Physica
Lessons

08 Ultrasound

A click, an echo, a shift

Impedance sends the echo home. Time is depth. Motion is Doppler. That is the whole craft.

For Sonographers · US physicists·7 min

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You will be able to

  1. 01Compute reflection from a Z mismatch.
  2. 02Turn round-trip time into millimetres at 1540 m/s.
  3. 03Read Doppler as speed, angle, and the PRF ceiling.

Chapter 01

Why anything comes back

Acoustic impedance is density times speed. A mismatch reflects a fraction of intensity: the square of Z2 minus Z1 over Z2 plus Z1. Soft tissue to air is almost a mirror — that is why gel exists. Soft tissue to bone is a bright echo and an acoustic shadow behind it.

No mismatch, no echo. No echo, no image.

Simulation

Acoustic impedance — Change the numbers; the scene follows.

Variables

Z = 1.632e+6 kg/(m²·s)

R=(Z2Z1Z2+Z1)2R=\left(\frac{Z_2-Z_1}{Z_2+Z_1}\right)^2

Keep thisNo mismatch, no echo. No echo, no image.

Open the calculator — Acoustic impedance

Chapter 02

Time is a ruler

Assume 1540 metres per second in soft tissue. Depth is speed times half the round-trip. Axial resolution is about half the spatial pulse length. A shorter pulse (more bandwidth, higher frequency) sharpens the axis and dies sooner in depth. That trade is every preset on the machine.

Simulation

Axial resolution — Change the numbers; the scene follows.

Variables

λ = 0.308 mm

Keep thisHigher frequency is not ‘better’. It is shallower and sharper.

Open the calculator — Axial resolution

Chapter 03

Blood moves the pitch

The Doppler shift is proportional to speed and to the cosine of the beam-flow angle. At ninety degrees the shift vanishes — that is a geometry error, not absent flow. PRF must be at least twice the shift or the spectrum aliases. Angle, scale, and wall filter are the three lies a bad tracing can tell.

Simulation

Doppler shift — Change the numbers; the scene follows.

Variables

Δf = 1,623.4 Hz

Δf=2vf0cosθc\Delta f=\frac{2v f_0\cos\theta}{c}

Keep thisNever quote a speed from a 60-degree tracing as if it were 0.

Open the calculator — Doppler shift

In this specialty

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