U.S. patent application number 14/326004 was filed with the patent office on 2017-01-05 for optical position and/or shape sensing.
The applicant listed for this patent is Intuitive Surgical Operations, Inc.. Invention is credited to Mark E. FROGGATT, Dawn K. Gifford, Justin W. Klein, Stephen Tod Kreger.
Application Number | 20170003119 14/326004 |
Document ID | / |
Family ID | 43759221 |
Filed Date | 2017-01-05 |
United States Patent
Application |
20170003119 |
Kind Code |
A9 |
FROGGATT; Mark E. ; et
al. |
January 5, 2017 |
OPTICAL POSITION AND/OR SHAPE SENSING
Abstract
An accurate measurement method and apparatus using an optical
fiber are disclosed. A total change in optical length in an optical
core in the optical fiber is determined that reflects an
accumulation of all of the changes in optical length for multiple
segment lengths of the optical core up to a point on the optical
fiber. The total change in optical length in the optical core is
provided for calculation of an average strain over a length of the
optical core based on the detected total change in optical
length.
Inventors: |
FROGGATT; Mark E.;
(Blacksburg, VA) ; Klein; Justin W.; (Blacksburg,
VA) ; Gifford; Dawn K.; (Blacksburg, VA) ;
Kreger; Stephen Tod; (Blacksburg, VA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Intuitive Surgical Operations, Inc. |
Sunnyvale |
CA |
US |
|
|
Prior
Publication: |
|
Document Identifier |
Publication Date |
|
US 20140320846 A1 |
October 30, 2014 |
|
|
Family ID: |
43759221 |
Appl. No.: |
14/326004 |
Filed: |
July 8, 2014 |
Related U.S. Patent Documents
|
|
|
|
|
|
Application
Number |
Filing Date |
Patent Number |
|
|
12874901 |
Sep 2, 2010 |
8773650 |
|
|
14326004 |
|
|
|
|
61350343 |
Jun 1, 2010 |
|
|
|
61255575 |
Oct 28, 2009 |
|
|
|
61243746 |
Sep 18, 2009 |
|
|
|
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G01B 11/16 20130101;
G01M 11/025 20130101; G02B 6/02042 20130101; G01M 11/331 20130101;
G01L 1/242 20130101; G01M 11/3172 20130101; G01B 11/18 20130101;
G01B 11/168 20130101; G01L 1/246 20130101; G01M 11/31 20130101;
G01B 11/24 20130101 |
International
Class: |
G01B 11/24 20060101
G01B011/24; G01B 11/16 20060101 G01B011/16 |
Claims
1. A measurement method for an optical fiber, comprising:
determining a total change in optical length in an optical core in
the optical fiber that reflects an accumulation of all of the
changes in optical length for multiple segment lengths of the
optical core up to a point on the optical fiber, and providing the
total change in optical length in the optical core for calculation
of an average strain over a length of the optical core based on the
detected total change in optical length.
2. The method in claim 1, wherein the determining step includes:
using optical frequency domain reflectometry (OFDR) to obtain phase
data values along the optical core; determining a phase change
between two sets of complex data values associated with the optical
core; and wherein the total change in optical length is determined
based on the determined phase change.
3. The method in claim 2, wherein the optical core is divided into
segments, and wherein determining step further comprises: obtaining
a reference measurement for each of the multiple segments for
producing a reference data set for each of the multiple segments;
obtaining a subsequent test measurement for each of the multiple
segments for producing a test data set for each of the multiple
segments; determining a delay to one of the segments in the
multiple segments; adjusting the delay to the one segment to align
the reference and test data sets; and calculating the phase change
between the aligned reference and test data sets.
4. The method in claim 1, wherein the detecting includes detecting
an incremental change in optical length in the one of the cores in
the optical fiber for each of multiple segment lengths up to a
point on the optical fiber, and wherein the detected changes in
optical length is based on a combination of the incremental
changes.
5. The method in claim 4, wherein the detecting step includes
detecting a phase response of a light signal reflected in the core
of the optical fiber from multiple segment lengths, and wherein
strain on the fiber at the segment lengths causes a shift in the
phase of the reflected light signal from the segment lengths in the
core.
6. The method in claim 5, further comprising monitoring the phase
response continuously along the optical length of the optical
fiber.
7. The method in claim 5, further comprising: detecting a reflected
Rayleigh scatter pattern in the reflected light signal for each
segment length, comparing the reflected Rayleigh scatter pattern
with a reference Rayleigh scatter pattern for each segment length,
and determining the phase response for each segment length based on
the comparison.
8. The method in claim 1, wherein the changes in optical length are
determined by calculating an optical phase change at each segment
length along the optical fiber and unwrapping the optical phase
change to determine the optical length.
9. The method in claim 1, further comprising: transmitting light
with at least two polarization states along the optical fiber, and
combining reflections of the light with the at least two
polarization states in determining changes in optical path
length.
10. The method in claim 9, wherein the two polarization states
include a first polarization state and a second polarization state
which are at least nominally orthogonal, and the method further
comprises: using a polarization controller to transmit a first
light signal at the first polarization state along the optical
fiber, using the polarization controller to transmit a second light
signal at the second polarization state along the optical fiber,
calculating a polarization-independent change in optical length in
the core of the optical fiber up to the point on the optical fiber
using reflections of the first and second light signals.
11. The method in claim 1, wherein Bragg gratings are present in
the optical fiber, and wherein adjacent ones of the Bragg gratings
are spaced apart by no more than 1 mm over the length of the
optical fiber.
12. The method in claim 11, where the Bragg gratings are present
the optical fiber without a gap between adjacent Bragg gratings
over the length of the optical fiber.
13. An apparatus for making measurements of using an optical fiber,
comprising: detection circuitry configured to determine a total
change in optical length in an optical core in the optical fiber
that reflects an accumulation of all of the changes in optical
length for multiple segment lengths of the optical core up to a
point on the optical fiber, and processing circuitry configured to
provide the total change in optical length in the optical core for
calculation of an average strain over a length of the optical core
based on the detected total change in optical length.
14. The apparatus in claim 13, wherein the detection circuitry is
configured to use optical frequency domain reflectometry to obtain
phase data values along the optical core and determine a phase
change between two sets of complex data values associated with the
optical core, wherein the total change in optical length is based
on the determined phase change.
15. The apparatus in claim 14, wherein the optical core is divided
into segments, and wherein the detection circuitry is configured
to: obtain a reference measurement for each of the multiple
segments for producing a reference data set for each of the
multiple segments; obtain a subsequent test measurement for each of
the multiple segments for producing a test data set for each of the
multiple segments; determine a delay to one of the segments in the
multiple segments; adjust the delay to the one segment to align the
reference and test data sets; and calculate the phase change
between the aligned reference and test data sets.
16. The apparatus in claim 13, wherein the detection circuitry is
configured to detect an incremental change in optical length in the
one of the cores in the optical fiber for each of multiple segment
lengths up to a point on the optical fiber, and wherein the
detected changes in optical length is based on a combination of the
incremental changes.
17. The apparatus in claim 13, wherein the detection circuitry is
configured to detect a phase response of a light signal reflected
in the core of the optical fiber from multiple segment lengths, and
wherein strain on the fiber at the segment lengths causes a shift
in the phase of the reflected light signal from the segment lengths
in the core.
18. The apparatus in claim 17, wherein the detection circuitry is
configured to monitor the phase response continuously along the
optical length of the optical fiber.
19. The apparatus in claim 17, the detection circuitry is
configured to: detect a reflected Rayleigh scatter pattern in the
reflected light signal for each segment length, compare the
reflected Rayleigh scatter pattern with a reference Rayleigh
scatter pattern for each segment length, and determine the phase
response for each segment length based on the comparison.
20. The apparatus in claim 13, wherein the changes in optical
length are determined by calculating an optical phase change at
each segment length along the optical fiber and unwrapping the
optical phase change to determine the optical length.
21. The apparatus in claim 13, further comprising: a transmitter
configured to transmit light with at least two polarization states
along the optical fiber, and a combiner configured to combine
reflections of the light with the at least two polarization states
in determining changes in optical path length.
22. The apparatus in claim 21, wherein the two polarization states
include a first polarization state and a second polarization state
which are at least nominally orthogonal, the apparatus comprising:
a polarization controller configured to transmit a first light
signal at the first polarization state along the optical fiber and
a second light signal at the second polarization state along the
optical fiber, wherein the processing circuitry is configured to
calculate a polarization-independent change in optical length in
the core of the optical fiber up to the point on the optical fiber
using reflections of the first and second light signals.
23. The apparatus in claim 13, further comprising: Bragg gratings
in the optical fiber, wherein adjacent ones of the Bragg gratings
are spaced apart by no more than 1 mm over the length of the
optical fiber.
24. The apparatus in claim 23, wherein the Bragg gratings are
positioned in the optical fiber without a gap between adjacent
Bragg gratings over the length of the optical fiber.
