Estimating propagation velocity through a surface acoustic wave sensor
Techniques are described for estimating the propagation velocity through a surface acoustic wave sensor. In particular, techniques which measure and exploit a proper segment of phase frequency response of the surface acoustic wave sensor are described for use as a basis of bacterial detection by the sensor. As described, use of velocity estimation based on a proper segment of phase frequency response has advantages over conventional techniques that use phase shift as the basis for detection.
1. A method comprising:
bringing a fluid into contact with the surface of a surface acoustic wave sensor;
propagating input waves through the surface acoustic wave sensor to produce transmitted waves;
determining a phase frequency response of the transmitted waves; identifying a segment of phase frequency response by determining first and second phase inflection frequencies, at +180 and −180 degree phase points, proximate to a running frequency associated with the surface acoustic wave sensor;
estimating a time delay associated with wave propagation through the surface acoustic wave sensor based on the identified segment of phase frequency response;
identifying a material in the fluid as a function of an estimated propagation velocity, the estimated propagation velocity being estimated based on the estimated time delay.
2. The method of claim 1 , wherein the surface acoustic wave sensor comprises a Love mode shear-horizontal surface acoustic wave sensor.
3. The method of claim 1 , wherein determining phase inflection frequencies comprises:
sampling a plurality of phase responses at frequencies proximate to the running frequency and initially estimating phase inflection frequencies as a function of the plurality of phase responses at frequencies proximate to the running frequency;
sampling a plurality of phase responses at frequencies proximate to the initially estimated phase inflection frequencies; and
more accurately estimating the phase inflection frequencies as a function of the plurality of phase responses at frequencies proximate to the initially estimated phase inflection frequencies.
4. The method of claim 1 , wherein the first and second phase inflection frequencies define edges of a monotonically changing subset of a graph of phase versus frequency of the surface acoustic wave sensor.
5. The method of claim 1 further comprising:
estimating the time delay associated with wave propagation through the surface acoustic wave sensor based on the identified segment of phase frequency response according to approximately the following equation:
τ
^
(
f
0
)
=
f
1
f
0
1
f
2
-
f
1
-
1
360
ϕ
(
f
0
)
f
0
+
0.5
f
0
where {circumflex over (τ)}(f 0 ) is the time delay at frequency f 0 , f 0 is the running frequency, f 1 is the first phase inflection frequency, f 2 , is the second phase inflection frequency, and φ(f 0 ) is a measured phase response of the surface acoustic wave sensor at frequency f 0 .
6. The method of claim 1 , further comprising estimating the time delay according to approximately the following equation:
τ
^
(
f
0
)
=
-
1
360
f
*
f
0
ϕ
.
(
f
*
)
-
1
360
1
f
0
ϕ
(
f
0
)
+
1
360
1
f
0
ϕ
(
f
*
)
where {circumflex over (τ)}(f 0 ) is the time delay, f 0 is the running frequency, φ(f 0 ) is a measured phase response of the surface acoustic wave sensor, f * is any frequency between a first phase inflection frequency and a second phase inflection frequency, φ(f * ) is a measured phase frequency response at the frequency f * , and {dot over (φ)}(f * ) is a first order of derivative of the measured phase response at the frequency f * .
7. The method of claim 1 , further comprising estimating the time delay according to approximately the following equation:
τ
^
=
(
f
0
)
=
-
1
360
ϕ
.
(
f
0
)
where {circumflex over (τ)}(f 0 ) is the time delay, and {dot over (φ)}(f 0 ) is a first order of derivative of a measured phase response at a frequency f 0 .
8. The method of claim 1 , further comprising estimating the time delay according to approximately the following equation:
τ
^
(
f
0
)
=
1
f
0
f
1
f
2
-
f
1
-
1
360
1
f
0
ϕ
(
f
0
)
+
0.5
f
0
+
1
180
1
f
0
1
f
2
-
f
1
∫
f
1
f
2
ϕ
(
f
00
)
ⅆ
f
00
where {circumflex over (τ)}(f 0 ) is the time delay, f 0 is the running frequency, f 1 is the first phase inflection frequency, f 2 is the second phase inflection frequency, and φ(f 0 ) is a measured phase response of the surface acoustic wave sensor, integral
∫
f
1
f
2
ϕ
(
f
00
)
ⅆ
f
00
is equal to integral
∫
f
1
f
2
ϕ
(
f
)
ⅆ
f
,
where φ(f) is a measured phase response at frequency f and f varies from f 1 to f 2 .
9. The method of claim 1 , further comprising estimating the propagation velocity of a surface acoustic wave through the surface acoustic wave sensor from the estimated time delay according to the following equation:
v
^
(
f
)
=
L
τ
^
(
f
)
,
where {circumflex over (v)}(f) is the estimated propagation velocity of the surface acoustic wave at frequency f, {circumflex over (τ)}(f) is the estimated time delay at the frequency f, and L is a distance between centers of an input inter-digitized transducer (IDT) and an output IDT which are part of the surface acoustic wave sensor.
