Calculation of sensor array induced phase angle
View Patent ↗A sensor array employs a parameter to induce a time-varying phase angle φ on an optical signal that comprises a phase generated carrier. The phase angle φ is calculated through employment of only four samples, where all the four samples are based on the optical signal.
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, the method comprising the steps of:
calculating a quadrature term Q through employment of one or more of a plurality of samples that are based on the optical signal;
calculating a peak value Q p of the quadrature term Q;
calculating an in-phase term I through employment of one or more of the plurality of samples that are based on the optical signal;
calculating a peak value I n of the in-phase term I;
I
p
(
M
,
β
)
=
2
·
B
·
(
cos
(
M
·
sin
β
)
-
cos
(
M
·
sin
(
π
2
+
β
)
)
)
.
wherein M is a modulation depth and β is a demodulation phase offset of the phase generated carrier;
calculating an operating point that comprises the modulation depth M and the demodulation phase offset β of the phase generated carrier through employment of the peak value I p of the in-phase term I and the peak value Q p of the quadrature term Q; and
calculating the phase angle φ through employment of the quadrature term Q; and the in-phase term, wherein the quadrature term Q and the in-phase term I are based on the optical signal.
2. The method of claim 1 , wherein the step of calculating the phase angle φ through employment of the in-phase term I and the quadrature term Q comprises the step of:
calculating the phase angle φ through employment of the in-phase term I and the quadrature term Q at the operating point.
3. The method of claim 1 , wherein the step of calculating the chase angle φ through employment of the in-phase term I and the quadrature term Q comprises the step of:
calculating the phase angle φ=arctangent(Q/I).
4. The method of claim 1 , wherein the phase generated carrier comprises a period T pgc , the method further comprising the step of:
sampling an output signal from the sensor array to obtain the plurality of samples from a same instance of the period T pgc .
5. The method of claim 4 , wherein the plurality of samples comprise samples S 0 , S 1 , S 2 , and S 3 , wherein the step of calculating the in-phase term I through employment of the one or more of the plurality of samples comprises the step of:
calculating the in-phase term I:
I =(S 0 +S 2 )−( S 1 +S 3 ).
6. The method of claim 5 , wherein the step of calculating the quadrature term Q through employment of one or more of the plurality of samples that are based on the optical signal comprises the step of:
calculating the quadrature term Q:
Q =2*( S 0 −S 2 ):
wherein the step of calculating the peak value Q p of the quadrature term Q comprises the step of:
calculating the peak value Q p of the quadrature term Q:
Q p ( M , β)=4 ·B ·sin( M ·sin β).
7. The method of claim 5 , wherein the step of calculating the quadrature term Q through employment of one or more of the plurality of samples that are based on the optical signal comprises the step of:
calculating the quadrature term Q:
Q=−( S 0 −S 2 ):
wherein the step of calculating the peak value Q 2 of the quadrature term Q comprises the step of:
calculating the peak value Q p of the quadrature term Q:
Q p ( M , β)=2 ·B ·sin( M ·β).
8. 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, wherein the phase generated carrier comprises a period T pgc , the method comprising the steps of:
calculating the phase angle φ through employment of a quadrature term Q and an in-phase term I, wherein the quadrature term Q and the in-phase term I are based on the optical signal;
wherein the phase generated carrier comprises a period T pgc , the method further comprising the step of:
sampling an output signal from the sensor array to obtain the plurality of samples from a same instance of the period T pgc ;
wherein the step of calculating the phase angle φ through employment of the quadrature term Q and the in-phase term I comprises the steps of:
calculating the in-phase term I through employment of one or more of the plurality of samples;
calculating a quadrature term Q through employment of one or more of the plurality of samples; and
calculating the phase angle φ through employment of the in-phase term I and the quadrature term Q;
further comprising the steps of:
calculating a peak value I p of the in-phase term I;
calculating a peak value Q p of the quadrature term Q; and
calculating an operating point that comprises a modulation depth M and a demodulation phase offset β of the phase generated carrier through employment of the peak value I p of the in-phase term I and the peak value Q p of the quadrature term Q;
wherein the plurality of samples comprise samples S 0 , S 1 , S 2 , and S 3 , wherein the step of calculating the in-phase term I through Q p employment of the one or more of the plurality of samples comprises the step of:
calculating the in-phase term I:
I =( S 0 +S 2 )−( S 1 +S 3 );
wherein the step of calculating the peak value I p of the in-phase term I comprises the step of:
calculating the peak value I p of the in-phase term I:
I
p
(
M
,
β
)
=
2
·
B
·
(
cos
(
M
·
sin
β
)
-
cos
(
M
·
sin
(
π
2
+
β
)
)
)
.
