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
Part (a)
Incident intensity = Transmitted intensity + Reflected intensity
I = IT + IR
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
- At the gel-soft tissue boundary, the intensity reflection coefficient is α = 0.001
- Therefore, the gel enables almost complete transmission of the ultrasound through the skin, with very little reflection
- At the air-soft tissue boundary, the intensity reflection coefficient is α ≈ 1