10. A computer-readable medium comprising instructions that when executed in a processor:
determine phase frequency response of transmitted waves of a surface acoustic wave sensor;
identify a segment of phase frequency response of the surface acoustic wave sensor by determining first and second phase inflection frequencies proximate to a running frequency associated with the surface acoustic wave sensor;
estimate a time delay associated with wave propagation through the surface acoustic wave sensor based on the identified frequency response according to approximately the following equation:
τ
^
(
f
0
)
=
f
1
f
0
1
f
2
-
f
1
-
1
360
ϕ
(
f
0
)
f
0
+
0.5
f
0
where {circumflex over (τ)}(f 0 ) is the time delay at frequency f 0 , f 0 is the running frequency, f 1 is the first phase inflection frequency, f 2 is the second phase inflection frequency, and φ(f 0 ) is a measured phase response of the surface acoustic wave sensor at the running frequency f 0 ; and
identify a concentration of a material in a fluid as a function of an estimated propagation velocity that is based on the estimated time delay.
11. The computer-readable medium of claim 10 , further comprising instructions that when executed determine phase inflection frequencies for a discrete phase frequency response by:
sampling a plurality of phase responses at frequencies proximate to the running frequency and initially estimating phase inflection frequencies as a function of the plurality of phase responses at frequencies proximate to the running frequency; sampling a plurality of phase responses at frequencies proximate to the initially estimated phase inflection frequencies; and
more accurately estimating phase inflection frequencies as a function of the plurality of phase responses at frequencies proximate to the initially estimated phase inflection frequencies.
12. The computer-readable medium of claim 10 , wherein the first and second phase inflection frequencies define edges of a monotonically changing subset of a graph of phase versus frequency of the surface acoustic wave sensor.
13. The computer-readable medium of claim 10 , further comprising instructions that when executed estimate a propagation velocity of the surface acoustic wave from the estimated time delay according to the following equation:
v
^
(
f
)
=
L
τ
^
(
f
)
,
where {circumflex over (v)}(f) is the estimated propagation velocity of the surface acoustic wave at frequency f, {circumflex over (τ)}(f) is the estimated time delay at frequency f, and L is a distance between centers of an input inter-digitized transducer IDT and an output IDT which are part of the surface acoustic wave sensor.
14. The computer-readable medium of claim 10 , wherein the surface acoustic wave sensor comprises a Love mode shear-horizontal surface acoustic wave sensor.
15. A system comprising:
a surface acoustic wave sensor;
a sensor analyzer to receive output of the surface acoustic wave sensor and determine a phase frequency response from the output; and
a processor to receive input from the sensor analyzer, identify a segment of phase frequency response of the surface acoustic wave sensor by determining first and second phase inflection frequencies proximate to a running frequency associated with the surface acoustic wave sensor, estimate a time delay associated with wave propagation through the surface acoustic wave sensor based on the identified segment of phase frequency response according to approximately the following equation:
τ
^
(
f
0
)
=
f
1
f
0
1
f
2
-
f
1
-
1
360
ϕ
(
f
0
)
f
0
+
0.5
f
0
where {circumflex over (τ)}(f 0 ) is the time delay at frequency f 0 , f 0 is the running frequency, f 1 is the first phase inflection frequency, f 2 is the second phase inflection frequency, and φ(f 0 ) is a measured phase response of the surface acoustic wave sensor at the running frequency f 0 , estimate a propagation velocity of the surface acoustic wave based on the estimated time delay, and identify a concentration of a material in a fluid as a function of the estimated propagation velocity.
16. The system of claim 15 wherein the processor determines the phase inflection frequencies by:
sampling a plurality of phase responses at frequencies proximate to the running frequency and initially estimating the phase inflection frequencies as a function of the plurality of phase responses at frequencies proximate to the running frequency;
sampling a plurality of phase responses at frequencies proximate to the initially estimated phase inflection frequencies; and
more accurately estimating the phase inflection frequencies as a function of the plurality of phase responses at frequencies proximate to the initially estimated phase inflection frequencies.
17. The system of claim 15 wherein the first and second phase inflection frequencies define edges of a monotonically changing subset of a graph of phase versus frequency of the surface acoustic wave sensor.
18. The system of claim 15 , wherein the processor estimates propagation velocity of the surface acoustic wave based on the estimated time delay according to the following equation:
v
^
(
f
)
=
L
τ
^
(
f
)
,
where {circumflex over (v)}(f) is an estimated propagation velocity of the surface acoustic wave at a frequency f, {circumflex over (τ)}(f) is the estimated time delay at the frequency f, and L is a distance between centers of an input inter-digitized transducer IDT and an output IDT which are part of the surface acoustic wave sensor.
19. The system of claim 15 , wherein the surface acoustic wave sensor comprises a Love mode shear-horizontal surface acoustic wave sensor.