Intensity reflection coefficient
- The intensity reflection coefficient α is defined as:
The ratio of the intensity of the reflected wave relative to the incident (transmitted) wave
- This can be calculated using the fraction:
- Where:
- α = intensity reflection coefficient
- IR = intensity of the reflected wave (W m-2)
- I0 = intensity of the incident wave (W m-2)
- Z1 = acoustic impedance of one material (kg m-2 s-1)
- Z2 = acoustic impedance of a second material (kg m-2 s-1)
- This equation will be provided on the datasheet for your exam
- This ratio shows:
- If there is a large difference between the impedance of the two materials, then most of the energy will be reflected
- If the impedance is the same, then there will be no reflection
Coupling medium
- When ultrasound is used in medical imaging, a coupler is needed between the transducer and the body
- The soft tissues of the body are much denser than air
- If air is present between the transducer and the body, then almost all the ultrasound energy will be reflected
- The coupling gel is placed between the transducer and the body, as skin and the coupling gel have a similar density, so little ultrasound is reflected
- This is an example of impedance matching
Worked example
A beam of ultrasound is incident at right angles to a boundary between two materials as shown in the diagram.
The materials have acoustic impedances of Z1 and Z2. The intensity of the transmitted ultrasound beam is IT, and the reflected intensity is IR.
medium | speed of ultrasound / m s–1 | acoustic impedance / kg m–2 s–1 |
air | 330 | 4.3 × 102 |
gel | 1500 | 1.5 × 106 |
soft tisuse | 1600 | 1.6 × 106 |
bone | 4100 | 7.0 × 106 |
Answer:
Part (a)
State the relationship between I, IT and IR:
Incident intensity = Transmitted intensity + Reflected intensity
Part (b)(i)
Step 1: Write down the equation for intensity reflection coefficient α
Step 2: Write down the acoustic impedances for gel and soft tissue
- Gel, Z1 = 1.5 × 106 kg m-2 s-1
- Soft tissue, Z2 = 1.6 × 106 kg m-2 s-1
Step 3: Calculate the intensity reflection coefficient
- This result means that only 0.1% of the incident intensity will be reflected, with the remaining being transmitted
Part (b)(ii)
Step 1: Write down the acoustic impedances for air and soft tissue
- Air, Z1 = 4.3 × 102 kg m-2 s-1
- Soft tissue, Z2 = 1.6 × 106 kg m-2 s-1
Step 2: Calculate the intensity reflection coefficient
- This result means that 100% of the incident intensity will be reflected, with none being transmitted
Part (c)
- At the air-soft tissue boundary, the intensity reflection coefficient is α ≈ 1
- Therefore, without gel, there is almost complete reflection, no ultrasound is transmitted through the skin
- Therefore, the gel enables almost complete transmission of the ultrasound through the skin, with very little reflection
- At the gel-soft tissue boundary, the intensity reflection coefficient is α = 0.001