Fundamentals of UltrasonicsFundamentals of Ultrasonics

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

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

UltrasonicsUltrasonics

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

Advantages:

•US can direct as a beam. •It obeys the laws of reflection and refraction. •It is reflected by objects of small sizeDisadvantages:

•It propagates poorly through a gaseous medium. •The amount of US reflected depends on the acoustic mismatch.

1. Characteristics of Sound1. Characteristics of SoundFrequencyFrequency

• 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.

Material Speed of Propagation

bone 4080 m/s

blood 1570 m/s

tissue 1540 m/s

fat 1450 m/s

air 330 m/s

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 < 15 Hz Audible sound ~ 15 Hz - 20 kHz Ultrasound > 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

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

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)

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

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

2. Interactions of Ultrasound with MatterReflectionSound 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)/(Z1+Z2)2

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), Snell’s law; for small ≤ 15o: t = i * (c2/c1) When c2 > c1, t > i , When c1 > c2, t < i Ultrasound machines assume straight line propagation, and refraction effects give rise to artifacts

c.f. Bushberg, et al. c.f. Bushberg, et al. The Essential Physics The Essential Physics of Medical Imaging, 2of Medical Imaging, 2ndnd ed., p. 478.ed., p. 478.

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. c.f. Bushberg, et al. The Essential Physics The Essential Physics of Medical Imaging, of Medical Imaging, 22ndnd ed., p. 480. ed., p. 480.

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

AttenuationAttenuation

• 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, Young’s modulus, etc.

• Attenuation coefficient: A=A0e-x

)(ln

0nepers

A

A

)(log200

10 dBA

A

Types of AttenuationTypes 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.

DiffractionDiffraction

• 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:

4

2Dd

4

2Dd

D

2.1

Acoustic ImpedanceAcoustic Impedance

• Definition: the resistance offered to the propagation of the ultrasonic wave in a material, Z=U. Depend on material properties only.

Reflection-Normal IncidentReflection-Normal Incident

• Reflection coefficient:

• Transmission coefficient:

2

12

122

1122

1122

ZZ

ZZ

UU

UU

I

I

i

rr

ri

TT

ZZ

ZZ

UU

UU

I

I

1

442

12

212

1122

2211

Reflection-Oblique IncidentReflection-Oblique Incident

• Snell’s Law:

• Reflection coefficient:

• Transmission coefficient:

B

A

r

i

U

U

sin

sin

2

22221

2

22221

2

sin//sin1

sin//sin1

iBAi

iBAir

UU

UU

2

22221

2

22221

sin//sin1

sin//4

iBAi

iBAt

UU

UU

Total Refraction AngleTotal Refraction Angle

222

22

21

)(arcsin

21A

rU

ZZ

Surface Skimmed Bulk WaveSurface Skimmed Bulk Wave

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

ResonanceResonance

Quality factor

f

f

ff

f

CyclePerDissipatedEnergy

CyclePerSuppliedEnergyQ rr

12

Typical Ultrasound Inspection SystemTypical Ultrasound Inspection System

•Transducer: convert electric signal to ultrasound signal

•Sensor: convert ultrasound signal to electric signal

Types of TransducersTypes of Transducers

• Piezoelectric

• Laser

• Mechanical (Galton Whistle Method)

• Electrostatic

• Electrodynamic

• Magnetostrictive

• Electromagnetic

What is Piezoelectricity?What is Piezoelectricity?

• Piezoelectricity means “pressure electricity”, which is used to describe the coupling between a material’s 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.

Quartz CrystalsQuartz Crystals

• Highly anisotropic• X-cut: vibration in the direction perpendicular to the

cutting direction• Y-cut: vibration in the transverse direction

Piezoelectric MaterialsPiezoelectric 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

Piezoelectric MaterialsPiezoelectric 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

Piezoelectric PropertiesPiezoelectric 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.

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.

orAppliedEnergy Electrical

StoredEnergy Mechanicalk

AppliedEnergy Mechanical

StoredEnergy Electricalk

Piezoelectric PropertiesPiezoelectric 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

Field Electric Applied

tDevelopmenStrain d

j

iij V

xd

Piezoelectric PropertiesPiezoelectric 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

Stress Mechanical Applied

Field ElectricCircuit Open g

SMART Layer for Structural Health SMART Layer for Structural Health MonitoringMonitoring

• 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.

Piezoelectric Wafer-active SensorPiezoelectric 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

Comparison of different PZ materials for Comparison of different PZ materials for Actuation and SensingActuation and Sensing

Thickness Selection of a PZ transducerThickness 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

Different Types of PZ TransducerDifferent Types of PZ Transducer

Normal beam transducer Dual element transducer

Angle beam transducerFocus beam transducer

Characterization of Ultrasonic BeamCharacterization 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

Beam Profile vs. DistanceBeam Profile vs. Distance

Beam profile vs. distance

Intensity vs. distance