Ultrasound Physics & Instrumentation
4th Edition
Volume II
Companion Presentation
Frank R. Miele
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Volume II Outline
 Chapter 7: Doppler
 Level 1
 Level 2
 Chapter 8: Artifacts
 Chapter 9: Bioeffects
 Chapter 10: Contrast and Harmonics
 Chapter 11: Quality Assurance
 Chapter 12: Fluid Dynamics
 Chapter 13: Hemodynamics
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Chapter 7: Doppler - Level 1
Level 1 focuses on:
 Developing a basic understanding of the Doppler Effect
 Developing a simplified form of the Doppler equation
Level 2 focuses on completing the Doppler equation, understanding
scattering from red blood cells, understanding the Doppler angle and
angle effects, the Doppler block diagram, Doppler processing, effects
of wall filters, PW vs. CW Doppler, range ambiguity, HPRF Doppler,
and color Doppler.
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Applications of the Doppler Effect
The Doppler effect has been employed for many different applications.
One of the most prevalent applications is radar. The Doppler effect has
been used with radar techniques to determine the velocity of moving
objects such as airplanes, automobiles, boats, trains, and even storm
systems.
The same Doppler principles have also been employed in the medical
field. This application has benefited from years of radar applications
including advances designed to overcome limitations and artifacts.
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The Doppler Effect
The Doppler Effect is an apparent change in frequency as a result of a
change in wavelength caused by motion of a wave source relative to an
observer.
To demonstrate how the change in wavelength occurs we will consider
what happens to a wave as it propagates over time. First we will
consider the wave emanating from a stationary train. Then we will
consider the wave as it emanates from a moving train. Finally, we will
consider what happens to the same emanating wave if the train’s
velocity is increased. From these three examples, we will appreciate
how the Doppler shift occurs.
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Stationary Train and Wavelength
Notice how the sound
propagates over time
creating uniform,
concentric circles as
the wave propagates
away from the
stationary source.
Both Observer A and
Observer B hear the
same pitch whistle - as
would be expected.
Fig. 1: (Pg 520)
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Stationary Plane (Animation)
(Pg 520)
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Moving Train and Change in Wavelength
Notice how the sound
propagating from the
moving source results
in a compression of the
wavefronts towards
Observer B and a
decompression of the
wavefronts relative to
Observer A. Therefore,
Observer A hears a
lower pitch than the
transmitted wave and
Observer B hears a
higher pitch than the
transmitted wave.
Fig. 2: (Pg 521)
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Moving Plane (Animation)
(Pg 521)
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Fast Moving Train and Greater Change in
Wavelength
Now notice that the
compression and
decompression effect
(the Doppler Effect) is
increased by a faster
moving train. This fact
implies that the Doppler
shifted frequency (fDop)
is related to the velocity
(v) of the train. As the
velocity increases, the
Doppler shift increases.
Fig. 3: (Pg 522)
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Fast Moving Plane (Animation)
(Pg 522)
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Doppler Shift and Velocity
From the animations, we saw that the Doppler shift increased with
increasing velocity. Mathematically, this relationship is expressed as:
f Dop  v
Where:
f Dop  Doppler shifted frequency
v  velocity of the sound source
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Doppler Shift (a change in frequency)
The Doppler shift is really a difference in frequency between the
frequency that was transmitted and the frequency that was received.
f Dop  fdetected - f transmitted  f
If the detected frequency is lower than the transmitted frequency, the
Doppler shift is negative. If the detected frequency is higher than the
transmitted frequency, the Doppler shift is positive.
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The Doppler Shift (Examples)
As just discussed, the Doppler shift fDop is relative to the transmit
frequency.
If the transmit frequency is 2.0 MHz: a received frequency of:
 2.001 MHz  fDop = 2.001 MHz – 2.000 MHz = + 0.001 MHz = +1 kHz
 1.999 MHz  fDop = 1.999 MHz – 2.000 MHz = - 0.001 MHz = -1 kHz
What is the Doppler shift (fDop) if the transmit frequency is 5.0 MHz
when the received frequency is:
 5.003 MHz  fDop = 5.003 MHz – 5.000 MHz = + 0.003 MHz = +3 kHz
 4.998 MHz  fDop = 4.998 MHz – 5.000 MHz = - 0.002 MHz = -2 kHz
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Doppler Shift and the Wavelength
We showed that the Doppler shift is caused by a change of wavelength
caused by motion relative to the observer. Since the wavelength is
determined by both the frequency and the propagation velocity, we
know that the Doppler equation will be effected by changes in both
frequency and propagation velocity.
c

f
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Effect of Frequency on Doppler Effect
As shown in the figure below, if the wavelength is 10 meters for a transmit
frequency of “f”, then the wavelength would be 5 meters for a transmitted
frequency of “2f” (frequency and wavelength are inversely related). Now
imagine if the train moved one meter. Clearly one meter relative to 5 meters is a
greater percentage than 1 meter relative to 10 meters.
Hence, as the frequency increases, the Doppler Effect also increases.
Fig. 4: (Pg 526)
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Doppler Shift and Operating Frequency
As just shown in the previous slide, as the frequency increases, the
Doppler shift increases:
f Dop  fo
Where:
f Dop  Doppler shifted frequency
f o  Transmitted frequency (Operating Frequency)
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Effect of Propagation Velocity on Doppler
Effect
As shown in the figure below, if the wavelength is 5 meters for a propagation
velocity of “c”, then the wavelength would be 10 meters for a propagation velocity
of “2c” (propagation velocity and wavelength are directly related). Now imagine if
the train moved one meter. Clearly one meter relative to 5 meters is a greater
percentage than 1 meter relative to 10 meters.
Hence, as the propagation velocity increases, the Doppler Effect decreases.
Fig. 5: (Pg 527)
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Doppler Shift and Propagation Velocity
As just shown in the previous slide, as the propagation velocity
increases, the Doppler shift decreases:
1
f Dop 
c
Where:
f Dop  Doppler shifted frequency
c  Propagation velocity of the wave in the medium
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Simplified Doppler Equation
If we combine the three relationships we have just seen into one
equation, we achieve the simplified form of the Doppler equation:
f Dop
2 fov

c
Note that the additional constant factor of 2. The factor of 2 can be
considered to account for the roundtrip effect.
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