Pegasus Lectures, Inc. COPYRIGHT 2006 Volume I Companion Presentation Frank R. Miele Pegasus Lectures, Inc. Ultrasound Physics & Instrumentation 4 th Edition

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Pegasus Lectures, Inc. COPYRIGHT 2006 Volume I Outline  Chapter 1: Mathematics  Chapter 2: Waves  Chapter 3: Attenuation  Level 1  Level 2  Chapter 4: Pulsed Wave  Chapter 5: Transducers  Chapter 6: System Operation

Pegasus Lectures, Inc. COPYRIGHT 2006 Chapter 3: Attenuation - Level 1

Pegasus Lectures, Inc. COPYRIGHT 2006 Chapter 3: Attenuation Attenuation is a measure of how the medium affects the wave. Attenuation will be divided into three subtopics:  Absorption  Reflection  Refraction

Pegasus Lectures, Inc. COPYRIGHT 2006 Absorption is the conversion of sound energy into heat. There are two very important points about absorption:  Absorption is the dominant form of attenuation in soft tissue  Absorption increases exponentially with increasing frequency Absorption

Pegasus Lectures, Inc. COPYRIGHT 2006 Reflection Reflection is the mechanism which make diagnostic ultrasound work. We will divide reflection into two categories:  Geometric aspects and effects  Acoustic properties and mismatches of materials

Pegasus Lectures, Inc. COPYRIGHT 2006 Reflection – Geometric Aspects Reflection will vary depending on the surface of the reflecting surface.  Large, smooth and flat relative to the wavelength  Large but rough relative to the wavelength  Small relative to the wavelength

Pegasus Lectures, Inc. COPYRIGHT 2006 Defining Angles and Terminology Fig. 1: Measuring the Incident Angle (Pg 145) Before discussing the types of reflection, it is important to understand the terminology used and references for angle measurements.

Pegasus Lectures, Inc. COPYRIGHT 2006 Wave Direction and Wavefront Fig. 2: (Pg 145) Notice that the wave direction is always perpendicular to the wavefront.

Pegasus Lectures, Inc. COPYRIGHT 2006 The Incident Angle The incident angle is measured between the incident wave direction and the line normal, as shown below. Fig. 3: (Pg 146)

Pegasus Lectures, Inc. COPYRIGHT 2006 Normal Incidence Fig. 4: (Pg 146) For “normal” incidence, the incident angle is 0 degrees and the wave direction is parallel to the normal line as shown in the figure below.

Pegasus Lectures, Inc. COPYRIGHT 2006 Visualizing Incident Angles Fig. 5: (Pg 147)

Pegasus Lectures, Inc. COPYRIGHT 2006 Visualizing Incident Angles (Animation) (Pg 147)

Pegasus Lectures, Inc. COPYRIGHT 2006 Angle of Reflection Fig. 6: (Pg 147) For specular reflections, the angle of incidence equals the angle of reflection.

Pegasus Lectures, Inc. COPYRIGHT 2006 Angle of Transmission Fig. 7: (Pg 148) The transmission angle, like the incident angle, is measured relative to the line normal as shown below.

Pegasus Lectures, Inc. COPYRIGHT 2006 Specular Reflection Specular reflections are mirror-like reflections which occur from structures which are large, smooth and flat relative to the wavelength. Note that specular reflections are highly angular dependent. Specular Reflection

Pegasus Lectures, Inc. COPYRIGHT 2006 Specular Reflection Animation (Pg 148)

Pegasus Lectures, Inc. COPYRIGHT 2006 Scattering Scattering occurs when the surface is rough relative to the wavelength. Scattering

Pegasus Lectures, Inc. COPYRIGHT 2006 Scattering Animation (Pg 149 A) IncidentScattered

Pegasus Lectures, Inc. COPYRIGHT 2006 Rayleigh Scattering Rayleigh scattering occurs when the reflecting structures are small in comparison to the wavelength. Note that Rayleigh Scattering is a very weak reflective mode. Rayleigh Scattering The diameter of red blood cells is small in comparison to the wavelength of most diagnostic ultrasound.

