Sono Physics Ch. 6 - 7 (Continued)

Incidence

The angle at which sound strikes a boundary.

Types of Incidence:

Normal and Oblique Incidence

The Angles of Incidence helps Determine:

◦ Reflection

◦ Refraction

◦ Transmission

Normal Incidence

Occurs when a sound beam strikes a boundary at exactly 90°

◦ Beam is perpendicular to interface

◦ Angle must be 90°

◦ Reflection is greatest when incidence is normal

Oblique Incidence

Occurs when a sound beam strikes a boundary at any angle other than 90°

Characteristics:

◦ Angle of incidence is not 90°

◦ May be an acute angle (< 90°)

◦ May be an obtuse angle (> 90°)

Law of Reflection

When reflection occurs:

◦ Angle of Reflection = Angle of Incidence

Reflection depends on what?

Impedance Difference

Reflection at Normal Incidence

Greater impedance mismatch = Greater reflection

Incident Intensity (Total amount of energy before it hits Boundary)

Sound arriving at boundary.

Reflected Intensity (Total that returns to transducer)

Portion that returns toward transducer.

Transmitted Intensity (The portion that continues on into the Medium)

Portion that continues into next medium.

Incident Intensity Formula

Reflected Intensity + Transmitted Intensity

Intensity Reflection Coefficient (IRC)

Percentage of incident intensity that is reflected.

◦ Represents amount of sound energy that returns to transducer

Units: None

Intensity Transmission Coefficient (ITC)

Percentage of incident intensity that is transmitted

◦ Represents amount of sound energy that continues deeper into body

Units: None

Typical Values

◦ IRC & ITC range from 0% to 100%

or 0 – 1.0

Intensity Coefficients

100% = IRC + ITC

Because energy is conserved, all of the incident intensity must either:

◦ Be reflected

◦ Be transmitted

Intensities = W/cm²

Coefficients = %

Reflection with Normal Incidence

Reflection Depends on Impedance Differences

-Reflection occurs when sound crosses a boundary between tissues with different acoustic impedances.

Intensity Reflection Coefficient (IRC)

◦ Measures the percentage of incident intensity that is reflected at a boundary

IRC (%) = Z2 - Z1 X 100

Z2 + Z1

Reflection w/ Normal Incidence Key Concepts

Key Concepts:

◦ Greater impedance mismatch → More reflection

◦ Similar impedances → Less reflection

◦ Equal impedances → No reflection

Transmission w/ Normal Incidence

Transmission Depends on Reflection

When sound reaches a boundary:

◦ Some intensity may be reflected

◦ The remaining intensity is transmitted

Complete Transmission:

If two media have the same acoustic impedance:

◦ No reflection occurs

◦ 100% of the sound is transmitted

Transmission w/ Normal Incidence

Intensity Transmission Coefficient (ITC)

Measures the % of incident intensity that is transmitted across a boundary

ITC (%) = T𝑟𝑎𝑛𝑠𝑚𝑖𝑡𝑡𝑒𝑑 𝐼𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 / 𝐼𝑛𝑐𝑖𝑑𝑒𝑛𝑡 𝐼𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 X 100

Oblique Incidence: Different Rules Apply

When the sound beam strikes a boundary at an angle (≠ 90°)

◦ Reflection may occur

◦ Transmission may occur

◦ Refraction may occur

◦ Impedance differences alone no longer predict what happens

New Factors Matter:

◦ Angle of incidence

◦ Propagation speed of each medium

◦ Acoustic impedance

Even with Oblique Incidence, Two Rules Never Change

1. Conservation of Energy

All of the incident sound must either:

◦ Be reflected

◦ Be transmitted ◦

100% = IRC + ITC

◦ Incident Intensity = Reflected Intensity + Transmitted Intensity

◦ Intensity has units of W/cm2

2. Law of Reflection

◦ Angle of Reflection = Angle of Incidence

◦ The reflected beam always leaves the boundary at the same angle it arrived

Reflection w/ Obliques Incidence

Law of Reflection:

◦Angle of Reflection = Angle of Incidence

Angle of Incidence

◦Angle between the incident beam and the normal line

Angle of Reflection

◦Angle between the reflected beam and the normal line

Reflection w/ Oblique Incidence Key Points

◦Reflected beam does not always return to transducer w/oblique incidence.

◦Reflected beam leaves boundary at same angle it arrived

◦Angles are measured from normal line

◦ (perpendicular to the boundary)

Refraction

Refraction = Transmission with a bend

◦ The transmitted beam changes direction as it enters a new medium

◦ The reflected beam does not refract.

Refraction ONLY Occurs When BOTH Conditions Are Present

◦ Oblique incidence (angle ≠ 90°)

◦ Different propagation speeds in the two media

No Refraction If:

✘ Normal incidence

✘ Same propagation speeds

Refraction - Snell’s Law

Snell's Law describes the physics of refraction

Mathematical Description of Refraction:

𝒔𝒊𝒏 ( transmission) = Speed of Medium 2

sin (Incident angle) Speed of Medium 1

Using Snell’s Law

If Medium 2 is Faster

◦ Refracted angle > Incident angle

◦ Beam bends away from the normal

If Medium 2 is Slower:

◦ Refracted angle < Incident angle

◦ Beam bends toward the normal

Time of Flight

Time needed for a pulse to travel to the reflector and back

Also called:

✓Go-return time

✓Round trip time

Ultrasound systems assume sound travels through soft tissue at 1.54 mm/μs

Key Relationship

✓ Time of Flight is directly related to reflector depth

Time of Flight Relationship with Reflected Depth is what?

Directly Related

Time Of Flight Equation

Depth (mm) = 𝟏.𝟓𝟒 𝒎𝒎 / µ𝐬 × 𝒈𝒐 𝒓ⅇ𝒕𝒖𝒓𝒏 𝒕𝒊𝒎𝒆 (µ𝒔) / 2

Why divide by 2?

The pulse travels:

-To the reflector

-Back to the transducer

The measured time includes both directions, so divide by 2 to find reflector depth

The 13 - Microsecond Rule

Always applies when sound travels through soft tissue

Every 13 μs of go-return time corresponds to 1 cm of reflector depth

From Time of Flight to PRP

Before another pulse can be sent

The system must wait for the first pulse to:

✓ Reach the deepest reflector

✓ Return to the transducer

This waiting time is called Pulse Repetition Period (PRP)

Pulse Repetition Period (PRP)

PRP is time from beginning of one pulse to beginning of next pulse

Think of PRP as the machine’s listening time:

◦ Send a pulse

◦ Listen for all echoes to return

◦ Sent the next pulse

PRP Relationship to Imaging Depth is what?

Directly Related

Shallow image → Short PRP

Deep image → Long PRP

PRP (µs) = Imaging depth (cm) x 13 µs / cm

Pulse Repetition Frequency (PRF)

PRF is the number of pulses the transducer sends each second

Units = Hz

Key Relationship:

✓ PRF is inversely related to imaging depth

Shallow image → High PRF

Deep image → Low PRF

PRF Equation

PRF (Hz) = 𝟕7,𝟎𝟎𝟎 𝒄𝒎/𝒔

𝒊𝒎𝒂𝒈𝒊𝒏𝒈 𝒅𝒆𝒑𝒕𝒉