9. The method of claim 8 , wherein the step of calculating the quadrature term Q through employment of the one or more of the plurality of samples comprises the step of:
calculating the quadrature term Q:
Q =−( S 0 −S 2 ).
10. The method of claim 9 , wherein the step of calculating the peak value Q p of the quadrature term Q comprises the step of:
calculating the peak value Q p of the quadrature term Q:
Q p ( M , β)=2 ·B ·sin( M ·sin β).
11. The method of claim 10 , wherein the step of calculating the phase angle φ through employment of the in-phase term I and the quadrature term Q comprises the step of:
calculating the phase angle φ arctangent(Q/I).
12. The method of claim 8 , wherein the step of calculating the quadrature term Q through employment of the one or more of the plurality of samples comprises the step of:
calculating the quadrature term Q:
Q =−2*( S 0 −S 2 ).
13. The method of claim 12 , wherein the step of calculating the peak value Q p of the quadrature term Q comprises the step of:
calculating the peak value Q p :
Q p ( M , β)=4 ·B ·sin( M ·sin β).
14. The method of claim 13 , wherein the step of calculating the phase angle φ through employment of the in-phase term I and the quadrature term Q comprises the step of:
calculating the phase angle φ=arctangent(Q/I).
15. 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, the apparatus comprising:
a processor component;
wherein the processor component employs one or more of a plurality of samples that are based on the optical signal to calculate an in-phase term I;
wherein the processor component employs one or more of the plurality of samples to calculate a quadrature term Q;
wherein the processor component calculates a peak value I p of the in-phase term I as
I
p
(
M
,
β
)
=
2
·
B
·
(
cos
(
M
·
sin
β
)
-
cos
(
M
·
sin
(
π
/
2
+
β
)
)
)
;
wherein M is a modulation depth and β is a demodulation phase offset of the phase generated carrier;
wherein the processor component calculates a peak value Q p of the quadrature term Q;
wherein the processor calculates an operating point that comprises the modulation depth M and the demodulation phase offset β of the phase generated carrier through employment of the peak value I p of the in-phase term I and the peak value Q p of the quadrature term Q;
wherein the processor component employs the quadrature term Q and the in-phase term I to calculate the phase angle φ, wherein the quadrature term Q and the in-phase term I are based on the optical signal.
16. The apparatus of claim 15 , wherein the phase generated carrier comprises a period T pgc , wherein the processor component obtains the plurality of samples from an output signal from the sensor array within a same instance of the period T pgc .
17. The apparatus of claim 16 ,
wherein the processor component employs the in-phase term I and the quadrature term Q to calculate the phase angle φ at the operating point.
18. The apparatus of claim 16 ,
wherein the plurality of samples comprises four samples that are based on the optical signal;
wherein the processor component obtains the four samples from the output signal from the sensor array within the same instance of the period T pgc .
19. The apparatus of claim 16 , wherein the plurality of samples comprise samples S 0 , S 1 , S 2 , and S 3 ;
wherein the processor component calculates the in-phase term I:
I =( S 0 +S 2 )−( S 1 +S 3 );
wherein the processor component calculates the quadrature term Q:
Q =−( S 0 −S 2 );
wherein the processor component calculates the phase angle φ:
φ=arctangent( Q/I ).
20. The apparatus of claim 19 ,
wherein the processor component calculates the peak value Q p :
Q p ( M , β)=2 ·B ·sin( M ·sin β)
21. The apparatus of claim 20 , wherein the processor component employs the peak value I p and the peak value Q p to calculate the operating point that comprises a modulation depth approximately equal to 2.75 radians.
