Calculation of sensor array induced phase angle independent from demodulation phase offset of phase generated carrier

1. A method, a sensor array that employs a parameter to induce a time-varying phase angle φ on an optical signal that comprises a phase generated carrier with a demodulation phase offset β, the method comprising the step of:

calculating the phase angle φ substantially independently of the demodulation phase offset β.

2. The method of claim 1 , further comprising the step of:

sampling an output signal from the sensor array to obtain a plurality of samples S n , wherein n=0 to x;

wherein the step of calculating the phase angle φ substantially independently of the demodulation phase offset β comprises the step of:

calculating the phase angle φ substantially independently of the demodulation phase offset β through employment of one or more of the plurality of samples S n .

3. The method of claim 2 , wherein the step of calculating the phase angle φ substantially independently of the demodulation phase offset β through employment of the one or more of the plurality of samples S n comprises the steps of:

calculating one or more quadrature terms and one or more in-phase terms through employment of one or more of the plurality of samples S n , wherein one or more of the one or more quadrature terms and one or more of the one or more in-phase terms are substantially independent from the demodulation phase offset β; and

calculating the phase angle φ through employment of the one or more quadrature terms and the one or more in-phase terms.

4. The method of claim 2 , wherein the output signal comprises a period T pulse , wherein the step of sampling the output signal from the sensor array to obtain the plurality of samples S n , wherein n=0 to x comprises the step of:

sampling the output signal from the sensor array to obtain a plurality of samples S n within a period T s , wherein n=0 to x, wherein T s is less than or equal to 1.125×T pulse .

5. The method of claim 4 , wherein T s is less than or equal to T pulse .

6. The method of claim 4 , wherein the step of calculating the phase angle φ substantially independently of the demodulation phase offset β through employment of the one or more of the plurality of samples S n , comprises the steps of:

calculating one or more quadrature terms and one or more in-phase terms through employment of one or more of the plurality of samples S n , wherein one or more of the one or more quadrature terms and one or more of the one or more in-phase terms are substantially independent from the demodulation phase offset β;

calculating the phase angle φ through employment of the one or more quadrature terms and the one or more in-phase terms.

7. The method of claim 6 , wherein the step of calculating the one or more quadrature terms and the one or more in-phase terms through employment of the one or more of the plurality of samples S n , wherein the one or more of the one or more quadrature terms and the one or more of the one or more in-phase terms are substantially independent from the demodulation phase offset β comprises the steps of:

calculating a set of quadrature terms Q j and a set of in-phase terms I k through employment of one or more of the plurality of samples S n , wherein j=0 to y, wherein k=0 to z;

calculating a quadrature term Q ab from a largest term of absolute values of the set of quadrature terms Q j ;

calculating a constant C 1 and a constant C 2 ;

calculating a quadrature term

Q

s

=

C

1

×

∑

j

=

0

j

=

y

⁢

⁢

Q

j

2

,

wherein Q s is substantially independent from the demodulation phase offset β; and

calculating an in-phase term

I

s

=

C

2

×

∑

k

=

0

k

=

z

⁢

⁢

I

k

2

,

wherein I s is substantially independent from the demodulation phase offset β.

8. The method of claim 7 , wherein the step of calculating the constant C 1 and the constant C 2 comprises the step of:

calculating the constant C 1 and the constant C 2 such that an amplitude of the quadrature term Q s , an amplitude of the quadrature term Q ab , and an amplitude of the in-phase term I s comprise a substantially same amplitude for a modulation depth M of an operating range for the phase generated carrier.

9. The method of claim 7 , wherein x=7, y=3, z=1, wherein the step of calculating the set of quadrature terms Q j and the set of in-phase terms I k through employment of the one or more of the plurality of samples S n , wherein j=0 to y, wherein k=0 to z comprises the steps of:

calculating Q 0 =S 0 −S 4 ;

calculating Q 1 =S 1 −S 5 ;

calculating Q 2 =S 2 −S 6 ;

calculating Q 3 =S 3 −S 7 ;

calculating I 0 =(S 0 +S 4 )−(S 2 +S 6 ); and

calculating I 1 =(S 1 +S 5 )−(S 3 +S 7 ).

