The technology described in this application relates to optical interrogation system measurements used for fiber optic shape and other sensing applications.
Optical strain sensing is a technology useful for measuring physical deformation of a waveguide caused by, for example, the change in tension, compression, or temperature of an optical fiber. Measuring the shape of an optical fiber using multiple single mode cores to determine parameters including pitch, yaw, twist, and strain has been demonstrated. Shape is the position or orientation of the fiber in three dimensions. A continuous measure of strain along the length of a core can be derived by interpreting the optical response of the core using swept wavelength inteferometery typically in the form of Optical Frequency Domain Reflectometry (OFDR) measurements. With knowledge of the relative positions of the cores along the length of the fiber, these independent strain signals may be combined to gain a measure of the strain profile applied to the multi-core optical fiber. The strain profile of the fiber refers to the measure of applied bend strain, twist strain, and/or axial strain along the length of the fiber at a high (e.g., less than 50 micrometers) sample resolution. A non-limiting example application is robotic arms used in surgical or other environments. Previous patents have described OFDR-based shape sensing with multiple single mode cores (e.g., see U.S. Pat. Nos. 7,781,724 and 8,773,650 incorporated by reference).
Fibers with multiple single mode cores are difficult and costly to manufacture. Cost is further increased when multi-core fibers must be spun or helically-twisted during manufacture, which is the case for prior multi-core shape sensing fiber. If a single core, unspun fiber could be used to sense shape, then the cost of the fiber sensor could be significantly reduced. For example, mass produced, standard telecom fiber that has single cores and is unspun sells for pennies per meter. But there are several technological challenges (described below) that must be addressed and overcome in order for a single core, multiple mode fiber to sense shape.
Example embodiments include an optical interrogation system and method that includes a sensing fiber having a single core, where the single core has multiple light propagating modes. The system includes interferometric apparatus that probes the single core over a range of predetermined wavelengths and detects measurement interferometric data associated with the multiple light propagating modes of the single core for each predetermined wavelength in the range. Data processing circuitry processes the measurement interferometric data associated with the multiple light propagating modes of the single core to determine a shape-sensing parameter of the sensing fiber. In an example application, the data processing circuitry determines a shape of the sensing fiber based on the shape-sensing parameter.
Examples of a shape-sensing parameter include a bend parameter and/or a twist parameter. In one example embodiment, the data processing circuitry processes the measurement interferometric data associated with the multiple light propagating modes of the single core to determine a plurality of shape-sensing parameters including the shape-sensing parameter, and wherein the plurality of shape-sensing parameters includes strain, bend, and twist parameters.
The single core may have a shape that limits a number of the multiple light propagating modes below a predetermined number while providing a predetermined sensitivity to the twist parameter. One example is where the single core is ring-shaped in cross-section. An even more specific ring-shaped core example is a ring-shaped cored that has a radius that permits fewer than 40 modes of light to propagate along the single core. Another example is where the single core is a solid core. A radius of the solid core permits less than six modes of light to propagate along the single core.
In example embodiments, the interferometric apparatus may include multiple interferometers with multiple reference branches and multiple measurement branches having an array of corresponding multiple single core, single mode fibers. A tunable laser generates light over the range of predetermined wavelengths. Each fiber of the array has a different optical delay. A collimator collimates light from the single core and de-collimate light to the single core, and a microlens array receives and focuses collimated light from the collimator onto the array of corresponding multiple single core, single mode fibers. The different optical delays produce multiple coupling coefficients that appear on different ones of the array of corresponding multiple single core, single mode fibers.
In an example implementation, the single core includes an overlapping grating pattern, where each overlapping grating in the overlapping grating pattern is tilted with respect to a longitudinal axis of the single core. The overlapping grating pattern varies with bend, strain, and twist applied to the sensing fiber. The overlapping grating pattern is associated with (i) a cross-sectional index perturbation for the sensing fiber as a function of distance along the sensing fiber and (ii) coupling coefficients between back-scattered light propagating modes for the sensing fiber.
In an example application, the interferometric apparatus measures a phase and an amplitude of the coupling coefficients, and the data processing circuitry determines a difference between the measured coupling coefficient phase and amplitude and a predetermined baseline coupling coefficient phase and amplitude for the sensing fiber.