22. The apparatus of claim 21 , wherein the processor component employs the peak value I p and the peak value Q p to calculate the operating point that comprises a demodulation phase offset approximately equal to 0.5073 radians.
23. The apparatus of claim 16 , wherein the plurality of samples comprise samples S 0 , S 1 , S 2 , and S 3 ;
wherein the processor component calculates the in-phase term I:
I =( S 0 +S 2 )−(S 1 +S 3 );
wherein the processor component calculates the quadrature term Q:
Q =−2·( S 0 −S 2 );
wherein the processor component calculates the phase angle φ:
φ=arctangent ( Q/I ).
24. The apparatus of claim 23 ,
wherein the processor component calculates the peak value Q p :
Q p ( M , β)=4 ·B ·sin( M ·sin β).
25. The apparatus of claim 24 , wherein the processor component employs the peak value I p and the peak value Q p to calculate the operating point that comprises a modulation depth approximately equal to 2.49 radians.
26. The apparatus of claim 25 wherein the processor component employs the peak value I p and the peak value Q p to calculate the operating point that comprises a demodulation phase offset approximately equal to 0.3218 radians.
27. 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, the article comprising:
one or more computer-readable signal-bearing media;
means in the one or more media for calculating a quadrature term Q through employment of one or more of the plurality of samples that are based on the optical signal;
means in the one or more media for calculating an in-phase term I through employment of one or more of a plurality of samples that are based on the optical signal;
means in the one or more media for calculating a peak value I p of the in-phase term I as
I
p
(
M
,
β
)
=
2
·
B
·
(
cos
(
M
·
sin
β
)
-
cos
(
M
·
sin
(
π
2
+
β
)
)
)
,
wherein M is a modulation depth and β is a demodulation phase offset of the phase generated carrier;
means in the one or more media for calculating peak value Q p of the quadrature term Q;
means in the one or more media for calculating an operating point that comprises the modulation depth M and the demodulation phase offset β of the phase generated carrier through employment of the peak value I p of the in-phase term I and the peak value Q p of the quadrature term Q; and
means in the one or more media for calculating the phase angle φ through employment of the quadrature term Q and the in-phase term I, wherein the quadrature term Q and the in-phase term I are based on the optical signal.
28. The article of claim 27 , wherein the plurality of samples comprise samples S 0 , S 1 , S 2 , and S 3 , wherein the means in the one or more media for calculating the quadrature term Q through employment of the one or more of the plurality of samples that are based on the optical signal comprises:
means in the one or more media for calculating the quadrature term Q:
Q =−( S 0 −S 2 );
wherein the means in the one or more media for calculating the peak value Q p of the quadrature term Q comprises:
means in the one or more media for calculating the peak value Q p of the quadrature term Q:
Q p ( M , β)=2 ·B ·sin( M ·sin β).
29. The article of claim 28 , wherein the plurality of samples comprise samples S 0 , S 1 , S 2 , and S 3 , wherein the means in the one or more media for calculating the quadrature term Q through employment of the one or more of the plurality of samples that are based on the optical signal comprises:
means in the one or more media for calculating the quadrature term Q:
Q =−2*( S 0 −S 2 );
wherein the means in the one or more media for calculating the peak value Q p of the quadrature term Q comprises:
means in the one or more media for calculating the peak value Q p of the quadrature term Q:
Q p ( M , β)=4 ·B ·sin( M ·sin β).
30. The article of claim 27 , wherein the means in the one or more media for calculating the phase angle φ through employment of the in-phase term I and the quadrature term Q comprises:
means in the one or more media for calculating the phase angle φ=arctangent(Q/I) at the operating point.
31. The method of claim 4 , wherein the step of sampling the output signal from the sensor array to obtain the plurality of samples from the same instance of the period T pgc comprises the step of:
sampling the output signal from the sensor array to obtain four samples from the same instance of the period T pgc .
32. The method of claim 8 , wherein the step of sampling the output signal from the sensor array to obtain the plurality of samples from the same instance of the period T pgc comprise the step of:
sampling the output signal from the sensor array to obtain four samples from the same instance of the period T pgc .