25. A non-transitory storage medium storing a program instructions
which when executed on a computerized measurement device cause the
computerized measurement device to make measurements using an
optical fiber by performing the following tasks: determining a
total change in optical length in an optical core in the optical
fiber that reflects an accumulation of all of the changes in
optical length for multiple segment lengths of the optical core up
to a point on the optical fiber, and providing the total change in
optical length in the optical core for calculation of an average
strain over a length of the optical core based on the detected
total change in optical length.
Description
PRIORITY APPLICATIONS
[0001] This application claims priority U.S. patent application
Ser. No. 12/874,901, filed Sep. 2, 2010, which claims priority from
U.S. provisional patent applications 61/350,343, filed on Jun. 1,
2010, 61/255,575, filed on Oct. 28, 2009, and 61/243,746, filed on
Sep. 18, 2009, the contents of which are incorporated herein by
reference.
TECHNICAL FIELD
[0002] The technical field relates to optical measurements.
BACKGROUND
[0003] Shape measurement is a general term that includes sensing a
structure's position in three dimensional space. This measurement
coincides with what the human eye perceives as the position of an
object. Since the eyes continually perform this task, one might
assume that the measurement is simple. If one considers a length of
rope, one can physically measure the position at every inch along
the rope to estimate the shape. But this task is tedious and is
increasingly difficult with more complex shapes. Another
consideration is how to perform the measurement if the rope cannot
be physically reached or seen. If the rope is contained within a
sealed box, its position cannot be determined by conventional
measurement techniques. The rope in this example can be replaced
with an optical fiber.
[0004] Sensing the shape of a long and slender deformed cylinder,
such as an optical fiber, is useful in many applications ranging
for example, from manufacturing and construction to medicine and
aerospace. In most of these applications, the shape sensing system
must be able to accurately determine the position of the fiber,
e.g., within less than one percent of its length, and in many
cases, less than one tenth of one percent of its length. There are
a number of approaches to the shape measurement problem, but none
adequately addresses the requirements of most applications because
they are too slow, do not approach the required accuracies, do not
function in the presence of tight bends, or fail to adequately
account for twist of the fiber. In many applications, the presence
of torsional forces that twist the fiber undermine the accuracy,
and thus, usefulness of these approaches.
[0005] Conventional approaches to measuring the shape of a fiber
use strain as the fundamental measurement signal. Strain is a ratio
of the change in length of a fiber segment post-stress verses the
original length of that segment (pre-stress). As an object like a
fiber is bent, material on the outside of the bend is elongated,
while the material on the inside of the bend is compressed. Knowing
these changes in local strain and knowing the original position of
the object, an approximation of the new position of the fiber can
be made.
[0006] In order to effectively sense position with high accuracy,
several key factors must be addressed. First, for a strain-based
approach, the strain measurements are preferably accurate to tens
of nanostrain (10 parts per billion) levels. But high accuracy
strain measurements are not readily attainable by conventional
resistive or optical strain gauges. Therefore, a new technique to
measure the strain to extremely high accuracy must be devised that
is not strain-based in the conventional sense.
[0007] Second, the presence of twist in the optical fiber must be
measured to a high degree of accuracy and accounted for in the
shape computation. By creating a multi-core fiber that is helixed
and has a central core, the twist of a fiber can be sensed. But the
problem is how to obtain an accuracy of rotational position better
than 1 degree. For a high accuracy rotational sensor, the position
of strain sensors along the length of the fiber must also be known
to a high degree of accuracy. Therefore, some way of measuring the
rotation rate of the outer cores in the helixed fiber is desirable,
which can then be used to correct the calculation of the fiber
position.
[0008] Third, fiber with multiple cores that is helixed at a
sufficient rate and with Bragg gratings (a conventional optical
strain gauge) is difficult and expensive to make. It is therefore
desirable to provide a method of achieving nanostrain resolutions
without Bragg gratings.
[0009] Fourth, multi-core fiber is typically not
polarization-maintaining, and so polarization effects are
preferably considered.
SUMMARY
[0010] The technology described below explains how to use the
intrinsic properties of optical fiber to enable very accurate shape
calculation in light of the above factors and considerations. In
essence, the fiber position is determined by interpreting the back
reflections of laser light scattered off the glass molecules within
the fiber. This measurement can be performed quickly, with a high
resolution, and to a high degree of accuracy.
[0011] A very accurate measurement method and apparatus are
disclosed for measuring position and/or direction using a
multi-core fiber. A change in optical length is detected in ones of
the cores in the multi-core fiber up to a point on the multi-core
fiber. A location and/or a pointing direction are/is determined at
the point on the multi-core fiber based on the detected changes in
optical length. The pointing direction corresponds to a bend angle
of the multi-core fiber at the position along the multi-core fiber
determined based on orthonormal strain signals. The accuracy of the
determination is better than 0.5% of the optical length of the
multi-core fiber up to the point on the multi-core fiber. In a
preferred example embodiment, the determining includes determining
a shape of at least a portion of the multi-core fiber based on the
detected changes in optical length.
[0012] The determination may include calculating a bend angle of
the multi-core fiber at any position along the multi-core fiber
based on the detected changes in length up to the position.
Thereafter, the shape of the multi-core fiber may be determined
based on the calculated bend angle. The bend angle may be
calculated in two or three dimensions.
[0013] Detecting the change in optical length preferably includes
detecting an incremental change in optical length in the ones of
the cores in the multi-core fiber for each of multiple segment
lengths up to a point on the multi-core fiber. The overall detected
change in optical length is then based on a combination of the
incremental changes. The change in optical length is determined by
calculating an optical phase change at each segment length along
the multi-core fiber and unwrapping the optical phase change to
determine the optical length.
[0014] More specifically, in a non-limiting example embodiment, a
phase response of a light signal reflected in at least two of the
multiple cores from multiple segment lengths may be detected.
Strain on the fiber at the segment lengths causes a shift in the
phase of the reflected light signal from the segment lengths in the
two cores. The phase response is preferably continuously monitored
along the optical length of the multi-core fiber for each segment
length.
[0015] In another non-limiting example embodiment, a reflected
Rayleigh scatter pattern in the reflected light signal is detected
for each segment length, thereby eliminating the need for Bragg
gratings or the like. The reflected Rayleigh scatter pattern is
compared with a reference Rayleigh scatter pattern for each segment
length. The phase response is determined for each segment length
based on the comparison.
[0016] A non-limiting example embodiment also determines a twist
parameter associated with the multi-core fiber at a point on the
multi-core fiber based on the detected changes in optical length of
the multi-core fiber. The location at the point on the multi-core
fiber is then translated to an orthonormal coordinate system based
on the determined twist parameter. Preferably, the determined twist
parameter is corrected for each of the segment lengths.
[0017] In one example application where the multi-core fiber
includes three peripheral cores spaced around a fourth core along
the center of the multi-core fiber, a phase response of a light
signal reflected in each of the four cores from each segment length
is determined Strain on the multi-core fiber at one or more of the
segment lengths causes a shift in the phase of the reflected light
signal in each core. The phase responses for the three peripheral
cores are averaged. The averaged phase response is combined with
the phase response of the fourth core to remove a common mode
strain. The twist parameter is then determined from the combined
phase response.
[0018] In another non-limiting example embodiment, bend-induced
optical length changes along the multi-core fiber are determined
and accounted for when determining the twist parameter. A bend at
one of the segment lengths is calculated and squared. The squared
bend is multiplied by a constant to produce a bend product which is
combined with the determined change in optical length of an outer
core of the multi-core fiber at the one segment length. One example
beneficial application for this embodiment is for bend radii less
than 50 mm.
[0019] Another non-limiting example embodiment determines a
rotational orientation of the multi-core fiber about its axis at a
point on the multi-core fiber at each of the segment lengths. A
correction is made for the effect of torsion and the resulting
twist on the determined orientation based on the detected changes
in optical length of the multiple fiber cores. This correction is
required to compute the correct bend direction.
[0020] Given a multi-core fiber characterized by a nominal spin
rate, another non-limiting example embodiment determines an angular
rotation of the multi-core fiber at a point on the multi-core fiber
at each of the segment lengths compared to the nominal spin rate of
the multi-core fiber. A variation in the nominal spin rate at the
point along the multi-core fiber is determined and corrected for. A
"wobble factor" is determined for the multi-core fiber by
constraining the multi-core fiber to a curved orientation in one
plane. Correction is then made for the wobble factor when
determining the location at the point on the multi-core fiber based
on the detected changes in optical length.
[0021] In another non-limiting example embodiment, light is
transmitted with at least two polarization states along the
multi-core fiber. Reflections of the light with the at least two
polarization states are combined and used in determining the
location or the pointing direction at the point on the multi-core
fiber based on the detected changes in optical length. The two
polarization states include a first polarization state and a second
polarization state which are at least nominally orthogonal. A
polarization controller is used to transmit a first light signal at
the first polarization state along the multi-core fiber and to
transmit a second light signal at the second polarization state
along the multi-core fiber. A polarization-independent change in
optical length in each one of multiple cores in the multi-core
fiber is calculated up to the point on the multi-core fiber using
reflections of the first and second light signals.
