Fundamentals of Ultrasonics

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Fundamentals of Ultrasonics
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Introduction
Ultrasound is a non-ionizing method which uses
sound waves of frequencies (20 to 10 MHz)
exceeding the range of human hearing for imaging
Medical diagnostic ultrasound uses ultrasound
energy and the acoustic properties of the body to
produce an image from stationary and moving
tissues Ultrasound is used in pulse-echo
format, whereby pulses of ultrasound produced
over a very brief duration travel through various
tissues and are reflected at tissue boundaries
back to the source
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Introduction

• Returning echoes carry the ultrasound information
  that is used to create the sonogram or measure
  blood velocities with Doppler frequency
  techniques
• Along a given beam path, the depth of an
  echo-producing structure is determined from the
  time between the pulse-emission and the echo
  return, and the amplitude of the echo is encoded
  as a gray-scale value
• In addition to 2D imaging, ultrasound provides
  anatomic distance and volume measurements, motion
  studies, blood velocity measurements, and 3D
  imaging

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Ultrasonics

• Definition the science and exploitation of
  elastic waves in solids, liquids, and gases,
  which have a frequency above 20KHz.
• -Sound with frequency greater than 20,000 cycles
  per second or 20kHz.
• Frequency range 20KHz-10MHz
• Applications
• Medical diagnosis
• Material characterization
• Range finding

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• Advantages
• US can direct as a beam.
• It obeys the laws of reflection and refraction.
• It is reflected by objects of small size
• Disadvantages
• It propagates poorly through a gaseous medium.
• The amount of US reflected depends on the
  acoustic mismatch.

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1. Characteristics of SoundFrequency
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• Cycle - the combination of one rarefaction and
  one compression equals one cycle.
• Wavelength - the distance between the onset of
  peak compression or cycle to the next.
• Velocity - the velocity is the speed at which
  sound waves travel through a particular medium.
  Velocity is equal to the frequency x wavelength.
• The velocity of US through human soft tissue is
  1540 meters per second.
• Frequency - the number of cycles per unit of
  time. Frequency and wavelength are inversely
  related. The higher the frequency the smaller the
  wavelength.

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Material Speed of Propagation
bone 4080 m/s
blood 1570 m/s
tissue 1540 m/s
fat 1450 m/s
air 330 m/s
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1. Characteristics of Sound Frequency
Frequency (f) is the number of times the wave
oscillates through a cycle each second
(sec) (Hertz Hz or cycles/sec) Infra sound lt 15
Hz Audible sound 15 Hz - 20 kHz Ultrasound gt
20 kHz for medical usage typically 2-10 MHz with
specialized ultrasound applications up to 50 MHz
period (?) - the time duration of one wave
cycle ? 1/f
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1. Characteristics of Sound Speed
The speed or velocity of sound is the distance
travelled by the wave per unit time and is equal
to the wavelength divided by the period (1/f)
speed wavelength / period speed wavelength
x frequency c ?f c m/sec ? m f
1/sec Speed of sound is dependent on the
propagation medium and varies widely in different
materials
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2. Interactions of Ultrasound with Matter
Ultrasound interactions are determined by the
acoustic properties of matter As ultrasound
energy propagates through a medium, interactions
that occur include reflection refraction
scattering Absorption (attenuation)
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2. Interactions of Ultrasound with
MatterAcoustic Impedance

• Acoustic Impedance, Z
• is equal to density of the material times speed
  of sound in the material in which ultrasound
  travels, Z ? c
• ? density (kg/m3) and c speed of sound
  (m/sec)
• measured in (kg/m2sec)
• Air and lung media have low values of Z, whereas
  bone and metal have high values
• Large differences in Z (air-filled lung and soft
  tissue) cause reflection, small differences allow
  transmission of sound energy
• The differences between acoustic impedance values
  at an interface determines the amount of energy
  reflected at the interface

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2. Interactions of Ultrasound with
MatterReflection

• A portion of the ultrasound beam is reflected at
  tissue interface
• The sound reflected back toward the source is
  called an echo and is used to generate the
  ultrasound image
• The percentage of ultrasound intensity reflected
  depends in part on the angle of incidence of the
  beam
• As the angle of incidence increases, reflected
  sound is less likely to reach the transducer

