Medical Physics

Ultrasound imaging

Ultrasound is sound of frequency above $20\ \text{kHz}$ (typically MHz for imaging). A piezo-electric transducer both emits pulses and detects reflected echoes. The acoustic impedance of a medium is:

$$Z = \rho c$$

where $\rho$ is its density and $c$ the speed of sound in it. At a boundary, the fraction of intensity reflected depends on the impedance mismatch:

$$\dfrac{I_r}{I_0} = \left(\dfrac{Z_2 - Z_1}{Z_2 + Z_1}\right)^2$$

Because air and tissue differ greatly, a coupling gel is used to exclude air and let ultrasound enter the body. The depth of a reflecting surface is found from the echo time: $d = \tfrac12 c t$.