BRIEF DESCRIPTION OF THE DRAWINGS
[0022] FIG. 1 shows a cross-section of an example multi-core
fiber;
[0023] FIG. 2 shows a bent multi-core fiber;
[0024] FIG. 3 shows that the bend in the fiber is proportional to
the strain in the off-center cores;
[0025] FIG. 4 shows that bend angle at any location along the fiber
can be determined by a summation of all previous angles;
[0026] FIG. 5 shows that as a fiber containing Bragg gratings is
strained, a phase difference measured from a reference state begins
to accumulate;
[0027] FIG. 6 shows a clock that helps to visualize the
relationship between the phase shift and position;
[0028] FIG. 7 illustrates how a lack of resolution in measuring
phase can be problematic;
[0029] FIG. 8 is a graph that shows a phase difference of a
Rayleigh scatter signal between a reference scan and a measurement
scan at the beginning of a section of fiber that is under
tension;
[0030] FIG. 9 is a graph that shows that coherence is lost with the
reference measurement at a greater distance down a fiber under
tension;
[0031] FIG. 10 shows optical phase plotted against frequency for
two different delays;
[0032] FIG. 11 shows a recovered phase over a section of fiber
where a third of an index shift has occurred;
[0033] FIG. 12 illustrates an example of helically-spun multi-core
shape sensing fiber;
[0034] FIG. 13 illustrates a non-limiting, example test multi-core
optical fiber;
[0035] FIG. 14 illustrates a cross-section of a helixed fiber where
the position of the outer cores appears to rotate around the center
core progressing down the length of the fiber;
[0036] FIG. 15 is a graph that illustrates an example of variations
in the spin rate of a fiber;
[0037] FIG. 16 is a graph that shows an example wobble signal with
a periodic phase variation from a manufactured spin rate along the
length of a shape sensing fiber;
[0038] FIG. 17 shows how torsion changes the spin rate of a shape
sensing fiber based on orientation of the force to the nominal spin
direction of the fiber;
[0039] FIG. 18 shows an outer core that experiences twist modeled
as a flattened cylinder as it translates along the surface;
[0040] FIG. 19 is a flowchart illustrating non-limiting example
procedures to calculate external twist along the fiber;
[0041] FIG. 20 shows an example data set for a generic shape that
illustrates the FIG. 19 procedures in more detail;
[0042] FIG. 21 is a graph that shows a slight deviation between the
two phase curves;
[0043] FIG. 22 is a graph illustrating a twist signal produced from
FIG. 21;
[0044] FIG. 23 illustrates the necessity of compensating for twist
in the shape calculation;
[0045] FIG. 24 depicts example orthogonal strain curves for a fiber
placed in several bends that all occur in the same plane;
[0046] FIG. 25 shows a flowchart diagram describing non-limiting,
example steps for calculating shape from strain;
[0047] FIG. 26 illustrates that if each of multiple pointing
vectors is placed head-to-tail an accurate measurement of the shape
results;
[0048] FIG. 27 is a non-limiting, example optical position and
shape sensing system;
[0049] FIG. 28 is flowchart diagram illustrating non-limiting,
example steps for calculating birefringence correction;
[0050] FIG. 29 shows a bend-induced strain profile of a cross
section of a shape sensing fiber;
[0051] FIG. 30 shows two phase plots comparing a center core phase
signal to an average phase of the outer cores;
[0052] FIG. 31 shows an example strain response for an outer core
for a 40 mm diameter fiber loop;
[0053] FIG. 32 is a graph showing a bend-induced birefringence
correction for the 40 mm diameter fiber loop;
[0054] FIG. 33 is a graph comparing a twist signal with and without
a 2.sup.nd order birefringence correction;
[0055] FIG. 34 shows a non-limiting, example loop polarization
controller between a shape sensing fiber and a position and shape
sensing system;
[0056] FIG. 35 shows an in-plane signal for a relatively simple
shape where 1.4 meters of shape sensing fiber is routed through a
single 180 degree turn with a bend radius of 50 mm;
[0057] FIG. 36 shows three successive out-of-plane measurements
where between each measurement, the polarization is varied using a
polarization controller;
[0058] FIG. 37 is a graph showing an example that two successive
measurements of the center core, with different input polarization
states do not have a significant variation in phase response;
[0059] FIG. 38 is a graph showing an example that two successive
measurements of an outer core respond differently to input
polarization providing evidence for birefringence in the shape
sensing fiber;
[0060] FIG. 39 is a graph showing that correcting for birefringence
improved the precision of the system; and
[0061] FIG. 40 is a graph showing that correcting for both first
and second order birefringence improved the accuracy and precision
of the system.
DETAILED DESCRIPTION
[0062] In the following description, for purposes of explanation
and non-limitation, specific details are set forth, such as
particular nodes, functional entities, techniques, protocols,
standards, etc. in order to provide an understanding of the
described technology. It will be apparent to one skilled in the art
that other embodiments may be practiced apart from the specific
details disclosed below. In other instances, detailed descriptions
of well-known methods, devices, techniques, etc. are omitted so as
not to obscure the description with unnecessary detail. Individual
function blocks are shown in the figures. Those skilled in the art
will appreciate that the functions of those blocks may be
implemented using individual hardware circuits, using software
programs and data in conjunction with a suitably programmed
microprocessor or general purpose computer, using applications
specific integrated circuitry (ASIC), and/or using one or more
digital signal processors (DSPs). The software program instructions
and data may be stored on computer-readable storage medium and when
the instructions are executed by a computer or other suitable
processor control, the computer or processor performs the
functions.
[0063] Thus, for example, it will be appreciated by those skilled
in the art that block diagrams herein can represent conceptual
views of illustrative circuitry or other functional units embodying
the principles of the technology. Similarly, it will be appreciated
that any flow charts, state transition diagrams, pseudocode, and
the like represent various processes which may be substantially
represented in computer readable medium and so executed by a
computer or processor, whether or not such computer or processor is
explicitly shown.
[0064] The functions of the various elements including functional
blocks, including but not limited to those labeled or described as
"computer", "processor" or "controller" may be provided through the
use of hardware such as circuit hardware and/or hardware capable of
executing software in the form of coded instructions stored on
computer readable medium. Thus, such functions and illustrated
functional blocks are to be understood as being either
hardware-implemented and/or computer-implemented, and thus
machine-implemented.
[0065] In terms of hardware implementation, the functional blocks
may include or encompass, without limitation, digital signal
processor (DSP) hardware, reduced instruction set processor,
hardware (e.g., digital or analog) circuitry including but not
limited to application specific integrated circuit(s) (ASIC), and
(where appropriate) state machines capable of performing such
functions.
[0066] In terms of computer implementation, a computer is generally
understood to comprise one or more processors or one or more
controllers, and the terms computer and processor and controller
may be employed interchangeably herein. When provided by a computer
or processor or controller, the functions may be provided by a
single dedicated computer or processor or controller, by a single
shared computer or processor or controller, or by a plurality of
individual computers or processors or controllers, some of which
may be shared or distributed. Moreover, use of the term "processor"
or "controller" shall also be construed to refer to other hardware
capable of performing such functions and/or executing software,
such as the example hardware recited above.
Phase Tracking for Increased Angular Accuracy
[0067] FIG. 1 shows a cross-section of an example multi-core fiber
1 that includes a center core 2 and three peripheral cores 3, 4,
and 5 surrounded by coating 6. These cores 3-5 shown in this
example are spaced apart by approximately 120 degrees.
[0068] Shape sensing with a multi-core fiber assumes that the
distances between cores in the fiber remain constant, when viewed
in cross section, regardless of the shape of the fiber. This
assumption is often valid because glass is very hard and very
elastic. Further, the cross section of the fiber (e.g., .about.125
microns) is small when compared with the dimensions of curves
experienced by the fiber (e.g., bend radii greater than 5 mm) This
maintenance of the cross-sectional position of the cores implies
that all deformation of the fiber must be accommodated by the
elongation or the compression of the cores. As shown in FIG. 2,
when a shape fiber is bent, a core on the outside 7 of the bend
will be elongated while a core on the inside 8 of the bend will
experience compression.
[0069] Since the average length of a fiber core segment is assumed
to remain unchanged, an exercise in geometry shows that the change
in the pointing direction, (i.e., a vector that describes the
position of the central axis of the fiber segment), can be
calculated based on the change in the core lengths and the distance
between the cores. Other effects, such as the strain-optic
coefficient, must be taken into account. The result is that the
change in pointing direction for a given segment of fiber is
directly proportional to the difference in length changes in the
cores within that segment.
[0070] FIG. 3 shows that the bend in the fiber .theta. is
proportional to the strain .epsilon. in the off-center cores, where
s is the segment length, r is radius, and k is a constant. In order
to eliminate tension and temperature from the measurement, a
differential measurement between the cores is used.