10. The method of claim 7 , wherein x=15, y=7, z=3, wherein the step of calculating the set of quadrature terms Q j and the set of in-phase terms I k through employment of the one or more of the plurality of samples S n , wherein j=0 to y, wherein k=0 to z comprises the steps of:

calculating Q 0 =S 0 −S 8 ;

calculating Q 1 =S 1 −S 9 ;

calculating Q 2 =S 2 −S 10 ;

calculating Q 3 =S 3 −S 11 ;

calculating Q 4 =S 4 −S 12 ;

calculating Q 5 =S 5 −S 13 ;

calculating Q 6 =S 6 −S 14 ;

calculating Q 7 =S 7 −S 15 ;

calculating I 0 =(S 0 +S 8 )−(S 4 +S 12 );

calculating I 1 =(S 1 +S 9 )−(S 5 +S 13 );

calculating I 0 =(S 2 +S 10 )−(S 6 +S 14 ); and

calculating I 1 =(S 3 +S 11 )−(S 7 +S 15 ).

11. The method of claim 7 , wherein the step of calculating the phase angle φ through employment of the one or more quadrature terms and the one or more in-phase terms comprises the steps of:

calculating a correction term ΔQ;

calculating a quadrature term Qfrom the quadrature term Q s and the correction term ΔQ;

calculating a quadrature term Q from a magnitude of the quadrature term Q m and one or more quadrature terms of the set of quadrature terms Q j ;

calculating an in-phase term I from a magnitude of the in-phase term I s and one or more in-phase terms of the set of in-phase terms I k ; and

calculating the phase angle φ from an arctangent of a quantity Q/I.

12. The method of claim 11 , wherein the step of calculating the correction term ΔQ comprises the step of:

calculating the correction term ΔQ=Q s −Q ab .

13. The method of claim 11 , wherein the step of calculating the quadrature term Q m from the quadrature term Q s and the correction term ΔQ comprises the step of:

calculating a constant C 3 ; and

calculating Q m =Q s +(C 3 ×ΔQ).

14. An apparatus, a sensor array that employs a parameter to induce a time-varying phase angle φ on an optical signal that comprises a phase generated carrier with a demodulation phase offset β, the apparatus comprising:

a processor component that calculates the phase angle φ substantially independent from the demodulation phase offset β.

15. The apparatus of claim 14 , wherein the processor component obtains a plurality of samples S n of an output signal from the sensor array, wherein n=0 to x;

wherein the processor component employs one or more of the plurality of samples S n to calculate the phase angle φ substantially independent from the demodulation phase offset β.

16. The apparatus of claim 15 , wherein the processor component employs one or more of the plurality of samples S n of the output signal to calculate one or more quadrature terms and one or more in-phase terms, wherein one or more of the one or more quadrature terms and one or more of the one or more in-phase terms are substantially independent from the demodulation phase offset β of the phase generated carrier;

wherein the processor component employs the one or more quadrature terms and the one or more in-phase terms to calculate the phase angle φ.

17. The apparatus of claim 15 , wherein the output signal comprises a period T pulse , wherein the processor component obtains the plurality of samples S n within a period T s , wherein T s is less than or equal to 1.125×T pulse .

18. The apparatus of claim 17 , wherein T s is less than or equal to T pulse .

19. The apparatus of claim 17 , wherein the processor component employs one or more of the plurality of samples S n of the output signal to calculate one or more quadrature terms and one or more in-phase terms, wherein one or more of the one or more quadrature terms and one or more of the one or more in-phase terms are substantially independent from the demodulation phase offset β of the phase generated carrier;

wherein the processor component employs the one or more quadrature terms and the one or more in-phase terms to calculate the phase angle φ.

20. The apparatus of claim 19 , wherein the one or more of the one or more quadrature terms comprise a quadrature term Q ab and a quadrature term Q s , wherein the one or more of the one or more in-phase terms comprise an in-phase term I s ;

wherein the processor component employs one or more of the plurality of samples S n , the quadrature term Q ab , the quadrature term Q s , and the in-phase term I s to calculate the phase angle φ.

