Optical position and/or shape sensing

1. A measurement method for a multi-core fiber, comprising:

detecting a total change in optical length in ones of the cores in the multi-core fiber that reflects an accumulation of all of the changes in optical length for multiple fiber segment lengths up to a point on the multi-core fiber, and

determining a location or a pointing direction at the point on the multi-core fiber based on the detected total change in optical length.

2. The method in claim 1 , wherein the determining includes determining both the location and the pointing direction at the point.

3. The method in claim 1 , wherein an accuracy of the determined location or pointing direction is better than 0.5% of the optical length of the multi-core fiber up to the point on the multi-core fiber.

4. The method in claim 1 , wherein the determining includes determining a shape of at least a portion of the multi-core fiber based on the detected changes in optical length.

5. The method in claim 1 , wherein the determining includes 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 and then determining the shape of the portion of the multi-core fiber at the position based on the calculated bend angle.

6. The method in claim 5 , wherein the bend angle is calculated in two or three dimensions.

7. The method in claim 1 , wherein the detecting 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, and wherein the detected total change in optical length is based on a combination of the incremental changes.

8. The method in claim 7 , wherein the detecting step includes detecting a phase response of a light signal reflected in at least two of the multiple cores 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 two cores.

9. The method in claim 8 , further comprising monitoring the phase response continuously along the optical length of the multi-core fiber.

10. The method in claim 7 , 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.

11. The method in claim 7 , further comprising:

determining a twist parameter associated with the multi-core fiber at the point on the multi-core fiber based on the detected total change in optical length of the multi-core fiber.

12. The method in claim 11 , wherein the determining of the location or the pointing direction at the point on the multi-core fiber is based on the determined twist parameter.

13. The method in claim 11 , further comprising:

correcting for the determined twist parameter at each of the segment lengths.

14. The method in claim 11 , wherein the multi-core fiber includes three peripheral cores spaced around a fourth core along the center of the multi-core fiber, the method further comprising:

determining a phase response of a light signal reflected in each of the four cores from each segment length, and wherein 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 of the four cores,

averaging the phase responses for the three peripheral cores,

combining the averaged phase response with the phase response of the fourth core to remove a common mode strain, and

determining the twist parameter from the combined phase response.

15. The method in claim 11 , further comprising:

determining bend-induced optical length changes along the multi-core fiber, and

accounting for the bend-induced optical length changes when determining the twist parameter.

16. The method in claim 15 , further comprising:

calculating a bend at one of the segment lengths,

squaring the calculated bend,

multiplying the squared bend by a constant to produce a bend product,

combining the bend product with the determined changes in optical length of an outer core of the multi-core fiber at the one segment length.

17. The method in claim 7 , further comprising:

determining an orientation of the multi-core fiber at the point on the multi-core fiber at each of the segment lengths,

correcting for the determined orientation when determining the location at the point on the multi-core fiber based on the detected total change in optical length.

18. The method in claim 7 , wherein the multi-core fiber is characterized by a nominal spin rate, further comprising:

determining an angular rotation of the multi-core fiber at the point on the multi-core fiber at each of the segment lengths compared to the nominal spin rate of the multi-core fiber,

determining a wobble factor for the multi-core fiber by constraining the multi-core fiber to a curved orientation in one plane, and

correcting for the wobble factor when determining the location at the point on the multi-core fiber based on the detected total change in optical length.

19. The method in claim 1 , wherein the multi-core fiber is helically wrapped and is characterized by a nominal spin rate, the method further comprising:

determining a variation in the nominal spin rate at the point along the multi-core fiber, and

correcting for the spin rate variation.

20. The method in claim 1 , wherein 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.

21. 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 multi-core fiber and unwrapping the optical phase change to determine the optical length.

22. The method in claim 1 , further comprising:

transmitting light with at least two polarization states along the multi-core fiber, and

combining reflections of the light with the at least two polarization states in determining the location or the pointing direction at the point on the multi-core fiber based on the detected total change in optical length.

23. The method in claim 22 , 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 multi-core fiber,

using the polarization controller to transmit a second light signal at the second polarization state along the multi-core fiber,

calculating a polarization-independent changes in optical length in the ones of the cores in the multi-core fiber up to the point on the multi-core fiber using reflections of the first and second light signals.