Pegasus Lectures, Inc. COPYRIGHT 2006 Rayleigh Scattering Animation (Pg 149 B)

Pegasus Lectures, Inc. COPYRIGHT 2006 Reflection – Acoustic Aspects The type of reflection that occurs is determined primarily by the geometric aspects as just discussed. The percentage of reflection and the percentage transmission at a boundary between two structures depends on the acoustic properties of the media at the interface.

Pegasus Lectures, Inc. COPYRIGHT 2006 Acoustic Impedance The acoustic impedance is a property of the medium.

Pegasus Lectures, Inc. COPYRIGHT 2006 Reflection and Transmission Fig. 11: (Pg 152)

Pegasus Lectures, Inc. COPYRIGHT 2006 Reflection – Acoustic Impedance The amount of reflection from a boundary is determined by the acoustic impedance mismatch. What this equation says is: the greater the acoustic impedance mismatch between mediums, the greater the amount of reflection. How much reflection would there be if z 2 = z 1 ?

Pegasus Lectures, Inc. COPYRIGHT 2006 Transmission All of the energy at an interface between media must be conserved. Excluding absorption, this means that whatever energy does not reflect must transmit (continue on through the patient). Can you imagine why it is so important to not have too much reflection from any one interface?

Pegasus Lectures, Inc. COPYRIGHT 2006 Refraction The portion of the beam that does not reflect or absorb at an interface between two media, transmits through. Sometimes the beam does not continue straight but instead is bent. This bending is called refraction. No RefractionRefraction cici ctct cici ctct

Pegasus Lectures, Inc. COPYRIGHT 2006 Refraction Whether or not refraction occurs depends on two parameters, if the angle of incidence is other than perpendicular, and if there is a change in propagation speeds at the boundary. No Refraction cici ctct Beam Perpendicular  i = 0º ) No Refraction cici ctct c i = c t

Pegasus Lectures, Inc. COPYRIGHT 2006 Refraction and Snell’s Law θ incident θ transmitted θ reflected c incident c transmitted Medium 2 Medium 1

Pegasus Lectures, Inc. COPYRIGHT 2006 What Causes Refraction t4t4 This edge of wave front is in a faster medium so it travels farther c1c1 c2c2 Medium 2 Medium 1 This edge of wave front is still in a slower medium so it travels a shorter distance t1t1 t2t2 t3t3 t5t5 t6t6 t7t7

Pegasus Lectures, Inc. COPYRIGHT 2006 Refraction (Animation) (Pg 154)

Pegasus Lectures, Inc. COPYRIGHT 2006 No Refraction Case Fig. 13: No Refraction if No Change in Propagation Velocity (Pg 155) At time t 4, the left edge of the Wavefront travels at the same Rate as the right edge of the Wavefront since no change in Propagation velocity.

Pegasus Lectures, Inc. COPYRIGHT 2006 Visualizing Refraction Fig. 15: 60 Degree Incidence (Pg 155)

Pegasus Lectures, Inc. COPYRIGHT 2006 No Refraction With Normal Incidence Fig. 16: (Pg 156)

Pegasus Lectures, Inc. COPYRIGHT 2006 Variables In Snell’s Law Fig. 17: (Pg 157) CiCi CtCt

Pegasus Lectures, Inc. COPYRIGHT 2006 Determining Degree of Refraction Fig. 18: No Refraction (Pg 157) In this case, the transmitted angle is equal to the incident angle. When the transmitted and incident angles are equal, there is no refraction, as pictured in this figure.

Pegasus Lectures, Inc. COPYRIGHT 2006 Determining Degrees of Refraction Fig. 19: 20 Degrees of Refraction (Pg 157) In this case, the transmitted angle does not equal to the incident angle, so refraction exists. The amount of refraction is the difference between the incident and transmitted angles. In this case, there is 20 degrees of refraction (80°- 60°).

Pegasus Lectures, Inc. COPYRIGHT 2006 The Critical Angle: Total Internal Reflection It is possible to have so much refraction that no energy crosses the boundary between two media such that all the energy is totally internally reflected. The incident angle at which “Total Internal Reflection” occurs is called the “Critical Angle”.

Pegasus Lectures, Inc. COPYRIGHT 2006 The Critical Angle Fig. 20b: (Pg 158)

Pegasus Lectures, Inc. COPYRIGHT 2006 Total Internal Reflection Fig. 20c: (Pg 158)

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