Sensor array induced phase angle calculation based on mixed signals
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 based on a single frequency. The time-varying phase angle φ is calculated through employment of a plurality of samples obtained approximately at a time t s , where the plurality of samples are based on a plurality of mixed signals output from a mixer component that employs an input signal based on the optical signal of the sensory array.
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 based on a single frequency, the method comprising the step of:
calculating the time-varying phase angle φ through employment of a plurality of samples obtained approximately at a time t s , wherein the plurality of samples are based on a plurality of mixed signals output from a mixer component that employs an input signal based on the optical signal of the sensor array.
2. The method of claim 1 , wherein the step of calculating the time-varying phase angle φ through employment of the plurality of samples obtained approximately at the time t s comprises the steps of:
mixing the input signal with one or more sinusoidal signals to create the plurality of mixed signals;
filtering the plurality of mixed signals to create a plurality of filtered signals;
sampling the plurality of filtered signals at the time t s to obtain the plurality of samples; and
calculating the time-varying phase angle φ through employment of the plurality of samples.
3. The method of claim 2 , wherein the step of mixing the input signal with the one or more sinusoidal signals to create the plurality of mixed signals comprises the steps of:
mixing the input signal with a sinusoidal signal I s (t)=sin [4πf(t+t 0 )] to create a mixed signal M is (t, φ);
mixing the input signal with a sinusoidal signal I c (t)=cos [4πf(t+t 0 )] to create a mixed signal M ic (t, φ);
mixing the input signal with a sinusoidal signal Q s (t)=sin [2πf(t+t 0 )] to create a mixed signal M qs (t, φ); and
mixing the input signal with a sinusoidal signal Q c (t)=cos [2πf(t+t 0 )] to create a mixed signal M qc (t, φ).
4. The method of claim 2 , wherein the phase generated carrier comprises a modulation depth M, wherein the input signal comprises an interference term signal level B, wherein a function J 1 (M) comprises a first order Bessel function, wherein a function J 2 (M) comprises a second order Bessel function, wherein the step of filtering the plurality of mixed signals to create the plurality of filtered signals comprises the steps of:
filtering the mixed signal M is (t, φ) to create a filtered signal:
F
is
(
t
,
φ
)
=
∫
0
t
h
(
t
-
v
)
·
S
(
v
,
φ
)
·
I
s
(
v
)
·
env
(
v
)
·
ⅆ
v
;
filtering the mixed signal M ic (t, φ) to create a filtered signal:
F
ic
(
t
,
φ
)
=
∫
0
t
h
(
t
-
v
)
·
S
(
v
,
φ
)
·
I
c
(
v
)
·
env
(
v
)
·
ⅆ
v
;
filtering the mixed signal M qs (t, φ) to create a filtered signal:
F
qs
(
t
,
φ
)
=
∫
0
t
h
(
t
-
v
)
·
S
(
v
,
φ
)
·
Q
s
(
v
)
·
env
(
v
)
·
ⅆ
v
;
and
filtering the mixed signal M qc (t, φ) to create a filtered signal:
F
qc
(
t
,
φ
)
=
∫
0
t
h
(
t
-
v
)
·
S
(
v
,
φ
)
·
Q
c
(
v
)
·
env
(
v
)
·
ⅆ
v
.
5. The method of claim 4 , further comprising the steps of:
calculating an in-phase term:
I
mag
(
t
s
,
φ
)
=
F
ic
(
t
s
,
φ
)
2
+
F
i
s
(
t
s
,
φ
)
2
∝
cos
φ
;
calculating a quadrature term:
Q
mag
(
t
s
,
φ
)
=
F
qc
(
t
s
,
φ
)
2
+
F
qs
(
t
s
,
φ
)
2
∝
sin
φ
;
and
calculating the time-varying phase angle φ through employment of the in-phase term I mag (t s , φ) and the quadrature term Q mag (t s , φ).
6. The method of claim 5 , further comprising the steps of:
determining a sign of an in-phase term I(t, φ), wherein the in-phase term I(t, φ) comprises a magnitude equal to the in-phase term I mag (t, φ); and
determining a sign of a quadrature term Q(t, φ), wherein the quadrature term Q(t, φ) comprises a magnitude equal to the quadrature term Q mag (t, φ).
7. The method of claim 6 , wherein the step of determining the sign of the in-phase term I(t, φ) comprises the step of:
determining the sign of the in-phase term I(t, φ) to be equal to a sign of the filtered signal F ic (t, φ) or F is (t, φ) with a largest magnitude;
wherein the step of determining the sign of the quadrature term Q(t, φ) comprises the step of:
determining the sign of the quadrature term Q(t, φ) to be equal to a sign of the filtered signal F qc (t, φ) or F qs (t, φ) with a largest magnitude.