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2. Interactions of Ultrasound with
MatterReflection

• Sound reflection occurs at tissue boundaries with
  differences in acoustic impedance
• The intensity reflection coefficient, R Ir/Ii
  ((Z2 Z1)/(Z2 Z1))2
• The subscripts 1 and 2 represent tissues proximal
  and distal to the boundary.
• Equation only applies to normal incidence
• The transmission coefficient T 1 R
• T (4Z1Z2)/(Z1Z2)2

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2. Interactions of Ultrasound with
MatterRefraction
Refraction is the change in direction of an
ultrasound beam when passing from one medium to
another with a different acoustic velocity
Wavelength changes causing a change in
propagation direction (c ?f) sin(?t) sin(?i)
(c2/c1), Snells law for small ? 15o ?t
?i (c2/c1) When c2 gt c1, ?t gt ?i , When c1 gt
c2, ?t lt ?i Ultrasound machines assume straight
line propagation, and refraction effects give
rise to artifacts
c.f. Bushberg, et al. The Essential Physics of
Medical Imaging, 2nd ed., p. 478.
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2. Interactions of Ultrasound with Matter Scatter
Acoustic scattering arises from objects within a
tissue that are about the size of the wavelength
of the incident beam or smaller, and represent a
rough or nonspecular reflector surface As
frequency increases, the non-specular (diffuse
scatter) interactions increase, resulting in an
increased attenuation and loss of echo intensity
Scatter gives rise to the characteristic speckle
patterns of various organs, and is important in
contributing to the grayscale range in the image
c.f. Bushberg, et al. The Essential Physics of
Medical Imaging, 2nd ed., p. 480.
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2. Interactions of Ultrasound with Matter
Attenuation
Ultrasound attenuation, the loss of energy with
distance traveled, is caused chiefly by
scattering and tissue absorption of the incident
beam (dB) The intensity loss per unit distance
(dB/cm) is the attenuation coefficient Rule of
thumb attenuation in soft tissue is approx. 1
dB/cm/MHz The attenuation coefficient is
directly proportional to and increases with
frequency Attenuation is medium dependent
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Attenuation

• Definition the rate of decrease of energy when
  an ultrasonic wave is propagating in a medium.
  Material attenuation depends on heat treatments,
  grain size, viscous friction, crystal structure,
  porosity, elastic hysterisis, hardness, Youngs
  modulus, etc.
• Attenuation coefficient AA0e-ax

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Types of Attenuation

• Scattering scattering in an inhomogeneous medium
  is due to the change in acoustic impedance by the
  presence of grain boundaries inclusions or pores,
  grain size, etc.
• Absorption heating of materials, dislocation
  damping, magnetic hysterisis.
• Dispersion frequency dependence of propagation
  speed
• Transmission loss surface roughness coupling
  medium.

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Diffraction

• Definition spreading of energy into high and low
  energy bands due to the superposition of plane
  wave front.
• Near Field
• Far Field
• Beam spreading angle

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Acoustic Impedance

• Definition the resistance offered to the
  propagation of the ultrasonic wave in a material,
  ZrU. Depend on material properties only.

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Reflection-Normal Incident

• Reflection coefficient
• Transmission coefficient

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Reflection-Oblique Incident

• Snells Law
• Reflection coefficient
• Transmission coefficient

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Total Refraction Angle
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Surface Skimmed Bulk Wave

• The refracted wave travels along the surface of
  both media and at the sub-surface of media B

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Resonance
Quality factor
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Typical Ultrasound Inspection System

• Transducer convert electric signal to ultrasound
  signal
• Sensor convert ultrasound signal to electric
  signal

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Types of Transducers

• Piezoelectric
• Laser
• Mechanical (Galton Whistle Method)
• Electrostatic
• Electrodynamic
• Magnetostrictive
• Electromagnetic

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What is Piezoelectricity?