21. The apparatus of claim 20 , wherein the processor component employs the plurality of samples S n to calculate a set of quadrature terms Q j and a set of in-phase terms I k , wherein j=0 to y, wherein k=0 to z;

wherein the processor component employs the set of quadrature terms Q j to calculate the quadrature term Q ab =max(|Q j |), wherein j=0 to y;

wherein the processor component employs the set of quadrature terms Q j and the set of in-phase terms I k to calculate the quadrature term Q s , and the in-phase term I s .

22. The apparatus of claim 21 , wherein the processor component calculates a constant C 1 and a constant C 2 , wherein the processor component calculates:

Q

s

=

C

1

×

∑

j

=

0

j

=

y

⁢

⁢

Q

j

2

;

wherein the processor component calculates:

I

s

=

C

2

×

∑

k

=

0

k

=

z

⁢

⁢

I

k

2

;

wherein the processor component calculates the constant C 1 and the constant C 2 such that a magnitude of the quadrature term Q s , a magnitude of the quadrature term Q ab , and a magnitude of the in-phase term I s comprise a substantially same magnitude at a modulation depth M of an operating range for the phase generated carrier.

23. The apparatus of claim 22 , wherein the processor component employs the quadrature term Q ab and the quadrature term Q s to calculate a correction term ΔQ=Q s −Q ab ;

wherein the processor component employs the quadrature term Q m and the correction term ΔQ to calculate a quadrature term Q m ;

wherein the processor component employs the quadrature term Q m , the in-phase term I s , the set of quadrature terms Q j , and the set of in-phase terms I k to calculate the phase angle φ.

24. The apparatus of claim 23 , wherein the processor component employs the quadrature term Q m and the set of quadrature terms Q j to calculate a quadrature term Q, wherein the processor component employs the in-phase term I s and the set of in-phase terms I k to calculate an in-phase term I;

wherein the processor component calculates:

Q=±Q m ;

wherein the processor component calculates:

I=±I s ;

wherein the processor component employs the set of quadrature terms Q j to determine a sign of Q;

wherein the processor component employs the set of in-phase terms I k to determine a sign of I;

wherein the processor component calculates:

φ=arctangent (Q/I).

25. The apparatus of claim 24 , wherein the processor component calculates a constant C 3 , wherein the processor component calculates:

Q m =Q s +( C 3 ×ΔQ ).

26. The apparatus of claim 25 , wherein x=7, y=3, and z=1;

wherein the processor component calculates:

Q 0 =S 0 −S 4 , Q 1 =S 1 −S 5 , Q 2 =S 2 −S 6 , and Q 3 =S 3 −S 7 ;

wherein the processor component calculates:

I 0 =( S 0 +S 4 )−( S 2 +S 6 ); and

I 1 =( S 1 +S 5 )−( S 3 +S 7 ).

27. The apparatus of claim 25 , wherein x=15, y=7, and z=3;

wherein the processor component calculates:

Q 0 =S 0 −S 8 , Q 1 =S 1 S 9 , Q 2 =S 2 −S 10 , Q 3 =S 3 −S 11 ,

Q 4 =S 4 −S 12 , Q 5 =S 5 −S 13 , Q 6 =S 6 −S 14 , and Q 7 =S 7 −S 15 ;

wherein the processor component calculates:

I 0 =(S 0 +S 8 )−( S 4 +S 12 ), I 1 =( S 1 +S 9 )−( S 5 +S 13 ),

I 2 =( S 2 +S 10 )−(S 6 +S 14 ), and I 3 =( S 3 +S 11 )−( S 7 +S 15 ).

28. An article, a sensor array that employs a parameter to induce a time-varying phase angle φ on an optical signal that comprises a phase generated carrier with a demodulation phase offset β, the article comprising:

one or more computer-readable signal-bearing media;

means in the one or more media for calculating the phase angle φ substantially independently of the demodulation phase offset β.

29. The article of claim 28 , further comprising:

means in the one or more media for sampling an output signal from the sensor array to obtain a plurality of samples S n , wherein n=0 to x;

wherein the means in the one or more media for calculating the phase angle φ substantially independently of the demodulation phase offset β comprises:

means in the one or more media for calculating the phase angle φ substantially independently of the demodulation phase offset β through employment of one or more of the plurality of samples S n .

