Methods and apparatus to determine a twist parameter and/or a bend angle associated with a multi-core fiber

1. A method for a multi-core fiber having multiple optical cores, the method comprising:

detecting, for each different core of a set of different cores of the multiple optical cores, a total change in optical length representing an accumulation of all changes in optical length for multiple segments of that different core up to a point on the multi-core fiber,

determining a difference between the total changes in optical length for cores of the set of different cores; and

determining a twist parameter associated with the multi-core fiber at the point on the multi-core fiber based on the difference.

2. The method in claim 1 , further comprising:

determining a location or a pointing direction at the point on the multi-core fiber based on the twist parameter.

3. The method in claim 1 , further comprising:

correcting for birefringence at each of the multiple segments of the cores of the set of different cores.

4. The method in claim 1 , wherein the detecting, for each different core of the set of different cores of the multiple optical cores, the total change in optical length includes:

for that different core, detecting an incremental change in optical length for each segment of the multiple segments up to the point on the multi-core fiber, and

combining the incremental changes to determine the total change in optical length for that different core.

5. The method in claim 1 , wherein the set of different cores includes a first optical core, a second optical core, a third optical core, and a fourth optical core, wherein the first, second, and third optical cores are peripheral cores spaced around the fourth optical core, wherein the fourth optical core is located along a center of the multi-core fiber, and wherein:

the determining the difference between the total changes in optical length for the cores of the set of different cores includes:

determining a corresponding phase response for a light signal reflected from each of the multiple segments of the first, second, third, and fourth optical cores, wherein strain on the multi-core fiber at one or more of the multiple segments causes a shift in phase of the light signal reflected in each core of the first, second, third, and the fourth optical cores,

averaging the corresponding phase responses for the first, second, and third optical cores to produce an average phase response, and

combining the averaged phase response with the corresponding phase response for the fourth optical core to remove a common mode strain and produce a combined phase response, and

the determining the twist parameter associated with the multi-core fiber at the point on the multi-core fiber based on the difference includes:

determining the twist parameter from the combined phase response.

6. The method in claim 1 , wherein the cores of the set of different cores include a first optical core, a second optical core, a third optical core, and a fourth optical core, wherein the first, second, and third optical cores are peripheral cores spaced around the fourth optical core, wherein the fourth optical core is located along a center of the multi-core fiber, and wherein the determining the difference between the total changes in optical length for the cores of the set of different cores includes:

averaging the total changes in optical length of the first, second, and third optical cores to produce an average total change, and

determining a difference between the average total change and the total change in optical length of the fourth optical core.

7. The method in claim 1 , 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.

8. A method for a multi-core fiber having multiple optical cores, comprising:

detecting, for each different core of a set of different cores of the multiple optical cores, a total change in optical length representing an accumulation of all changes in optical length for multiple segments of that different core up to a position on the multi-core fiber,

determining a difference between the total changes in optical length for cores of the set of different cores; and

calculating a bend angle of the multi-core fiber at the position along the multi-core fiber based on the difference.

9. The method in claim 8 , further comprising:

determining a shape of a portion of the multi-core fiber at the position along the multi-core fiber based on the bend angle.

10. An apparatus for making measurements of a multi-core fiber having multiple optical cores, comprising:

detection circuitry configured to detect, for each different core of a set of different cores of the multiple optical cores, a total change in optical length representing an accumulation of all changes in optical length for multiple segments of that different core up to a point on the multi-core fiber; and

calculation circuitry configured to determine a difference between the total changes in optical length for cores of the set of different cores and a twist parameter associated with the multi-core fiber at the point on the multi-core fiber based on the difference.

11. The apparatus in claim 10 , wherein the calculation circuitry is further configured to determine a location or a pointing direction at the point on the multi-core fiber based on the twist parameter.

12. The apparatus in claim 10 , wherein an accuracy of the twist parameter is better than 1 degree of fiber rotation up to the point on the multi-core fiber.

13. The apparatus in claim 10 , wherein the calculation circuitry is further configured to correct for birefringence at each of the multiple segments of the cores of the set of different cores.

14. The apparatus in claim 10 , wherein the calculation circuitry is configured to for each different core of the set of different cores of the multiple optical cores, detect an incremental change in optical length for each segment of the multiple segments up to the point on the multi-core fiber, and combine the incremental changes to determine the total change in optical length for that different core.

15. The apparatus in claim 10 , wherein the set of different cores includes a first optical core, a second optical core, a third optical core, and a fourth optical core, wherein the first, second, and third optical cores are peripheral cores spaced around the fourth optical core, wherein the fourth optical core is located along a center of the multi-core fiber, wherein the calculation circuitry is configured to determine the difference between the total changes in optical length for the cores of the set of different cores by:

determining a corresponding phase response for a light signal reflected for each core of the first, second, third, and the fourth optical cores, the light signal reflected from each of the multiple segments of the first, second, third, and fourth optical cores, wherein strain on the multi-core fiber at one or more of the multiple segments causes a shift in phase of the light signal reflected in each core of the first, second, third, and the fourth optical cores,

averaging the corresponding phase responses for the first, second, and third optical cores to produce an average phase response, and

combining the averaged phase response with the corresponding phase response for the fourth optical core to remove a common mode strain and produce a combined phase response.

16. The apparatus in claim 10 , wherein the cores of the set of different cores include a first optical core, a second optical core, a third optical core, and a fourth optical core, wherein the first, second, and third optical cores are peripheral cores spaced around the fourth optical core, wherein the fourth optical core is located along a center of the multi-core fiber, and wherein the calculation circuitry is configured to determine the difference between the total changes in optical length for the cores of the set of different cores by:

averaging the total changes in optical length of the first, second, and third optical cores to produce an average total change, and

determining a difference between the average total change and the total change in optical length of the fourth optical core.

17. The apparatus in claim 10 , wherein the calculation circuitry is configured to:

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

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

18. The apparatus in claim 10 , wherein the calculation circuitry is configured to, for at least one core of the multiple optical cores:

calculate a bend at a segment length of the multiple segments to produce a calculated bend,

square the calculated bend to produce a squared bend,

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

combine the bend product with a detected total change in optical length of a peripheral one of the multiple optical cores of the multi-core fiber at the segment length of the multiple segments.

19. The apparatus in claim 10 , wherein the calculation circuitry is configured to determine a shape of at least a portion of the multi-core fiber based on the total change in optical length.

20. The apparatus of in claim 10 , wherein the cores of the set of different cores include a peripheral core located peripherally relative to a center core located along a center of the multi-core fiber, and wherein to determine the difference between the total changes in optical length for the cores of the set of different cores, the detection circuitry is configured to:

determine a difference in the total change in optical length between the peripheral core and the center core.

21. An apparatus for making measurements of a multi-core fiber having multiple optical cores, comprising circuitry configured to:

detect a total change in optical length between different cores of the multiple optical cores, the total change in optical length representing an accumulation of all changes in optical length for multiple segments between the different cores of the multiple optical cores up to a position on the multi-core fiber, and

calculate a bend angle of the multi-core fiber at the position along the multi-core fiber based on the total change in optical length up to the position along the multi-core fiber.

22. The apparatus in claim 21 , wherein the bend angle corresponds to a pointing direction at the position along the multi-core fiber.

23. The apparatus in claim 21 , wherein the circuitry is configured to determine a shape of a portion of the multi-core fiber at the position along the multi-core fiber based on the bend angle.

24. The apparatus in claim 21 , wherein the circuitry is configured to correct for birefringence effects in the multi-core fiber.