• 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
  • I_R = 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: Intensity reflection coefficient

Part (a)

Incident intensity = Transmitted intensity + Reflected intensity

I = I_T + I_R

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