In an example embodiment, a non-transitory machine-readable medium stores a plurality of machine-readable instructions which, when executed by one or more processors associated with a medical device, are adapted to cause the one or more processors to perform processing steps of the methods described herein.
The following description sets forth specific details, such as particular embodiments for purposes of explanation and not limitation. But it will be appreciated by one skilled in the art that other embodiments may be employed apart from these specific details. In some instances, detailed descriptions of well-known methods, interfaces, circuits, components, and devices are omitted so as not to obscure the description with unnecessary detail. It will be appreciated by those skilled in the art that diagrams herein can represent conceptual views of illustrative circuitry, components, or other functional units.
Before considering a single core fiber in three dimensions, consider a fiber with two single-mode cores displaced from the central axis and a Bragg grating present in the structure from two dimensions.
If there is only a single core in the fiber, but one that supports two field propagation modes, then the two modes will have electric field envelopes that look like those in
By using the sum and difference of the modes, reflections preferentially weighted in the top or the bottom of the core can be used to detect bending of the waveguide, i.e., to detect strain which is one of the shape determination parameters.
Rather than directly measuring the propagating modes, measuring the cross coupling of those modes in the core grating can provide a measurement of the deformation of the grating which can be used to determine shape parameters. Cross coupling coefficients, κ, represent the scattering of light from the forward propagating modes to the backward propagating modes in the core grating.
For a two mode, two dimensional wave guide, four types of backward coupling can occur including: coupling from the forward propagating first order mode to the backward propagating first order mode (and having a coupling coefficient κ00), coupling from the forward propagating first order mode to the backward propagating second order mode (and having a coupling coefficient κ01), coupling from the forward propagating second order mode to the backward propagating second order mode (and having a coupling coefficient κ11), and coupling from the forward propagating second order mode to the backward propagating first order mode (and having a coupling coefficient κ10).
Modeling waveguide systems as ideal lossless waveguide systems, coupling coefficients κ01=κ*10, and so there are three independent coupling coefficients available to measure: κ00, κ01, and κ11. The local pattern of the Bragg grating determines the magnitude of the cross coupling or the coupling coefficients. As a result, distributed measurements of these three coupling coefficients can be used to calculate the local frequency of the grating (which determined by the tilt of the grating, which in turn determined by the amount of bending of the grating) at every point along the fiber wave guide. The manner in which these coupling coefficients are measured, and the corrections used to calculate the local frequency of a Bragg grating in the fiber core are described in detail below for a non-limiting and example case of a three dimensional waveguide.
Previous fiber-optic shape sensing systems use a multi-core fiber or multiple single core fibers, where each core is a single mode fiber and typically has gratings written along the length of the core. Bend, twist, and/or strain cause local stretching or compressing of the grating pattern. These grating changes relate directly to the applied bend, twist, or strain and can be quantified by measuring the phase change vs. distance along the fiber with respect to a reference state. A matrix can be calculated via knowledge of the fiber geometry and/or calibration, and used to convert phase change in four cores to bend, twist, and strain.
In this example case of a single core fiber with multiple modes, the variations in the core grating pattern are measured and processed with distance along the fiber and with cross-sectional location in the fiber core. For example, if the fiber is bent in one direction, the grating pattern is compressed on the side of the core on the inside of the bend, stretched on the side of the core on the outside of the bend, and unchanged along the neutral axis.
Although a single grating in the core may be used to determine strain, it is not sufficient by itself to determine another important shape parameter-twist. Twist may be measured using a helixed fiber that uses multiple single mode cores disposed in a helical manner as described in the patents referenced in the introduction. But with a single core, multiple mode sensing fiber, a helixed fiber is no longer available for measuring twist.
In various embodiments, a grating pattern can be used to detect twist in the fiber. Construction of an example grating pattern is now described.
This type of grating can be written in a fiber core using a phase mask that is tilted with respect to the fiber.
Then, a second tilted grating is written on the core as shown in the example intensity plot of the index modulation or index change of
A grating pattern (like the pattern described above and an amplitude like that shown in
Applying coupled-mode theory, the index perturbation in a fiber core determines the cross-coupling between forward traveling and backward traveling modes. In this application, the index perturbation is the core grating. The core is probed with light having forward traveling modes, and the backward traveling modes created by the grating are detected. Because the input (forward traveling) modes may be determined in advance, and because the output (backward traveling) modes can be measured and the coupling coefficients determined, mode coupling is used the example embodiments to determine the index perturbation (the state of the grating such as pulled, compressed, bent, and/or twisted) that was present.