.DELTA..theta. = k ( d s 2 - d s 1 s ) = k ( 2 - 1 ) Eq . 1
##EQU00001##
[0071] The above equation describes the angular change for a given
fiber segment and how it relates to a change in strain. Moving to
the next segment in the fiber, the angular change of the previous
segment must be added to the next change in angle for the next
segment to calculate the current pointing direction of the fiber.
In two dimensions, all of the previous angles can be accumulated to
find the bend angle at any particular location along the fiber.
FIG. 4 shows the bend angle at any point or location along the
fiber can be determined by a summation of all angles leading up to
that point, e.g.,
.theta..sub.5=.theta..sub.1+.theta..sub.2+.theta..sub.3+.theta..sub.4+.th-
eta..sub.5. If there are errors in measuring the angles, these
errors accumulate along the fiber and result in a total error. This
error becomes greater the longer the fiber, growing as the square
root of the number of segments.
[0072] To avoid this accumulated angle measurement error, the
inventors conceived of directly measuring the change in length of a
segment rather than measuring strain. Mathematically, the summation
of angles then becomes the summation of the length changes along
the fiber as shown in equation (2) where L corresponds to fiber
length.
.theta. = .DELTA..theta. = k ( d s 2 - d s 1 ) s = k ( .DELTA. L 2
- .DELTA. L 1 ) s Eq . 2 ##EQU00002##
[0073] Thus, the angle at any position Z along the fiber then
becomes linearly proportional to the difference between the total
changes in length of the cores up to that position as shown in
equation (3).
.theta.(z).varies..DELTA.L.sub.2(z)-.DELTA.L.sub.1(z) Eq. 3
[0074] Therefore, if the total length change along the fiber can be
accurately tracked continuously, rather than summing each
individual local change in strain, the angular error can be
prevented from growing. Later, it will be shown how it is possible
to track the change in length of a core to an accuracy better than
10 nm, and to maintain this accuracy over the entire length of the
fiber. This level of accuracy yields 0.3 degrees of angular
accuracy with a 70 micron separation between cores and,
theoretically, about 0.5% of fiber length position accuracy.
[0075] Unfortunately, the cumulative relationship defined in (3)
does not hold in three dimensions. But most three dimensional
shapes can be accurately represented as a succession of two
dimensional curves, and in the presence of small angular changes
(<10 degrees), three dimensional angles also have this simple
cumulative relationship. As a consequence, this approach is useful
to assess error contributions in three dimensions.
[0076] The insight provided by this geometric exercise is that the
total length change as a function of distance along the multi-core
fiber is used rather than local strain. In other words, relatively
larger errors in the measured local strain values can be tolerated
as long as the integral of the measured strain corresponding to the
total length change up to that point, remains accurate. Nanostrain
accuracies are achieved without requiring extremely large
signal-to-noise ratios as the distances over which the nanostrains
are calculated are relatively large (e.g., many centimeters such as
10-1000 cm). As explained later in description, the tracking of the
change in length can also be used to assess rotation along the
length of the fiber allowing higher than expected accuracies to be
achieved in the measurement of fiber roll, or rotational angle
around the fiber's axis, as well.
Phase Tracking in Optical Fiber
[0077] As a sensor, optical fiber can provide spatially continuous
measurements along its entire length. Continuous measurements are
important because optical phase shifts are used to provide very
high resolution displacement measurements. Later it is explained
how the intrinsic scatter in the fiber can be used to achieve this
measurement, but it is conceptually easier to begin the explanation
with Fiber Bragg Gratings (FBGs). A Fiber Bragg Grating is a
periodic modulation of the index of refraction of the fiber. Each
period is about one half of the wavelength of the light in the
fiber. The vacuum wavelength of the light is about 1550 nm, and its
wavelength in the fiber is about 1000 nm. The period of the grating
is therefore about 500 nm. Typically a Bragg grating is used as a
sensor by measuring its reflected spectrum. The Bragg grating
condition is calculated using the equation below.
.lamda..sub.B=2n.lamda. Eq. 4
[0078] In this equation, .lamda..sub.B represents wavelength, n is
the index of refraction of fiber, and .lamda. corresponds to the
period of the grating. If it is assumed that the index of
refraction remains constant, then the reflected wavelength is
solely dependent on the period of the grating. As the fiber is
strained, the period of the grating is distorted, creating a shift
in the reflected wavelength. Thus, for a shift in wavelength, it is
possible to derive the amount of strain that was applied to the
fiber. The period of a Bragg grating is highly uniform, and it is
convenient to model this periodicity as a sinusoidal modulation.
When represented as a sinusoid, distortions in the period of the
grating can be described as phase shifts. To illustrate this
concept, consider the example in FIG. 5 which shows that as a fiber
containing Bragg gratings is strained, a phase difference measured
from a reference state begins to accumulate.
[0079] The depiction of a strained Bragg grating shown in FIG. 5
illustrates the local changes in index of refraction as alternating
white and hatched segments. Assuming an ideal Bragg grating, all of
the periods are identical, and the phase of the modulation pattern
increases linearly moving along the grating. In other words, the
rate of change of the phase with distance is inversely proportional
to the period of the grating. If a small portion of the grating is
stretched, then the rate of change of the phase decreases in the
stretched portion.
[0080] In FIG. 5, the top pattern depicts an undistorted grating
with a perfectly linear phase as a function of position. The lower
shifted pattern depicts a grating distorted due to strain. The
bottom graph shows the difference in phase between the two gratings
at each location. The distortion in the grating results in a phase
shift in the reflected signal of the grating with respect to the
original undistorted phase. A phase shift of 90 degrees is
illustrated. After the strained segment, the rate of change returns
to the unstrained state. However, the phase in this region is now
offset from the original phase by an amount equal to the total
phase change in the strained segment. This phase offset is directly
proportional to the actual length change of the optical fiber.
[0081] This illustration shows only fifteen periods of the grating.
Since a period is 500 nm, this amounts to 7.5 um in length.
Stretching the fiber to induce a 90 degree phase shift displaced
the remaining unstrained gratings by a quarter of a period, or 125
nm. A typical Optical Frequency Domain Reflectometry (OFDR)
measurement may have a spatial resolution on the order of 50
microns. In other words, each OFDR data point, or index, is
separated by 50 um. So a distortion of 125 nm results in only a
small fraction of an OFDR index shift in the actual position of the
grating. While the 125 nm change in position is not detectable
itself, the 90 degree phase shift is relatively easily measured
with an OFDR system.
[0082] OFDR can therefore be used to measure distortions within
Bragg gratings, and instead of only measuring the rate-of-change of
the phase (i.e., wavelength), the absolute phase can be measured,
and from the phase, distance changes at each segment along the
fiber core. This is important for accurate shape measurements in a
situation where the phase in the grating is observed to have
changed, while the position of the grating shows no readily
discernable change. Conventional optical fiber measurement
technologies treat the phase shift and the position as separate
effects.
[0083] One way to visualize the relationship between the phase
shift and position is to imagine that the phase of the optical
signal is represented by the second hand on a clock, and that the
location along the fiber in index is represented by the hour hand
on a clock. FIG. 6 illustrates a clock with no minute hand. Such a
clock makes it difficult to determine the time to a resolution of
one minute. But this clock is still useful for timing both short
duration events with the second hand and long duration events with
the hour hand. Lacking a minute hand, it is not useful for
measuring intermediate midscale duration events (e.g., 1 hour 12
minutes and 32 seconds) to one second precision. This difficulty of
linking the two scales has caused conventional optical measurement
systems to treat the phenomena separately.
[0084] This clock analogy helps to clarify why a continuous
measurement is needed along the entire length of the fiber. By
monitoring the position of the second hand continuously, the number
of complete revolutions can be measured, which allows the
simultaneous monitoring of long durations to a high precision.
Linking the clock analogy to the previous discussion of Bragg
gratings, each 360 degrees, or 2.pi., of phase change equates to a
500 nm shift in location. By continuously tracking phase along the
optical fiber, both local strains and overall length changes of the
optical fiber can be measured to a very high precision.
[0085] A challenge in tracking the phase continuously is that the
resolution of the measurement must be sufficient such that the
phase does not change from one segment to the next by more than
2.pi.. FIG. 7 illustrates how this lack of resolution can be
problematic because there is no way to distinguish, for example,
between a change of .pi./3 and a change of .pi./3+2.pi.. So two
different phase shifts will appear to have the same value on the
unit circle. In other words, an error of one index would be
incurred in a count of full 2.pi. revolutions. In this example,
measurement of the overall change in length of the optical fiber
would be deficient by 500 nm.
[0086] So it is it is important that a shape sensing system has
sufficient resolution to guarantee the ability to track phase along
the entire length of a shape sensing fiber to ensure the accuracy
of a shape sensing system.