• Piezoelectricity means pressure electricity,
  which is used to describe the coupling between a
  materials mechanical and electrical behaviors.
• Piezoelectric Effect
• when a piezoelectric material is squeezed or
  stretched, electric charge is generated on its
  surface.
• Inverse Piezoelectric Effect
• Conversely, when subjected to a electric voltage
  input, a piezoelectric material mechanically
  deforms.

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Quartz Crystals

• Highly anisotropic
• X-cut vibration in the direction perpendicular
  to the cutting direction
• Y-cut vibration in the transverse direction

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Piezoelectric Materials

• Piezoelectric Ceramics (man-made materials)
• Barium Titanate (BaTiO3)
• Lead Titanate Zirconate (PbZrTiO3) PZT, most
  widely used
• The composition, shape, and dimensions of a
  piezoelectric ceramic element can be tailored to
  meet the requirements of a specific purpose.

Photo courtesy of MSI, MA
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Piezoelectric Materials

• Piezoelectric Polymers
• PVDF (Polyvinylidene flouride) film
• Piezoelectric Composites
• A combination of piezoelectric ceramics and
  polymers to attain properties which can be not be
  achieved in a single phase

Image courtesy of MSI, MA
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Piezoelectric Properties

• Anisotropic
• Notation direction X, Y, or Z is represented by
  the subscript 1, 2, or 3, respectively, and shear
  about one of these axes is represented by the
  subscript 4, 5, or 6, respectively.

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Piezoelectric Properties

• The electromechanical coupling coefficient, k, is
  an indicator of the effectiveness with which a
  piezoelectric material converts electrical energy
  into mechanical energy, or vice versa.
• kxy, The first subscript (x) to k denotes the
  direction along which the electrodes are applied
  the second subscript (y) denotes the direction
  along which the mechanical energy is developed.
  This holds true for other piezoelectric constants
  discussed later.
• Typical k values varies from 0.3 to 0.75 for
  piezoelectric ceramics.

or
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Piezoelectric Properties

• The piezoelectric charge constant, d, relates the
  mechanical strain produced by an applied electric
  field,
• Because the strain induced in a piezoelectric
  material by an applied electric field is the
  product of the value for the electric field and
  the value for d, d is an important indicator of a
  material's suitability for strain-dependent
  (actuator) applications.
• The unit is Meters/Volt, or Coulombs/Newton

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Piezoelectric Properties

• The piezoelectric constants relating the electric
  field produced by a mechanical stress are termed
  the piezoelectric voltage constant, g,
• Because the strength of the induced electric
  field in response to an applied stress is the
  product of the applied stress and g, g is
  important for assessing a material's suitability
  for sensor applications.
• The unit of g is volt meters per Newton

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SMART Layer for Structural Health Monitoring

• Smart layer is a think dielectric film with
  built-in piezoelectric sensor networks for
  monitoring of the integrity of composite and
  metal structures developed by Prof. F.K. Chang
  and commercialized by the Acellent Technology,
  Inc. The embedded sensor network are comprised of
  distributed piezoelectric actuators and sensors.

Image courtesy of FK Chang, Stanford Univ.
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Piezoelectric Wafer-active Sensor

• Read paper
• Embedded Non-destructive Evaluation for
  Structural Health Monitoring, Damage Detection,
  and Failure Prevention by V. Giurgiutiu, The
  Shock and Vibration Digest 2005 37 83
• Embedded piezoelectric wafer-active sensors
  (PWAS) is capable of performing in-situ
  nondestructive evaluation (NDE) of structural
  components such as crack detection.

Image courtesy of V. Giurgiutiu, USC
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Comparison of different PZ materials for
Actuation and Sensing
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Thickness Selection of a PZ transducer

• Transducer is designed to vibrate around a
  fundamental frequency
• Thickness of a transducer element is equal to one
  half of a wavelength

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Different Types of PZ Transducer
Normal beam transducer
Dual element transducer
Angle beam transducer
Focus beam transducer
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Characterization of Ultrasonic Beam

• Beam profile or beam path
• Near field planar wave front
• Far field spherical wave front, intensity varies
  as the square of the distance
• Determination of beam spread angle
• Transducer beam profiling

Near field planar wave front
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Beam Profile vs. Distance
Beam profile vs. distance
Intensity vs. distance