve a free space is
included.
[0067] Please refer to FIG. 4(b), and it is the third better
implementation example for this case. It is the schematic diagram
in compensating for fiber coil 406 in order to let fiber coil
become a free space unit matrix 407 in a fiber optic gyroscope. It
contains a light source 400, a detector 401, a fiber coupler 402,
IOC 403, and fiber coil 406. At the end of fiber coil, twisting
part of fiber to compensate for fiber coil is used to make the
fiber coil to act like the free space 407. The twisted part is not
limited to the end of the fiber coil 406 but any optical path
between IOC 403 and fiber coil 406 is included. And the method to
compensate for fiber coil 406 is not limited in twisting but any
method that can make fiber coil 406 become free space 407 is
included. According to this implementation example, if a free-space
unit matrix is finally achieved, the input polarization states into
the compensated fiber coil are exactly same as the output
polarization states. The light traveling in the fiber coil is just
like the light traveling in air.
[0068] In conclusion, by means of the compensation method with or
without adding the optical component, the equivalent free space
compensation is accomplished by the optical system such as fiber
optic gyros provided by the present invention. Besides, the optical
verification method is proposed to verify that the polarization
state of the input light remain the same with the output light when
the light propagates in the compensated fiber or fiber component,
i.e., the equivalent free space. Therefore, the compensation method
of the present invention is particularly suitable for the fiber
sensors applications, such as fiber gyros, which greatly enhances
the fiber or fiber component repeatability and stability throughout
the fiber or fiber component production line.
[0069] Based on the above descriptions, it is understood that the
present invention is indeed an industrially applicable, novel and
obvious one with values in industrial development. While the
invention has been described in terms of what are presently
considered to be the most practical and preferred embodiments, it
is to be understood that the invention should not be limited to the
disclosed embodiment. On the contrary, it is intended to cover
numerous modifications and variations included within the spirit
and scope of the appended claims which are to be accorded with the
broadest interpretation so as to encompass all such modifications
and variations. Therefore, the above description and illustration
should not be taken as limiting the scope of the present invention
which is defined by the appended claims.
* * * * *