Rayleigh Scatter-Based Measurements
[0087] As explained above, the typical use of an FBG for sensing
involves measuring shifts in the reflected spectrum of individual
Bragg gratings spaced at some interval down a fiber. Strain is
derived for each section of fiber from the measurement for each
Bragg grating. For shape sensing using FBGs, each strain
measurement indicates how much a given segment is bent and in which
direction. This information is summed for all measured segments to
give the total fiber position and/or shape. However, using this
method, an error in each segment accumulates along the fiber. The
longer the fiber, the larger the error in the measurement. This
error using multiple Bragg gratings limits the speed of operation
and the range of applications.
[0088] If there were a continuous grating along the fiber, then the
phase could be tracked at every point along the fiber as described
above. Tracking the phase along the entire length of the core
avoids accumulating error. Instead of accumulating error as the
square root of the number of fiber segments, the total length error
remains constant at a fraction of the optical wavelength in the
material. As mentioned earlier, a wavelength of light can be about
1550 nm in a vacuum and about 1000 nm in the fiber, which is
effectively 500 nm in reflection. A signal-to-noise ratio of 50
provides for an accuracy of 10 nm due to the round trip
(reflective) nature of the measurement. The resulting strain
accuracy over one meter of fiber will be 10 nanostrain.
[0089] Rayleigh scatter can be viewed as a Bragg grating with
random phases and amplitudes or a Bragg grating consisting entirely
of defects. This Rayleigh scatter pattern, while random, is fixed
within a fiber core when that core is manufactured. Strain applied
to an optical fiber causes shifts or distortions in the Rayleigh
scatter pattern. These induced distortions of the Rayleigh scatter
pattern can be used as a high resolution strain measurement for
shape sensing by comparing a reference scan of the fiber when the
fiber is in a known shape with a new scan of the fiber when it has
been bent or strained.
[0090] FIG. 8 shows example results of such a comparison. This
figure shows the phase difference of the Rayleigh scatter signal
between a reference scan and a measurement scan at the beginning of
a section of fiber that enters a region that is under tension. The
data is plotted as a function of fiber index, which represents
distance along the fiber. Once the region of tension is entered,
the phase difference begins to accumulate. Since .pi. and -.pi.
have the same value on the unit circle, the signal experiences
"wrapping" every multiple of 2.pi. as the phase difference grows
along the length of the fiber. This can be seen around index 3350
where the values to the left of this are approaching .pi., and then
suddenly the values are at -.pi.. As shown, each wrap represents
about 500 nm of length change in the fiber. Since an index
represents about 50 microns of length, it takes about one hundred
wraps of the phase to accumulate a full index of delay change
between measurement and reference.
[0091] The data in FIG. 9 is from the same data set as that for
FIG. 8, but from an area further down the fiber after about 35
wraps of the phase, or, roughly one third of an index. The noise on
the phase difference data has increased and is caused by the
increasing shift between the reference and measurement scatter
patterns. This decreases the coherence between the reference and
measurement data used to determine the phase difference. If the
apparent location of an individual scattering fiber segment shifts
by more than an index, then the coherence between the reference and
the measurement is lost, and no strain measurement can be obtained
from the comparison of scatter signals.
[0092] Therefore, the reference data should be matched to the
measurement data by accounting for the shifting due to strain along
the fiber. In the case of one index being about 50 microns, over a
one meter segment, this amounts to only 50 parts per million, which
is not a large strain. In fact, the weight of the fiber itself can
induce strains on this order. Also, a change in temperature of only
a few degrees Celsius can induce a similar shift. Therefore, this
shift in index should be accounted for in the calculation of the
distortion of the core.
[0093] A shift as a result of tension is a physical expansion of
the individual segments which results in an increased time of
flight of the scattered light. The shift between reference and
measurement is referred to as delay. The delay can be accounted for
by looking at a model of how a shift in the delay to any point in
the sensing core affects the signal reflected from this point. If a
field (light) is oscillating at a frequency, v, and it undergoes a
delay of .tau., then the optical phase as a function of delay is
given by,
.phi.=2.pi..tau.v Eq. 5
[0094] If the optical phase, .phi., is plotted as a function of
frequency, v, a straight line is obtained that intersects the
origin. In practice, passing through a material such as glass
distorts this curve from a perfect line, which should be kept in
mind when comparing measured values to the values predicted by this
model. But for immediate purposes, this model is sufficient. FIG.
10 shows this phase for two different delays. In an example,
non-limiting measurement system using the principle described
above, a typical sweep of the laser might cover a range of 192.5 to
194.5 THz. These frequencies represent a sweep from 1542 nm (194.5
THz) to 1558 nm (192.5 THz), which has been a test sweep range for
a non-limiting, test shape sensing application. Over this range of
interest, the phase for a given delay sweeps over a range of
.DELTA..phi.. For the two delays shown, .tau..sub.1 and
.tau..sub.2, the difference in this sweep range,
.DELTA..phi..sub.2-.DELTA..phi..sub.1, is less than the change in
phase at the center frequency, (193.5 THz), labeled d.phi.. The
factor between the change in phase at the center frequency and the
change in phase sweep range will be the ratio of the center
frequency to the frequency sweep range. In this example case, the
ratio is 96.7.
[0095] In the example test application, the sweep range, .DELTA.v,
determines the spatial resolution, .delta..tau., of the
measurement. In other words, it determines the length of an index
in the time domain. These are related by an inverse
relationship:
.delta..tau.=1/(.DELTA.v) Eq. 6
[0096] For the example frequency range described above, the length
of an index is 0.5 ps, or 50 microns in glass. At the center
frequency, a phase shift of 2.pi. is induced by a change in delay
of only 0.00516 ps, or 516 nm in glass. A phase shift of 2.pi.,
then, represents only a fractional index shift in the time domain
data. In order to shift the delay by one index in the time domain,
the delay must change enough to induce a phase change at the center
frequency of 96.7.times.2.pi..
[0097] These examples illustrate that a linear phase change
represents a shift in the location of events in the time, or delay,
domain. As seen above, a shift of one index will completely distort
the measurements of phase change along the length of the fiber. To
properly compare the phases, then, these shifts should be accounted
for as they happen, and the reference data should be aligned with
the measurement data down the entire length of the core. To correct
for this degradation of coherence, a temporal shift of the
reference data is required. This may be accomplished by multiplying
the reference data for a given segment, r.sub.n, by a linear phase.
Here n represents the index in the time domain, or increasing
distance along the fiber. The slope of this phase correction,
.gamma., is found by performing a linear fit on the previous delay
values. The phase offset in this correction term, .phi., is
selected such that the average value of this phase is zero.
{tilde over (r)}.sub.n=r.sub.ne.sup.i(.gamma.n+.phi.) Eq. 7
[0098] FIG. 11 shows the corrected phase difference over a section
of fiber where a third of an index shift has occurred. The phase
difference at this location maintains the same signal-to-noise
ratio as the closer part of the fiber. By applying a temporal shift
based on the delay at a particular distance, coherence can be
recovered reducing phase noise.
Example Shape Sensing Fiber
[0099] Tracking distortions in the Rayleigh scatter of optical
fiber provides high resolution, continuous measurements of strain.
The geometry of the multi-core shape sensing fiber is used to
explain how this multi-core structure enables measurements of both
bend and bend direction along the length of the fiber.
[0100] The optical fiber contains multiple cores in a configuration
that allows the sensing of both an external twist and strain
regardless of bend direction. One non-limiting, example embodiment
of such a fiber is shown in FIG. 1 and described below. The fiber
contains four cores. One core is positioned along the center axis
of the fiber. The three outer cores are placed concentric to this
core at 120 degree intervals at a separation of 70 um. The outer
cores are rotated with respect to the center core creating a helix
with a period of 66 turns per meter. An illustration of this
helically-wrapped multi-core shape sensing fiber is depicted in
FIG. 12. A layout of a non-limiting test multi-core optical fiber
used in this discussion is pictured in FIG. 13.
[0101] Another non-limiting example of a shape sensing fiber
contains more than three outer cores to facilitate manufacture of
the fiber or to acquire additional data to improve system
performance.
[0102] In a cross-section of a helixed fiber, the position of each
outer core appears to rotate around the center core progressing
down the length of the fiber as illustrated in FIG. 14.
Wobble Correction in Twisted Fiber
[0103] To translate strain signals from the outer cores in to bend
and bend direction, the rotational position of an outer core must
be determined with a high degree of accuracy. Assuming a constant
spin rate of the helix (see FIG. 12), the position of the outer
cores may be determined based on the distance along the fiber. In
practice, the manufacture of helixed fiber introduces some
variation in the intended spin rate. The variation in spin rate
along the length of the fiber causes an angular departure from the
linear variation expected from the nominal spin rate, and this
angular departure is referred to as a "wobble" and symbolized as a
wobble signal W(z).