The following assumes that the single core guides three modes for a detailed example. However, a single core that guides more than three modes may also be used.
A representation of the index perturbation (the core grating) across the cross section of the example fiber at any given location may be determined by measuring the coupling coefficients between the back scattered modes. Assume that the single core fiber supports three modes E0 (circular), EH (horizontal), and EV (vertical), two of them degenerate. The three modes correspond to three linear polarizations LP01 (circular), LP11x (horizontal), LP11y (vertical) as set forth here:
The variables r and θ and the z axis are shown in
Based on perturbation theory, (see, e.g., Fundamentals of Optical Waveguides, Katsunari Okamoto, Elsevier 2006), the coupling factor, κmn between any forward propagating mode, Em and any backward propagating mode En is given by the equation below.
κmn=∫∫Em(x,y)η(x,y)E*n(x,y)ei(β
Here η(x,y)e−ikz is the periodic index perturbation (the grating in the core) within the optical fiber, βm and βn are the propagation constants of the two non-degenerate modes, x and y are the cross sectional axes, and z is the dimension along the axis of the fiber.
Expressing this equation in polar coordinates:
Six different decomposition functions, ξmn(r,θ) are available for determining η(r, θ):
ξmn(r,θ)=Em(r,θ)E*n(r,θ)
By measuring the phase and amplitude of all six coupling coefficients, κmn, the grating modulation (e.g., changes in the grating caused by strain, stress, and/or twist), η(r,θ)e−ikz, may be reconstructed using these coefficients, κmn, as the weight factor on summation of the decomposition function ξmn(r,θ).
η(
This decomposition method of determining the distribution of a Bragg grating across the cross section of a single multimode core was simulated for two tilted and overlapped Bragg gratings, such as described above. The plots in
Before measurements are taken with a single multimode core, a “baseline” or reference measurement with the fiber in a known orientation, in this case straight and untwisted, as performed. Thereafter, normal measurements may be made with fiber moved, e.g., bent and/or twisted. A phase “deformation” δϕ is then calculated based upon the phase change between these baseline and normal measurements.
δϕ(r,θ)=∠{ηmove(r,θ)·η*base(r,θ)}
Or equivalently in the x, y coordinate system:
δϕ(x,y)=∠{ηmove(x,y)·η*base(x,y)}
Between the base and the moved measurement for this example, there can be a horizontal bend, bx, that will be a linear phase change as a function of x, a vertical bend, by, that will be a linear phase change as a function of y, a stretch, ε, that will be constant change over the surface, or a twist, τ, that will be a rotation of the entire complex (phase and amplitude) scattering cross section.
Estimates can be determined for each of these shape parameters bx, by, ε, and τ. These estimates can essentially function as a shape conversion matrix to convert from phase measurements to pitch, yaw, twist and strain.
With the bend, twist, and strain terms bx, by, ε, and τ, the shape of the fiber may be determined using three dimensional rotations and projections described in U.S. Pat. Nos. 7,781,724 and 8,773,650 identified in the introduction.
In addition to using the measured coupling coefficients (κmn) to determine the index perturbation in a single multimode core, some embodiments also measure the coupling coefficients. Some embodiments get the energy from single mode fibers into and out of each of the different modes in a way that is power efficient (the detecting fibers are typically coupled to photodiode detectors in an Optical Frequency Domain Reflectometry (OFDR) system). As one option, a fused tapered coupler, tapering multiple single mode fibers and fusing them to different locations on the multimode core, may be an option if the tapering can be done as the mode coupling was monitored in a 3×3 coupler. Another option abuts a bundle of single mode cores up against the larger multimode core. Some embodiments use this option when the cores are surrounded by little or no cladding. Another option is to image the multimode core directly onto a bundle of single mode fibers with a large magnification. Some embodiments use this option when the system can function with the inefficiencies resulting from light that may be captured by the cladding surrounding each of the single mode fibers.