8. 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 based on a single frequency, the apparatus comprising:
a processor component that calculates the time-varying phase angle φ through employment of a plurality of samples obtained approximately at a time t s , wherein the plurality of samples are based on a plurality of mixed signals output from a mixer component that employs an input signal based on the optical signal of the sensor array.
9. The apparatus of claim 8 in combination with the mixer component,
wherein the mixer component mixes the input signal with one or more sinusoidal signals from an oscillator component to create the plurality of mixed signals;
wherein the mixer component sends the plurality of mixed signals through a filter component to create a plurality of filtered signals;
wherein the processor component calculates the time-varying phase angle φ through employment of the plurality of samples based on the plurality of filtered signals.
10. The apparatus of claim 9 , wherein the one or more sinusoidal signals comprise signals:
I s ( t )=sin [4 πf ( t+t 0 )], I c ( t )=cos [4 πf ( t+t 0 )]; and
Q s ( t )=sin [2 πf ( t+t 0 )], Q c ( t )=cos [2 πf ( t+t 0 )];
wherein the mixer component mixes the sinusoidal signals I s (t), I c (t), Q s (t), and Q c (t) with the input signal to create the plurality of mixed signals:
M is (t, φ), M ic (t, φ), M qs (t, φ), and M qc (t, φ).
11. The apparatus of claim 10 , wherein the phase generated carrier comprises a modulation depth M, wherein the input signal comprises an interference term signal level B, wherein a function J 1 (M) comprises a first order Bessel function, wherein a function J 2 (M) comprises a second order Bessel function;
wherein the mixer component sends the plurality of mixed signals M is (t, φ), M ic (t, φ), M qs (t, φ), and M qc (t, φ) through the filter component to create the plurality of filtered signals:
F
qs
(
t
,
φ
)
=
∫
0
t
h
(
t
-
v
)
·
S
(
v
,
φ
)
·
Q
s
(
v
)
·
env
(
v
)
·
ⅆ
v
,
F
qc
(
t
,
φ
)
=
∫
0
t
h
(
t
-
v
)
·
S
(
v
,
φ
)
·
Q
c
(
v
)
·
env
(
v
)
·
ⅆ
v
,
F
i
s
(
t
,
φ
)
=
∫
0
t
h
(
t
-
v
)
·
S
(
v
,
φ
)
·
I
s
(
v
)
·
env
(
v
)
·
ⅆ
v
,
and
F
i
c
(
t
,
φ
)
=
∫
0
t
h
(
t
-
v
)
·
S
(
v
,
φ
)
·
I
c
(
v
)
·
env
(
v
)
·
ⅆ
v
.
12. The apparatus of claim 11 in combination with the filter component, wherein the filter component comprises a Gaussian low-pass filter, a fourth order Bessel filter, or a fourth order real pole filter.
13. The apparatus of claim 11 , wherein the processor component employs the filtered signals F is and F ic to calculate an in-phase term:
I
mag
(
t
s
,
φ
)
=
F
i
c
(
t
s
,
φ
)
2
+
F
i
s
(
t
s
,
φ
)
2
∝
cos
φ
;
wherein the processor component calculates a quadrature term:
Q
mag
(
t
s
,
φ
)
=
F
q
c
(
t
s
,
φ
)
2
+
F
q
s
(
t
s
,
φ
)
2
∝
sin
φ
;
wherein the processor component employs the in-phase term I mag (t, φ) and the quadrature term Q mag (t, φ) to calculate the time-varying phase angle φ.
14. The apparatus of claim 13 , wherein the processor component employs the filtered signals F ic (t, φ) and F is (t, φ) to determine a sign of an in-phase term I(t, φ), wherein the in-phase term I(t, φ) comprises a magnitude equal to the in-phase term I mag (t, φ);
wherein the processor component employs the filtered signals F qs (t, φ) and F qc (t, φ) to determine a sign of a quadrature term Q(t, φ), wherein the quadrature term Q(t, φ) comprises a magnitude equal to the quadrature term Q mag (t, φ).
15. The apparatus of claim 14 , wherein the processor component determines the sign of the in-phase term I(t, φ) to be equal to a sign of the filtered signal F ic (t, φ) or F is (t, φ) with a largest magnitude;
wherein the processor component determines the sign of the quadrature term Q(t, φ) to be equal to a sign of the filtered signal F qc (t, φ) or F qs (t, φ) with a largest magnitude.