24. An apparatus for making measurements of a multi-core fiber, comprising:

detection circuitry configured to detect a total change in optical length in cores in the multi-core fiber that reflects an accumulation of all of the changes in optical length for multiple fiber segment lengths up to a point on the multi-core fiber, and

calculation circuitry configured to determine a location or a pointing direction at the point on the multi-core fiber based on the detected total change in optical length.

25. The apparatus in claim 24 , wherein the calculation circuitry is configured to determine both the location and the pointing direction at the point.

26. The apparatus in claim 24 , wherein an accuracy of the determined location or point direction is better than 0.5% of the optical length of the multi-core fiber up to the point on the multi-core fiber.

27. The apparatus in claim 24 , wherein the calculation circuitry is configured to determine a shape of at least a portion of the multi-core fiber based on the detected total change in optical length.

28. The apparatus in claim 24 , wherein the calculation circuitry is configured to calculate a bend angle of the multi-core fiber at any position along the multi-core fiber based on the detected total change in optical length up to the position and then determine the shape of the portion of the multi-core fiber at the position based on the calculated bend angle.

29. The apparatus in claim 24 , wherein the detection circuitry is configured to detect 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, and wherein the detected total change in optical length are based on a combination of the incremental changes.

30. The apparatus in claim 29 , wherein the detection circuitry is configured to detect a phase response of a light signal reflected in at least two of the multiple cores 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 two cores.

31. The apparatus in claim 30 , wherein the detection circuitry is configured to monitor the phase response continuously along the optical length of the multi-core fiber.

32. The apparatus in claim 29 , wherein the detection circuitry is configured to detect a reflected Rayleigh scatter pattern in the reflected light signal for each segment length, and wherein the calculation circuitry is configured to 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.

33. The apparatus in claim 29 , wherein the calculation circuitry is configured to determine a twist parameter associated with the multi-core fiber at the point on the multi-core fiber based on the detected total change in optical length of the multi-core fiber.

34. The apparatus in claim 33 , wherein the determining of the location or the pointing direction at the point on the multi-core fiber is based on the determined twist parameter.

35. The apparatus in claim 33 , wherein the calculation circuitry is configured to correct for the determined twist parameter at each of the segment lengths.

36. The apparatus in claim 33 , wherein the multi-core fiber includes three peripheral cores spaced around a fourth core along the center of the multi-core fiber, the detection circuitry is configured to determine a phase response of a light signal reflected in each of the four cores from each segment length, the strain on the multi-core fiber at one or more of the segment lengths causing a shift in the phase of the reflected light signal in each of the four cores, and the calculation circuitry is configured to average the phase responses for the three peripheral cores, combine the averaged phase response with the phase response of the fourth core to remove a common mode strain, and determine the twist parameter from the combined phase response.

37. The apparatus in claim 29 , wherein the multi-core fiber is characterized by a nominal spin rate, the calculation circuitry is configured to determine an angular rotation of the multi-core fiber at the point on the multi-core fiber at each of the segment lengths compared to the nominal spin rate of the multi-core fiber, and the calculation circuitry is configured to determine a wobble factor for the multi-core fiber by constraining the multi-core fiber to a curved orientation in one plane and correct for the wobble factor when determining the location at the point on the multi-core fiber based on the detected total change in optical length.

38. The apparatus in claim 24 , wherein calculation circuitry is configured to determine the changes in optical length 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.

39. The apparatus in claim 24 , further comprising:

a laser configured to transmit light with at least two polarization states along the multi-core fiber,

wherein the calculation circuitry is configured to combine reflections of the light with the at least two polarization states in determining the location or the pointing direction at the point on the multi-core fiber based on the detected total change in optical length.

40. The apparatus in claim 39 , wherein the two polarization states include a first polarization state and a second polarization state which are at least nominally orthogonal, the apparatus further comprising a polarization controller configured to transmit a first light signal at the first polarization state along the multi-core fiber and transmit a second light signal at the second polarization state along the multi-core fiber, and wherein the calculation circuitry is configured to calculate a polarization-independent change in optical length in the ones of the cores in the multi-core fiber up to the point on the multi-core fiber using reflections of the first and second light signals.

41. 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 of a multi-core fiber by performing the following tasks:

detecting a total change in optical length in ones of the cores in the multi-core fiber that reflects an accumulation of all of the changes in optical length for multiple fiber segment lengths up to a point on the multi-core fiber, and

determining a location or a pointing direction at the point on the multi-core fiber based on the detected total change in optical length.