Some embodiments including this last option of directly imaging the multimode core reduce the inefficiencies by using a micro lens array with a sufficiently large fill-factor and a numerical aperture (NA) that matches the optical fiber with the multimode core more closely (e.g., between 0.1 and 0.25 in some cases). An example of a bulk-optic design for getting energy from each of the different modes into a corresponding single-mode detecting fiber in a way that is power efficient is shown in
The optical coupling mechanism shown in
If the delays of the three input fibers are larger than the total delay associated with the single core multimode sensing fiber 10, then all of the cross coupled terms between input and output fibers of the measurement interferometer will appear at different delays and on unique detectors. If the fiber lengths for each output fiber are the same, then the overall delay is determined by the input fiber in this example.
Extraction of Fiber Modal Coupling from Instrumentation Coefficients
As demonstrated above, the index perturbation (grating) may be determined by measuring the cross coupling coefficients detected at the multiple (three in the example) single mode fibers in the fiber array 20 that correspond to but are not identical to the modes of the single core 13 in the single core multimode sensing fiber 10.
Some embodiments make this connection or conversion using a matrix,
where {right arrow over (A)}out is the vector formed by the fields in each of the single-mode input/probe fibers in the fiber array 20, {right arrow over (E)} is the vector composed of the field in each of the three fiber modes in the single core 13, and
The expression is now written for the light travelling from the single-mode fibers in the fiber array 20, through the optics (microlens array 22 and lens 24) into the single core multimode sensing fiber 10, then being coupled into the backward travelling mode, and then back through the optics (microlens array 22 and lens 24) and into the single-mode fibers in the fiber array 20 as follows:
The combination of the above three matrices,
In this example,
Embodiments determine the elements that form the matrix
To implement this isolation in this example, the OFDR controller applies a time domain window filter (like a bandpass filter) around the E0(LP01) delay peak.
Next, the light that travels exclusively in the EV and EH (LP11) modes and corresponding to the following is isolated:
And finally the light that crosses between E0(LP01) and the EV and EH (LP11) modes at the cleave is isolated as follows:
Next, assuming a flat, 0 degree cleave at the end of the fiber, the cross coupling terms (κ13 and κ31) are driven to zero because the perturbations function η(r,θ) for a zero degree cleave is a constant, giving a simplified matrix:
Adding
which can be rewritten as by moving the inverse matrix to the left side of the equality:
This last equation takes the form of an eigenvalue problem:
=
where S is a matrix whose columns are the eigenvectors of A and Λ is a diagonal matrix whose elements are the eigenvalues. Since matrix A can be measured by the OFDR interrogation system, the coupling coefficients (κ11, κ22, and κ33) can be determined.
Finding the matrices that convert the measurements,
The connector matrix:
can be constructed from the eigenvectors of
Once the connector
The approach described above provides measurements of the coupling between modes along the length of the single core multimode sensing fiber 10 as a function of time delay. In some embodiments, further corrections are made to address differing group velocities between modes. For example, to address the differing group velocities causing the mode coupling coefficients (
In addition to propagating with different group delays, each mode also propagates with a different wavenumber, or effective refractive index, meaning that each mode accumulates phase at a different rate as it propagates down the single core multimode sensing fiber 10.
The LP11 and LP01 self-coupling terms are both weighted integrals over the single core multimode sensing fiber 10 in this example. As a result, even for random Rayleigh scatter, the LP11 and LP01 self-coupling terms are substantially similar. If the sensing fiber is straight, this common term in the coupling terms allows precise measurements of the difference between the phase propagation terms for the LP11 and LP01 modes along the fiber length. Further, this difference in effective refractive index can be used to predict the phase change in the cross term phases, such as by assuming the cross term phase accumulations are exactly halfway between the pure LP11 and LP01 phase delays. These calculated phase changes due to the different effective refractive indexes of the modes are then applied to the measured and resampled coupling coefficients before the scattering cross section is calculated.
In step S20, the single core multimode fiber is connected to a multimode interrogation system such as the OFDR system shown in
Moving over to the next process stage of the flowchart, step S30 describes changing the shape of the fiber to a measurement orientation. In step S31, the fiber response is measured using the interrogation system. Then, the decoupling or alpha matrix is applied to the measured response in step S32. The coupling coefficients are resampled in step S33, and the wavenumber corrections are applied in step S34. The index modulation profile change is calculated at each point along the sensing fiber in step S35. In step S36, the bend, twist, and strain are calculated each point along the fiber, and from these values, the shape of the sensing fiber is calculated in step S37.
