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

License Agreement This presentation is the sole property of Pegasus Lectures, Inc. No part of this presentation may be copied or used for any purpose other than as part of the partnership program as described in the license agreement. Materials within this presentation may not be used in any part or form outside of the partnership program. Failure to follow the license agreement is a violation of Federal Copyright Law. All Copyright Laws Apply. 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 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 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 Before discussing the types of reflection, it is important to understand the terminology used and references for angle measurements. Fig. 1: Measuring the Incident Angle (Pg 145) Pegasus Lectures, Inc. COPYRIGHT 2006

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

The Incident Angle Fig. 3: (Pg 146) 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. Fig. 4: (Pg 146) 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. Fig. 6: (Pg 147) 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. Fig. 7: (Pg 148) Pegasus Lectures, Inc. COPYRIGHT 2006

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

Scattering Animation (Pg 149 A) Incident Scattered 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 z2 = z1? 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 No Refraction 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 Refraction Refraction ci ct Pegasus Lectures, Inc. COPYRIGHT 2006

Refraction ci = ct No Refraction ci ct Beam Perpendicular ( qi = 0º ) 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 ci ct Beam Perpendicular ( qi = 0º ) No Refraction ci ct ci = ct Pegasus Lectures, Inc. COPYRIGHT 2006

Refraction and Snell’s Law θincident θtransmitted θreflected cincident ctransmitted Medium 2 Medium 1 Pegasus Lectures, Inc. COPYRIGHT 2006

What Causes Refraction This edge of wave front is in a faster medium so it travels farther c1 c2 Medium 2 Medium 1 This edge of wave front is still in a slower medium so it travels a shorter distance t1 t2 t3 t5 t6 t7 Pegasus Lectures, Inc. COPYRIGHT 2006

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

Fig. 13: No Refraction if No Change in Propagation Velocity (Pg 155) No Refraction Case At time t4, the left edge of the Wavefront travels at the same Rate as the right edge of the Wavefront since no change in Propagation velocity. Fig. 13: No Refraction if No Change in Propagation Velocity (Pg 155) 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 Ci Ct Fig. 17: (Pg 157) Pegasus Lectures, Inc. COPYRIGHT 2006

Determining Degree of Refraction 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. Fig. 18: No Refraction (Pg 157) Pegasus Lectures, Inc. COPYRIGHT 2006

Determining Degrees of Refraction 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°). Fig. 19: 20 Degrees of Refraction (Pg 157) 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) Pegasus Lectures, Inc. COPYRIGHT 2006

Notes: Pegasus Lectures, Inc. COPYRIGHT 2006