24.1.4 Intensity Reflection Coefficient

Definition: Intensity Reflection Coefficient ( $\alpha$)

• Ratio of the intensity of the reflected wave to the intensity of the incident wave.

Math

The Intensity Reflection Coefficient can be calculated using the fraction: $\alpha =\frac{I_R}{I_0}=\frac{(Z_2-Z_1{)}^2}{(Z_2+Z_1{)}^2}$

• Where:
  • $\alpha$ = intensity reflection coefficient
  • $I_R$ = intensity of the reflected wave (${\text{W m}}^{-2}$)
  • $I_0$ = intensity of the incident wave (${\text{W m}}^{-2}$)
  • $Z_1$ = acoustic impedance of one material (${\text{kg m}}^{-2}{\text{ s}}^{-1}$)
  • $Z_2$ = acoustic impedance of a second material (${\text{kg m}}^{-2}{\text{ s}}^{-1}$)

Concept

This ratio shows that:

1. If there is a large difference between the impedance of the two materials, then most of the energy will be reflected.
2. If the impedance is the same, then there will be no reflection.

Tip

The ratio of transmitted wave intensity to incident wave intensity is given by $\frac{I_T}{I_0}=1-\frac{I_R}{I_0}$

Important

Effect using a coupling gel

• The specific acoustic impedances of air and skin are very different.
• The intensity reflection coefficient is high and most of the ultrasound waves would be reflected at the skin.
• To minimise reflection and ensure most of the waves enter the body, a coupling gel is used.
• The coupling gel has a similar specific acoustic impedance to the skin, leading to a small intensity reflection coefficient.