Methods and systems for correcting for nonlinear twist response in optical shape sensing with spun multicore fibers

1. Method of obtaining a twist rate of a twist applied to an optical fiber about a longitudinal axis of the optical fiber at least in a part along a length of the optical fiber, the optical fiber having a center core extending along the length of the optical fiber and at least one outer core helically wound around the center core with a spin rate, the method comprising:

acquiring a twist rate phase signal from an optical measurement of strain along the center core and the at least one outer core of the optical fiber,

calculating from the twist rate phase signal a noise filtered version of the twist rate phase signal,

calculating from the twist rate phase signal a first order term of the twist rate, which is proportional to one of: i) the twist rate phase signal, ii) the noise filtered version of the twist rate phase signal, and

calculating a correction term to the twist rate, which is proportional to one of the following:

iii) a product of the twist rate phase signal with the noise filtered version of the twist rate phase signal,

iv) a square of the noise filtered version of the twist rate phase signal.

2. Method of claim 1 , wherein calculating the correction term further comprises multiplying the product according to iii) or the square according to iv) with a numerical factor which is larger than 1 and smaller than 3.

3. Method of claim 2 , wherein the numerical factor is larger than 1.1 and smaller than 2.5.

4. Method of claim 2 , wherein the numerical factor is in a range from about 1.3 to about 1.7.

5. Method of claim 1 , wherein the correction term is inversely proportional to the spin rate of the at least one outer core.

6. Method of claim 1 , wherein the first order term of the twist rate is calculated as one of

τ 0 =TG· S τ   i)

τ f =TG·< S τ >  ii)

wherein TG is a twist gain calibration parameter, S τ is the acquired twist rate phase signal, and <S τ > is the noise filtered version of the acquired twist rate phase signal.

7. Method of claim 1 , wherein the correction term of the twist rate is calculated as one of:

F·τ 0 ·τ f /2 k   i)

F·τ f 2 /2 k   ii)

wherein k is the spin rate of the at least one outer core, τ 0 is the first order term of the twist rate calculated based on the twist rate phase signal, and τ f is the first order term of the twist rate calculated based on the noise filtered version of the twist rate phase signal, and F is a numerical factor larger than 1.

8. Method of claim 7 , wherein the twist rate is calculated as one of the following:

τ=τ 0 −( F·τ 0 ·τ f /2 k )  i)

τ=τ 0 −( F·τ f 2 /2 k )  ii)

9. Method of claim 1 , wherein the twist rate phase signal is acquired from a strain signal of the at least one outer core minus a strain signal of the center core.

10. Method of claim 1 , further comprising integrating the twist rate along the length of the optical fiber from a starting position to a selected position to obtain a twist angle at the selected position relative to the starting position.

11. System for obtaining a twist rate of a twist applied to an optical fiber about a longitudinal axis of the optical fiber at least in a part along a length of the optical fiber, the optical fiber having a center core extending along the length of the optical fiber and at least one outer core helically wound around the center core with a spin rate, the system comprising:

an optical measuring device configured to measure strain along the center core and the at least one outer core of the optical fiber to acquire a twist rate phase signal,

a calculating unit configured to:

calculate from the twist rate phase signal a noise filtered version of the twist rate phase signal,

calculate a first order term of the twist rate, which is proportional to one of: i) the twist rate phase signal, ii) the noise filtered version of the twist rate phase signal, and

calculate a correction term of the twist rate, which is proportional to one of the following:

iii) a product of the twist rate phase signal with the noise filtered version of the twist rate phase signal,

iv) a square of the noise filtered version of the twist rate phase signal.

12. System of claim 11 , wherein the optical measuring device is an optical shape sensing device based on optical frequency domain reflectometry.

13. Optical shape sensing system, comprising a system according to claim 11 for obtaining a twist rate of a twist applied to an optical fiber about a longitudinal axis of the optical fiber at least in a part along a length of the optical fiber, the optical fiber having a center core extending along the length of the optical fiber and at least one outer core helically wound around the center core with a spin rate.

14. A non-transitory computer readable medium with instructions stored thereon to control a processor to perform the method as claimed in claim 1 .