[0104] One example test fiber manufactured with a helical
multi-core geometry has a very high degree of accuracy in terms of
the average spin rate, 66 turns per meter. However, over short
distances (e.g., 30 cm) the spin rate varies significantly, and can
cause the angular position to vary as much as 12 degrees from a
purely linear phase change with distance. This error in the spin
rate is measured by placing the fiber in a configuration that will
cause a continuous bend in a single plane, as is the case for a
coiled fiber on a flat surface. When the fiber is placed in such a
coil, a helical core will alternate between tension and compression
as it travels through the outside portion of a bend and the inside
portion of a bend. If phase distortion is plotted verse distance, a
sinusoidal signal is formed with a period that matches the spin
rate of the fiber. Variations in the manufacture of the multi-core
fiber can be detected as small shifts in the phase from the
expected constant spin rate of the fiber.
[0105] An example of these variations in the spin rate is shown in
FIG. 15. The solid curve is the phase data (bend signal) taken from
a planar coil, and the dotted line is a generated perfect sinusoid
at the same frequency and phase as the helix. Note that at the
beginning of the data segment the curves are in phase with aligned
zero crossings. By the middle of the segment, the solid curve has
advanced slightly ahead of the dotted curve, but by the end of the
data segment, a significant offset is observed. If the DC component
of the phase signal is removed, and a phase shift calculated, the
difference between these two signals is significant and somewhat
periodic.
[0106] FIG. 16 shows an example Wobble signal, W(z), with a
periodic variation from a manufactured spin rate along the length
of a shape sensing fiber. The phase variation is shown as a
function of length in fiber index. The example data set represents
about three meters of fiber. On the order of a third of a meter, a
periodicity in the nature of the spin rate of the fiber is
detected. Over the length of the fiber, a consistent average spin
rate of the fiber is produced, but these small fluctuations should
be calibrated in order to correctly interpret the phase data
produced by the multi-core twisted fiber. This measurement in the
change in spin rate or "wobble" is reproducible and is important to
the calculation of shape given practical manufacture of fiber.
Twist Sensing in Multi-Core Fibers
[0107] Torsion forces applied to the fiber also have the potential
to induce a rotational shift of the outer cores. To properly map
the strain signals of the cores to the correct bend directions,
both wobble and applied twist must be measured along the entire
length of the shape sensing fiber. The geometry of the helixed
multi-core fiber enables direct measurement of twist along the
length of the fiber in addition to bend-induced strain as will be
described below.
[0108] If a multi-core fiber is rotated as it is drawn, the central
core is essentially unperturbed, while the outer cores follow a
helical path down the fiber as shown in the center of FIG. 17. If
such a structure is then subjected to torsional stress, the length
of the central core remains constant. However, if the direction of
the torsional stress matches the draw of the helix, the period of
the helix increases and the outer cores will be uniformly elongated
as shown at the top of FIG. 17. Conversely, if the torsional
direction is counter to the draw of the helix, the outer cores are
"unwound" and experience a compression along their length as shown
at the bottom of FIG. 17.
[0109] To derive the sensitivity of the multi-core configuration to
twist, the change in length that an outer core will experience due
to torsion is estimated. A segment of fiber is modeled as a
cylinder. The length L of the cylinder corresponds to the segment
size, while the distance from the center core to an outer core
represents the radius r of the cylinder. The surface of a cylinder
can be represented as a rectangle if one slices the cylinder
longitudinally and then flattens the surface. The length of the
surface equals the segment length L while the width of the surface
corresponds to the circumference of the cylinder 2.pi.r. When the
fiber is twisted, the end point of fiber moves around the cylinder,
while the beginning point remains fixed. Projected on the flattened
surface, the twisted core forms a diagonal line that is longer than
the length L of the rectangle. This change in length of the outer
core is related to the twist in the fiber.
[0110] FIG. 18 shows an outer core that experiences twist can be
modeled as a flattened cylinder as it translates along the surface.
From the above flattened surface, the following can be shown:
.differential. d .apprxeq. 2 .pi. r 2 L .differential. .phi. Eq . 8
##EQU00003##
[0111] In the above equation, .differential.d is the change in
length of the outer core due to the change in rotation,
.differential..phi., of the fiber from its original helixed state.
The radial distance between a center core and an outer core is
represented by r, and
2 .pi. L ##EQU00004##
is the spin rate of the helical fiber in rotation per unit
length.
[0112] The minimum detectable distance is assumed in this example
to be a tenth of a radian of an optical wave. For the example test
system, the operational wavelength is 1550 nm, and the index of the
glass is about 1.47, resulting in a minimum detectable distance of
approximately 10 nm. If the radius is 70 microns and the period of
the helix is 15 mm, then equation (8) indicates that the shape
sensing fiber has a twist sensitivity of 0.3 deg. If the sensing
fiber begins its shape by immediately turning 90 degrees, so that
the error due to twist were maximized, then the resulting position
error will be 0.5% of the fiber length. In most applications, 90
degree bends do not occur at the beginning of the fiber, and
therefore, the error will be less than 0.5%.
Calculating Twist in a Four Core Fiber
[0113] The sensitivity of the twist measurement is based on the
sensitivity of a single core, but the sensing of twist along the
length of the fiber is dependent on all four cores. If the
difference in the change in the length between the average of the
outer cores and the center core is known, then the twist (in terms
of the absolute number of degrees) present in the fiber can be
calculated.
[0114] The external twist along the fiber may be calculated using
non-limiting, example procedures outlined in the flow chart shown
in FIG. 19. The phase signals for all four cores A-D are
determined, and the signals for outer cores B-D are averaged. The
calculation of extrinsic twist is performed by comparing the
average of the outer core phase signals to that of the center core.
If the fiber experiences a torsional force, all outer cores
experience a similar elongation or compression determined by the
orientation of the force to the spin direction of the helix. The
center core does not experience a change in length as a result of
an applied torsional force. However, the center core is susceptible
to tension and temperature changes and serves as a way of directly
measuring common strain modes. Hence, if the center core phase
signal is subtracted or removed from the average of the three outer
cores, a measure of phase change as a result of torsion is
obtained. This phase change can be scaled to a measure of extrinsic
twist, or in other words, fiber rotation. Within the region of an
applied twist over the length of the fiber less than a full
rotation, this scale factor can be approximated as linear. In the
presence of high torsional forces, a second order term should
preferably be considered. Further, twist distributes linearly
between bonding points such that various regions of twist can be
observed along the length of the fiber.
[0115] FIG. 20 shows an example data set for a generic shape that
illustrates the FIG. 19 algorithm in more detail. The graph shows
phase distortion as a result of local change in length of the
center core (black) and an outer core (gray) of a shape sensing
fiber for a general bend. The two phase curves shown in FIG. 20
represent the local changes in length experience by two of the
cores in the multi-core shape sensing fiber. The curves for two of
the outer cores are not shown in an effort to keep the graphs
clear, but the values from these other two cores are used in
determining the final shape of the fiber.
[0116] The center core phase signal does not experience periodic
oscillations. The oscillations are a result of an outer core
transitioning between compressive and tensile modes as the helix
propagates through a given bend. The central core accumulates phase
along the length of the shape sensing fiber even though it is not
susceptible to bend or twist induced strain. The center core phase
signal describes common mode strain experienced by all cores of the
fiber. The outer cores are averaged (gray) and plotted against the
center core (black) in FIG. 21.
[0117] As the outer cores are 120 degrees out of phase, the bend
induced variation in the phase signals averages to zero. FIG. 21, a
slight deviation between the two phase curves is observed.
Subtracting the center core phase, a direct measure of common mode
strain, leaves the phase accumulated as a result of torsional
forces. With proper scaling, this signal can be scaled to a measure
of fiber roll designated as the "twist" signal T(z) produced from
FIG. 21 which is shown in FIG. 22. From the twist signal, T(z), the
shift in rotational position of the outer cores as a result of
torsion along the length of the shape sensing fiber tether can be
determined. This allows a bend signal to be mapped to the correct
bend direction.
[0118] The desirability of compensating for twist in the shape
calculation is illustrated by the data set shown in FIG. 23. The
tip of the shape sensing fiber was translated in a single plane
through a five point grid forming a 250 mm square with a point at
its center with shape processing considering twist (filled). The
correction for external twist was not used in the processing of the
data set plotted as unfilled dots. In the plot, it is impossible to
distinguish the original shape traced with the tip of the fiber if
the twist calculation is not used. Even for small fiber tip
translations, significant twist is accumulated along the length of
the fiber. Thus, if this twist is not accommodated for in the shape
sensing, then significant levels of accuracy cannot be
achieved.
Calculation of Bend Induced Strain
[0119] Along with information describing the amount of twist
applied to the shape sensing fiber, a multi-core fiber also enables
extraction of bend information in an ortho-normal coordinate
system. The phase signals for four optical cores of the shape
sensing fiber can be interpreted to provide two orthogonal
differential strain measurements as described below. These strain
values can then be used to track a pointing vector along the length
of the fiber, ultimately providing a measure of fiber position
and/or shape.