16. The apparatus of claim 15 , wherein the in-phase term I(t, φ) and the quadrature term Q(t, φ) comprise respective pulses centered near t s ;
wherein the processor component calculates the time-varying phase angle φ:
φ
=
arc
tan
(
Q
(
t
s
,
φ
)
I
(
t
s
,
φ
)
)
.
17. 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 based on a single frequency, the article comprising:
one or more computer-readable signal-bearing media; and
means in the one or more media for calculating the time-varying phase angle φ through employment of a plurality of samples obtained approximately at a time t s , wherein the plurality of samples are based on a plurality of mixed signals output from a mixer component that employs an input signal based on the optical signal of the sensor array.
18. The article of claim 17 , wherein the means in the one or more media for calculating the time-varying phase angle φ through employment of the plurality of samples obtained at the time t s comprises:
means in the one or more media for mixing the input signal with one or more sinusoidal signals to create the plurality of mixed signals;
means in the one or more media for filtering the plurality of mixed signals to create a plurality of filtered signals;
means in the one or more media for sampling the plurality of filtered signals to obtain the plurality of samples; and
means in the one or more media for calculating the time-varying phase angle φ through employment of the plurality of samples.
19. The article of claim 18 , wherein the means in the one or more media for mixing the input signal with the one or more sinusoidal signals to create the plurality of mixed signals comprises:
means in the one or more media for mixing the input signal with a sinusoidal signal I s (t)=sin [4πf(t+t 0 )] to create a mixed signal M is (t, φ);
means in the one or more media for mixing the input signal with a sinusoidal signal I c (t)=cos [4πf(t+t 0 )] to create a mixed signal M ic (t, φ);
means in the one or more media for mixing the input signal with a sinusoidal signal Q s (t)=sin [2πf(t+t 0 )] to create a mixed signal M qs (t, φ); and
means in the one or more media for mixing the input signal with a sinusoidal signal Q s (t)=cos [2πf(t+t 0 )] to create a mixed signal M qc (t, φ).
20. The article of claim 18 , wherein the phase generated carrier comprises a modulation depth M, wherein the input signal comprises an interference term signal level B, wherein a function J 1 (M) comprises a first order Bessel function, wherein a function J 2 (M) comprises a second order Bessel function, wherein the means in the one or more media for filtering the plurality of mixed signals to create the plurality of filtered signals comprises:
means in the one or more media for filtering the mixed signal M is (t, φ) to create a filtered signal
F
i
s
(
t
,
φ
)
=
∫
0
t
h
(
t
-
v
)
·
S
(
v
,
φ
)
·
I
s
(
v
)
·
env
(
v
)
·
ⅆ
v
;
means in the one or more media for filtering the mixed signal M ic (t, φ) to create a filtered signal
F
ic
(
t
,
φ
)
=
∫
0
t
h
(
t
-
v
)
·
S
(
v
,
φ
)
·
I
c
(
v
)
·
env
(
v
)
·
ⅆ
v
;
means in the one or more media for filtering the mixed signal M qs (t, φ) to create a filtered signal
F
qs
(
t
,
φ
)
=
∫
0
t
h
(
t
-
v
)
·
S
(
v
,
φ
)
·
Q
s
(
v
)
·
env
(
v
)
·
ⅆ
v
;
and
means in the one or more media for filtering the mixed signal M qc (t, φ) to create a filtered signal
F
qc
(
t
,
φ
)
=
∫
0
t
h
(
t
-
v
)
·
S
(
v
,
φ
)
·
Q
c
(
v
)
·
env
(
v
)
·
ⅆ
v
.
21. The article of claim 20 , further comprising:
means in the one or more media for calculating an in-phase term:
I
mag
(
t
s
,
φ
)
=
F
ic
(
t
s
,
φ
)
2
+
F
is
(
t
s
,
φ
)
2
∝
cos
φ
;
means in the one or more media for calculating a quadrature term:
Q
mag
(
t
s
,
φ
)
=
F
qc
(
t
s
,
φ
)
2
+
F
qs
(
t
s
,
φ
)
2
∝
sin
φ
;
and
means in the one or more media for calculating the time-varying phase angle φ through employment of the in-phase term I mag (t, φ) and the quadrature term Q mag (t, φ).
22. The article of claim 21 , further comprising:
means in the one or more media for determining a sign of an in-phase term I(t, φ) to be equal to a sign of the filtered signal F ic (t, φ) or F is (t, φ) with a largest magnitude; and
means in the one or more media for determining a sign of a quadrature term Q(t, φ) to be equal to a sign of the filtered signal F qc (t, φ) or F qs (t, φ) with a largest magnitude.