30. The article of claim 29 , wherein the means in the one or more media for calculating the phase angle φ substantially independently of the demodulation phase offset β through employment of the one or more of the plurality of samples S n comprises:

means in the one or more media for calculating one or more quadrature terms and one or more in-phase terms through employment of one or more of the plurality of samples S n , wherein one or more of the one or more quadrature terms and one or more of the one or more in-phase terms are substantially independent from the demodulation phase offset β; and

means in the one or more media for calculating the phase angle φ through employment of the one or more quadrature terms and the one or more in-phase terms.

31. The article of claim 29 , wherein the output signal comprises a period T pulse , wherein the means in the one or more media for sampling the output signal from the sensor array to obtain the plurality of samples S n , wherein n=0 to x comprises:

means in the one or more media for sampling the output signal from the sensor array to obtain the plurality of samples S n within a period T s , wherein n=0 to x, wherein T s is less than or equal to 1.125×T pulse .

32. The article of claim 31 , wherein T s is less than or equal to T pulse .

33. The article of claim 31 , wherein the means in the one or more media for calculating the phase angle φ substantially independently of the demodulation phase offset β through employment of the one or more of the plurality of samples S n comprises:

means in the one or more media for calculating one or more quadrature terms and one or more in-phase terms through employment of one or more of the plurality of samples S n , wherein one or more of the one or more quadrature terms and one or more of the one or more in-phase terms are substantially independent from the demodulation phase offset β;

means in the one or more media for calculating the phase angle φ through employment of the one or more quadrature terms and the one or more in-phase terms.

34. The article of claim 33 , wherein the means in the one or more media for calculating the one or more quadrature terms arid the one or more in-phase terms through employment of the one or more of the plurality of samples S n comprises:

means in the one or more media for calculating a set of quadrature terms Q j and a set of in-phase terms I k through employment of one or more of the plurality of samples S n , wherein j=0 to y, wherein k=0 to z;

means in the one or more media for calculating a quadrature term Q ab from a largest term of absolute values of the set of quadrature terms Q j ;

means in the one or more media for calculating a constant C 1 and a constant C 2 ;

means in the one or more media for calculating a quadrature term

Q

s

=

C

1

×

∑

j

=

0

j

=

y

⁢

⁢

Q

j

2

,

wherein Q s is substantially independent from the demodulation phase offset β; and

means in the one or more media for calculating an in-phase term

I

s

=

C

2

×

∑

k

=

0

k

=

z

⁢

⁢

I

k

2

,

wherein I s is substantially independent from the demodulation phase offset β.

35. The article of claim 34 , wherein the means in the one or mom media for calculating the constant C 1 and the constant C 2 comprises:

means in the one or more media for calculating the constant C 1 and the constant C 2 such that an amplitude of the quadrature term Q s , an amplitude of the quadrature term Q ab , and an amplitude of the in-phase term I s comprise a substantially same amplitude for a modulation depth M of an operating range for the phase generated carrier.

36. The article of claim 34 , wherein the means in the one or more media for calculating the phase angle φ through employment of the one or more quadrature terms and the one or more in-phase terms comprises:

means in the one or more media for calculating a correction term ΔQ;

means in the one or more media for calculating a quadrature term Q m from the quadrature term Q s and the correction term ΔQ;

means in the one or more media for calculating a quadrature term Q from a magnitude of the quadrature term Q m and one or more quadrature terms of the set of quadrature terms Q j ;

means in the one or more media for calculating an in-phase term I from a magnitude of the in-phase term I s and one or more in-phase terms of the set of in-phase terms I k ; and

means in the one or more media for calculating the phase angle φ from an arctangent of a quantity Q/I.

37. The article of claim 34 , wherein the means in the one or more media for calculating the correction term ΔQ comprises:

means in the one or more media for calculating the correction term ΔQ=Q s −Q ab ;

wherein the means in the one or more media for calculating the quadrature term Q m from the quadrature term Q s and the correction term ΔQ comprises:

means in the one or more media for calculating a constant C 3 ; and

means in the one or more media for calculating Q m =Q s +(C 3 ×ΔQ).