[0120] With the common mode strain removed, the three, corrected,
outer core phase signals are used to extract a measure of bend
along the shape sensing fiber. Due to symmetry, two of the outer
cores can be used to reconstruct the strain signals along the
length of the fiber. First, the derivative of the phase signal for
two of the outer cores is taken. This derivative is preferably
calculated so that the error on the integral of the derivative is
not allowed to grow, which translates to a loss in accuracy of the
system. For double-precision operations, this is not a concern. But
if the operations are done with a limited numeric precision, then
rounding must be applied such that the value of the integral does
not accumulate error (convergent rounding).
[0121] Assume for this explanation that strain can be projected in
a linear fashion. Thus, the phase response of a given core is a
combination of two orthogonal strains projected against their
radial separation.
.phi. n z = b y ( z ) sin ( kz + .DELTA. n ) + b x ( z ) cos ( kz +
.DELTA. n ) Eq . 9 ##EQU00005##
[0122] In the above equation, b.sub.x and b.sub.y are the
orthogonal strain signals used to calculate bend. The phase,
.phi..sub.n, represents the phase response of a core, z is the
axial distance along the fiber, k is the spin rate of the helix,
and the delta .DELTA. represents the radial position of the core
(120 degree separation).
[0123] The phase response from two of the outer cores is:
.phi. 1 z = b y ( z ) sin ( kz + .DELTA. 1 ) + b x ( z ) cos ( kz +
.DELTA. 1 ) Eq . 10 .phi. 2 z = b y ( z ) sin ( kz + .DELTA. 2 ) +
b x ( z ) cos ( kz + .DELTA. 2 ) Eq . 11 ##EQU00006##
Solving for b.sub.x and b.sub.y:
b y ( z ) = 1 sin ( .DELTA. 1 - .DELTA. 2 ) [ .phi. 1 z cos ( kz +
.DELTA. 2 ) + .phi. 2 z cos ( kz + .DELTA. 1 ) ] Eq . 12 b x ( z )
= 1 sin ( .DELTA. 2 - .DELTA. 1 ) [ .phi. 1 z sin ( kz + .DELTA. 2
) + .phi. 2 z sin ( kz + .DELTA. 2 ) ] Eq . 13 ##EQU00007##
[0124] In the above equations 12 and 13, k, the spin rate, is
assumed constant along the length of the fiber. The above
derivation remains valid if correction terms are added to the spin
rate. Specifically, the measured wobble W(z) and twist signals T(z)
are included to compensate for the rotational variation of the
outer cores along the length of the fiber. The above expressions
(12) and (13) then become the following:
b y ( z ) = 1 sin ( .DELTA. 1 - .DELTA. 2 ) [ .phi. 1 z cos ( kz +
T ( z ) + W ( z ) + .DELTA. 2 ) + .phi. 2 z cos ( kz + T ( z ) + W
( z ) + .DELTA. 1 ) ] Eq . 14 b x ( z ) = 1 sin ( .DELTA. 1 -
.DELTA. 2 ) [ .phi. 1 z sin ( kz + T ( z ) + W ( z ) + .DELTA. 2 )
+ .phi. 2 z sin ( kz + T ( z ) + W ( z ) + .DELTA. 1 ) ] Eq . 15
##EQU00008##
Calculation of Shape from Orthogonal Differential Strain
Signals
[0125] Equations (14) and (15) produce two differential, orthogonal
strain signals. FIG. 24 depicts the orthogonal strain curves for a
fiber placed in several bends that all occur in the same plane.
These two differential, orthogonal strain signals are processed to
perform the final integration along the length of the shape sensing
fiber to produce three Cartesian signals representing the position
and/or shape of the fiber.
[0126] FIG. 25 shows a flowchart diagram describing non-limiting,
example steps for calculating shape from strain. Orthonormal strain
signals A and B are determined according to the equations 14 and
15.
[0127] The acquired data at the data acquisition network is
preferably stored in discrete arrays in computer memory. To do
this, a change in representation from the continuous representation
in equation 15 to a discrete representation based on index is
needed at this point. Further, the bend at each point in the array
can be converted to an angular rotation since the length of the
segment (.DELTA.z) is fixed and finite using equation (1). The
parameter, a, is determined by the distance of the cores from the
center of the fiber and the strain-optic coefficient which is a
proportionality constant relating strain to change in optical path
length.
.theta..sub.y,n=ab.sub.y,n.DELTA.z Eq. 16
.theta..sub.x,n=ab.sub.x,n.DELTA.z Eq. 17
[0128] These measures of rotation .theta. due to local bend in the
fiber can be used to form a rotation matrix in three dimensions. If
one imagines beginning with the fiber aligned with the z axis, the
two bend components rotate the vector representing the first
segment of the fiber by these two small rotations. Mathematically,
this is done using a matrix multiplication. For small rotations,
the simplified rotation matrix shown in equation (18) below can be
used.
R n _ = [ 1 0 .theta. x , n 0 1 .theta. y , n - .theta. x , n
.theta. y , n 1 ] Eq . 18 ##EQU00009##
[0129] The above rotation matrix is valid if .theta..sub.x<<1
and .theta..sub.y<<1. If the resolution of the system is on
the order of micrometers, this is a condition that is not difficult
to maintain. After rotation, the fiber segment will have a new end
point and a new direction. All further bends are measured from this
new pointing direction. Therefore, the pointing direction (or
vector) at any position on the fiber depends upon all of the
pointing directions between that location in the fiber and the
starting location. The pointing vector at any point of the fiber
can be solved in an iterative process tracking the rotational
coordinate system along the length of the fiber as seen in the
following expression:
C.sub.n+1=C.sub.nR.sub.n Eq. 19
[0130] In other words, each segment along the fiber introduces a
small rotation proportional to the size and direction of the bend
along that segment. This iterative calculation can be written in
mathematical notation below:
C p _ _ = C 0 _ _ n = 0 p R n _ _ Eq . 20 ##EQU00010##
[0131] Here again, for small rotations and nearly planar rotations,
the angles are effectively summed, and by maintaining an accurate
measure of the integral of the strain (the length change)
throughout the length of the shape sensing fiber, better accuracy
is achieved than is possible using the strain alone. The matrix
calculated above contains information about the local orientation
of the cores, which allows for the proper rotations to be applied.
If the primary interest is in determining the position along the
fiber, then only the local vector that describes the pointing
direction of the fiber at that location is needed. This pointing
vector can be found by a simple dot product operation.
P = C 0 _ _ [ 0 0 1 ] Eq . 21 ##EQU00011##
[0132] If each of these pointing vectors is placed head-to-tail, as
illustrated in the FIG. 26, an accurate measurement of the shape
results. Thus, the position and/or direction at any point along the
length of the fiber can be found by the summation of all previous
pointing vectors, scaled to the resolution of the system:
[ x y z ] .PHI. = .DELTA. d p = 0 q [ { C 0 _ _ n = 0 p R n _ _ } ]
[ 0 0 1 ] Eq . 22 ##EQU00012##
[0133] One non-limiting example of a shape sensing system is
described in conjunction with FIG. 27. Other implementations and/or
components may be used. Moreover, not every component shown is
necessarily essential. The System Controller and data processor (A)
initiates two consecutive sweeps of a tunable laser (B) over a
defined wavelength range and tuning rate. Light emitted from the
tunable laser is routed to two optical networks via an optical
coupler (C). The first of these two optical networks is a Laser
Monitor Network (E) while the second is designated as an
Interrogator Network (D). Within the Laser Monitor Network (E),
light is split via an optical coupler (F) and sent to a gas (e.g.,
Hydrogen Cyanide) cell reference (G) used for C-Band wavelength
calibration. The gas cell spectrum is acquired by a photodiode
detector (L) linked to a Data Acquisition Network (U).
[0134] The remaining portion of light split at optical coupler (F)
is routed to an interferometer constructed from an optical coupler
(H) attached to two Faraday Rotator Mirrors (I,J). The first
Faraday Rotator Mirror (FRMs) (I) serves as the reference arm of
the interferometer while the second Faraday Rotator Mirror (J) is
distanced by a delay spool (K) of optical fiber. This
interferometer produces a monitor signal that is used to correct
for laser tuning nonlinearity and is acquired by the Data
Acquisition Network (U) via a photodiode detector (M).
[0135] Light routed to the Interrogator Network (D) by optical
coupler (C) enters a polarization controller (N) that rotates the
laser light to an orthogonal state between the two successive laser
scans. This light is then split via a series of optical couplers
(0) evenly between four acquisition interferometers (P, Q, R, S).
Within the acquisition interferometer for the central core, light
is split between a reference path and a measurement path by an
optical coupler (AA). The "probe" laser light from coupler AA
passes through an optical circulator (T) and enters a central core
of a shape sensing fiber (W) through a central core lead of a
multi-core fanout (V) for the shape sensing fiber (W). The shape
sensing fiber (W) contains a central optical core concentric to
three helically wound outer optical cores. The cross section of the
fiber (X) depicts that the outer cores (Z) are evenly spaced,
concentric, and separated by a given radial distance from the
central core (Y). The resulting Rayleigh backscatter of the central
optical core (Y) as a consequence of a laser scan passes through
the optical circulator (T) and interferes with the reference path
light of the acquisition interferometer when recombined at optical
coupler (BB).