Having determined how to make and use a single core multimode fiber to determine shape using an OFDR interrogation method and overlapped tilted gratings, the inventors tested different fiber core sizes and estimated their sensitivity to detecting twist.
An example fiber that admits only three modes was designed and then checked to verify that this fiber provides reasonable twist sensitivity. The number of modes in a step-index multimode fiber is described by a normalized frequency parameter known as the V-number. A V-number of around 3.5 was selected in order to guide the LP11 modes tightly, while excluding the LP21 and LP02 modes.
where n1 is the index of refraction of the core, n2 is the index of the cladding, λ is the wavelength of the light, r is the core radius, and NA is the Numerical Aperture. Using V=3.5, the selected operating wavelength, and a selected Numerical Aperture permits calculation of the core radius as follows:
Solving for r yields:
The rotational period of the skew rays (e.g., as shown in
where β is the propagation constant and k is the wavenumber. The definition of the wave number is
The propagation constant β as a function of b is solved in accordance with:
√{square root over (b(k12−k22)+k22)}=β
Factoring out the vacuum wavenumber,
collecting terms, and applying the definition of Numerical Aperture (NA) in an optical fiber, NA=√{square root over (n12−n22)}, this equation may be expressed as:
An expression for the beat length between the two non-degenerate modes is:
Pulling the common terms out from under the radicals and factoring out the common terms results in:
A binomial approximation is applied to the terms under the radicals, and terms are canceled and common factors removed to yield:
Substituting numerical values gives:
gives a beat length of 270 microns.
Estimating twist sensitivity using an approximate radius for the higher order modes of r=0.002 mm produces:
This twist sensitivity may be doubled to a value that is about half of the sensitivity in a multi-core shape sensing fiber. This demonstrates that a simple step-index, three-mode single core fiber has sufficient twist sensitivity to function as an effective shape sensor.
Different shape cores with different numbers of multimodes may be used. For example, a single small core as shown in
The technology described provides a single core multimode fiber that can be used to accurately sense shape and can be manufactured quite simply and cost effectively as compared to multicore shape sensing fiber.
The technology described above also has wide and diverse applications. One non-limiting example application is to a fiber optic shape sensing system for a robotic surgical arm in which one or more of the various technical features and/or embodiments described above may be used.
The techniques described herein can be implemented using a control system including at least one memory and at least one processor, and often a plurality of processors. The control system also includes programmed instructions (e.g., a computer-readable medium storing the instructions) to implement some or all of the methods described in accordance with aspects disclosed herein. The control system may include two or more data processing circuits with one portion of the processing optionally being performed on or adjacent the tool, and another portion of the processing being performed at a station (e.g. an operator input system or central processing system or the like) remote from the tool. Any of a wide variety of centralized or distributed data processing architectures may be employed. Similarly, the programmed instructions may be implemented as a number of separate programs or subroutines, or they may be integrated into a number of other aspects of the teleoperational systems described herein. In one embodiment, the control system supports wireless communication protocols such as Bluetooth, IrDA, HomeRF, IEEE 802.11, DECT, and Wireless Telemetry.
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 technology described, for it to be encompassed by the present claims. No claim is intended to invoke 35 USC § 112(f) 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.
This application is a U.S. National Stage Filing under 35 U.S.C. 371 from International Application No. PCT/US2017/067588, filed on Dec. 20, 2017, and published as WO 2018/125713 A1 on Jul. 5, 2018, which claims the priority and benefit of U.S. Provisional Patent Application 62/440,035, filed Dec. 29, 2016, entitled “METHODS AND APPARATUS FOR DETERMINING SHAPE PARAMETER(S) USING A SENSING FIBER HAVING A SINGLE CORE WITH MULTIPLE LIGHT PROPAGATING MODES,” each of which is incorporated herein by reference in its entirety.
Filing Document | Filing Date | Country | Kind |
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PCT/US2017/067588 | 12/20/2017 | WO | 00 |
Number | Date | Country | |
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62440035 | Dec 2016 | US |