[0136] The interference pattern passes through an optical
polarization beam splitter (DD) separating the interference signal
into the two principle polarization states (S.sub.1, P.sub.1). Each
of the two polarization states is acquired by the Data Acquisition
Network (U) using two photodiode detectors (EE, FF). A polarization
rotator (CC) can be adjusted to balance the signals at the
photodiode detectors. The outer optical cores of the shape sensing
fiber are measured in a similar manner using corresponding
acquisition interferometers (Q, R, S). The System Controller and
Data Processor (A) interprets the signals of the four individual
optical cores and produces a measurement of both position and
orientation along the length of the shape sensing fiber (W). Data
is then exported from the System Controller (A) for display and/or
use (GG).
Birefringence Corrections
[0137] When an optical fiber is bent, the circular symmetry of the
core is broken, and a preferential "vertical" and "horizontal" is
created by the distinction between directions in the plane of the
bend and perpendicular to the plane of the bend. Light traveling
down the fiber then experiences different indices of refraction
depending upon its polarization state. This change in the index as
a function of polarization state is referred to as birefringence.
This presents a significant problem for shape measurement because
the measured phase change depends on the incident polarization
state, and this incident state cannot be controlled in standard
fiber.
[0138] This problem can be solved by measuring the optical core
response at two orthogonal polarization states. If the response of
these two states is averaged properly, the variation in the
measured response as a function of polarization can be eliminated
or at least substantially reduced. The flowchart diagram in FIG. 28
outlines a non-limiting, example process for correcting for
birefringence such as intrinsic birefringence, bend-induced
birefringence, etc. both in measured and in reference values. The
non-limiting example below relates to bend-induced birefringence
but is more generally applicable to any birefringence.
[0139] The first step in the process is to measure the response of
the core at two orthogonal polarization states called "s" and "p".
An s response and a p response are measured at each polarization
state resulting in four arrays. For simplicity, the responses to
the first polarization state are called a and b, and the responses
to the second polarization state are called c and d, where a and c
are the responses at the s detector and b and d are the responses
at the p detector.
[0140] The second step is to calculate the following two array
products:
x=ad* Eq. 23
y=bc* Eq. 24
[0141] A low-pass filtered version of each of these signals is
calculated which is written as, (x) and (y). The expected value
notation is used here to indicate a low-pass filtering operation.
The phases of the relatively slowly varying functions are used to
align the higher frequency scatter signals in phase so that they
can be added:
p=a+ Eq. 25
q=b+ Eq. 26
[0142] This process is then repeated to produce a final scalar
value:
u=p+ Eq. 27
[0143] Now, a slowly varying vector can be created that represents
the vector nature of the variation down the fiber without wideband
Rayleigh scatter components, since these are all subsumed into
u:
{right arrow over (v)}=.left
brkt-bot.ae.sup.i.angle.u*,be.sup.i.angle.u*,ce.sup.i.angle.u*,de.sup.i.a-
ngle.u*.right brkt-bot. Eq. 28
[0144] The correction due to birefringence effects is then
calculated using:
.phi..sub.n=.angle.({right arrow over (v)}.sub.n{right arrow over
(v)}.sub.0*) Eq. 29
where .phi..sub.n is the correction due to birefringence effects
and n is the index into the array. Here the vector is shown
compared to the first element (index 0) in the array, but it can
just as easily be compared with any arbitrarily selected element in
the vector array.
[0145] The birefringence correction compensates for birefringence
as result of core asymmetry during manufacture and for bend radii
in excess of 100 mm. As the shape sensing fiber is placed into
tight bends with radii less than 100 mm, a second order
birefringence effect becomes significant.
[0146] Assuming that significant levels of strain only manifest in
the direction parallel to the central core of the multi-core shape
sensing fiber, consider the diagram in FIG. 29. As the fiber is
bent, tensile strain is measured in the region between
0<X.ltoreq.r while compressive strain is measured in the region
-r.ltoreq.X<0. The expansion of the outer bend region exerts a
lateral force increasing the internal pressure of the fiber. As the
internal pressure of the fiber increases, a second order strain
term becomes significant, .epsilon..sub.x. As shown in the second
graph, this pressure strain term is a maximum along the central
axis of the fiber and falls off towards the outer edges of the
fiber as the square of distance. In tight bends, this pressure
strain term can modify the index of refraction of the fiber
resulting in measurable birefringence. Further, the outer
peripheral helical cores experience a sinusoidal response to this
pressure induced strain while the center core responds to the
maximum.
[0147] FIG. 30 shows two phase plots produced from a 40 mm diameter
fiber loop. Oscillations in these signals are a result of the
multi-core assembly being off center of the fiber. In tighter
bends, strain signals are high enough to elicit a response from
this subtle deviation from concentricity. The plot shows that the
average of the helical outer cores accumulates significantly less
phase in the region of the bend when compared to the center core.
This phase deficiency serves as evidence for bend induced
birefringence. Recall that the extrinsic twist calculation is
performed by finding the absolute phase difference between the
center core and the average of the three outer cores. The graph in
FIG. 30 shows that a false twist signal will be measured in the
region of the bend.
[0148] The measured phase response of an outer core indicates its
position relative to the pressure-induced strain profile,
.epsilon..sub.x. Therefore, the square of an outer core strain
response provides a measure of both location and magnitude relative
to the pressure field. This response may be scaled and used as a
correction to the outer cores to match the level of .epsilon..sub.x
perceived by the central core, thereby correcting for the false
twist.
.phi. ncorr = .phi. n - k .intg. [ ( .phi. n z - i - u N .phi. n z
N ) 2 ] Eq . 30 ##EQU00013##
.phi..sub.n is the phase response on an outer core, N is the number
of outer cores, and k serves as a scale factor. FIG. 31 shows the
strain response of an outer core for a 40 mm diameter fiber loop,
with common mode strain subtracted. From this strain response
signal a correction for bend induced birefringence can be
approximated as is seen in the graph shown in FIG. 32.
[0149] Applying this correction has a significant impact on the
measured twist in the region of the bend as shown in FIG. 33.
Comparing the twist signal with and without 2.sup.nd order
correction reveals that a 25 degree error is accumulated in the
bend region without the 2.sup.nd order birefringence correction in
this example.
Applying Birefringence Corrections and Impact on Accuracy
[0150] The following describes the effects of polarization on the
accuracy of a shape sensing system. To achieve a varying input
polarization between measurements, a loop polarization controller
is added between the shape sensing fiber and the shape sensing
system as illustrated in FIG. 34.
[0151] To illustrate the impact of the above-described corrections
on the accuracy of the system, consider the in-plane signal for a
relatively simple shape as shown in FIG. 35, where 1.4 meters of
shape sensing fiber is routed through a single 180 degree turn with
a bend radius of 50 mm. FIG. 36 shows out-of-plane measurements for
three successive measurements. Between each measurement, the
polarization is varied using the polarization controller in FIG.
34.
[0152] If birefringence is not considered, a significant loss in
accuracy and precision is observed. A large response is observed in
the out-of-plane signal as the polarization state is varied. The
fiber picks up an angular error only in the region of the bend as a
result of the system measuring an erroneous twist signal. Thus,
when exiting this bend, there is a significant error in the
pointing direction of the fiber. Predicting the polarization
response of the fiber is a difficult problem, and not every core
responds to the same extent for a given bend. FIG. 37 illustrates
this point showing the birefringence corrections for cores.
However, the same two measurements for the center core have a
significant variation in their phase responses as seen in FIG. 38.
Two successive measurements respond differently to input
polarization providing evidence for birefringence in the shape
sensing fiber.
[0153] Activating a correction for birefringence improved the
precision of the system as seen in FIG. 39. The variation between
shape measurements as the input polarization state varies is
minimized which greatly increases the precision of the system.
However, a significant error in the accuracy of the system is still
observed. If the second order correction based on bend induced
birefringence is also performed, there is further improvement of
the system as shown in FIG. 40. Both the precision and accuracy of
the out of plane signal are dramatically improved.
[0154] Although various embodiments have been shown and described
in detail, the claims are not limited to any particular embodiment
or example. None of the above description should be read as
implying that any particular element, step, range, or function is
essential such that it must be included in the claims scope. The
scope of patented subject matter is defined only by the claims. The
extent of legal protection is defined by the words recited in the
allowed claims and their equivalents. All structural and functional
equivalents to the elements of the above-described preferred
embodiment that are known to those of ordinary skill in the art are
expressly incorporated herein by reference and are intended to be
encompassed by the present claims. Moreover, it is not necessary
for a device or method to address each and every problem sought to
be solved by the present invention, for it to be encompassed by the
present claims. No claim is intended to invoke paragraph 6 of 35
USC .sctn.112 unless the words "means for" or "step for" are used.
Furthermore, no embodiment, feature, component, or step in this
specification is intended to be dedicated to the public regardless
of whether the embodiment, feature, component, or step is recited
in the claims.
* * * * *