Physics › Medical physics › Ultrasound imaging
Ultrasound imaging
Bats and shipwreck hunters had the idea first: send out a pulse, time the echo, and you know how far away something is. Do it with megahertz sound from a crystal that both shouts and listens, and you can map a baby without a single ionising photon.
Builds on Progressive waves and Refraction and total internal reflection.
IN THIS TOPIC
- Explain how a piezoelectric transducer generates and detects ultrasound pulses.
- Use the pulse-echo technique and d = ct/2 to locate a boundary in tissue.
- Use acoustic impedance Z = ρc to explain reflection at boundaries and the need for coupling gel.
WHAT YOU PROBABLY THINK
Ultrasound scans photograph the inside of the body with sound.
A crystal that shouts and listens
Ultrasound is sound above about 20 kHz; medical scanners run in megahertz. It is made and detected by the same component, a piezoelectric transducer: a crystal that deforms when a pd is applied across it, and generates a pd when deformed. Drive it with an alternating pd at its resonant frequency and it vibrates, launching a sound pulse; let a returning echo squeeze it and it produces a measurable pd.
So the transducer spends its life alternating between two jobs. It shouts for a microsecond, then listens for the echoes, and the switching is what makes the whole technique work with one probe held against the skin.
Pulse and echo
Everything else is timing. A pulse leaves the transducer, part of it reflects off each boundary between tissues, and the echoes arrive back after a delay. Sound of speed c that took time t to go there and back has found a boundary at depth
The factor of two is the whole exam question: the pulse covers the distance twice. An A-scan plots echo strength against time along one line, good for a single depth such as an eye measurement. A B-scan sweeps the beam and builds each echo into a brightness map, which is the moving picture of an antenatal scan: not a photograph, but a map of boundaries, assembled from arrival times.
WORKED EXAMPLE
How deep is the organ boundary?
An echo returns 65 μs after the pulse enters soft tissue, where ultrasound travels at 1540 m s−1. Find the depth of the reflecting boundary.
d = ct/2 = (1540 × 65 × 10−6)/2 = 5.0 cm.
Without the factor of two the answer comes out at 10 cm, twice as deep as the truth. The mark scheme is waiting for exactly that slip.
Acoustic impedance, and the gel
How much of a pulse reflects at a boundary is set by the acoustic impedance of the media either side,
the product of density and sound speed. Similar impedances let the pulse pass; badly mismatched ones reflect most of it. The fraction of intensity reflected is
This equation is why the sonographer reaches for the coupling gel. Air's impedance is thousands of times smaller than tissue's, so an air gap between probe and skin reflects nearly all the ultrasound before it ever gets in. The gel displaces the air with a material whose impedance is close to tissue, letting the pulse through. Inside the body, the useful echoes come from the mild mismatches between organs, and the strong ones from tissue meeting bone.
Ultrasound also fades as it travels: absorption and scattering attenuate the pulse exponentially with depth, just as matter attenuates X-rays, and the attenuation rises steeply with frequency. That sets the sonographer's trade: high frequency resolves finer detail but dies sooner, so shallow work uses high megahertz and deep organs use low.
The other non-ionising imagers
AQA's option puts two more non-ionising instruments alongside ultrasound. The endoscope is applied total internal reflection: a coherent bundle of optical fibres carries an image out of the body, with each fibre keeping its place in the bundle so the picture arrives intact, while a second, incoherent bundle carries light in.
The MR scanner uses no rays at all: the patient lies in a strong magnetic field, the protons in the body's water precess about it, and radio-frequency pulses tip and release them. How quickly they relax back depends on the tissue they sit in, so mapping the radio signal maps soft tissue in fine detail, with no ionising dose. Its costs are the machine itself and the strong field, which rules out patients with certain implants.
THE EXAM BIT
- State both halves of the piezoelectric effect: a pd deforms the crystal (transmission), and deformation of the crystal produces a pd (detection). One sentence each direction.
- Every pulse-echo calculation carries the factor of two. Write d = ct/2 before substituting, and check the answer against sense: organs live centimetres down, not tens of centimetres.
- Z = ρc takes the density and sound speed of the same medium. Mixing media across the product is the standard error.
- Explain the gel in impedance language: it excludes the air gap, whose impedance mismatch with tissue would reflect nearly all the intensity at the surface.
- Ultrasound is the non-ionising option: no photon energy argument, no dose. Comparisons with X-ray imaging score for saying so explicitly.
CHECK YOURSELF
Ultrasound crosses a boundary where Z₁ = 1.6 × 106 kg m−2 s−1 and Z₂ = 1.7 × 106 kg m−2 s−1. Roughly what fraction of the intensity reflects, and why is that useful?
Show a hint
Put the numbers into the reflection coefficient; the answer is small.
Show the answer
Ir/I0 = (0.1/3.3)2 ≈ 0.001: about a tenth of a per cent reflects.
Useful because imaging needs most of the pulse to carry on to deeper boundaries. Tiny reflections at each interface give faint but detectable echoes from every layer, rather than one blinding echo from the first.
Depth is ct over two: the echo travelled there and back.
Reflection is set by impedance mismatch, which is why the gel exists.
WORKBOOK
Printable practice for this topic: original exam-style questions with room to work, and a fully worked answer book. Free to use; please do not redistribute or sell.
CHECK YOUR PROGRESS
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- Explain how a piezoelectric transducer generates and detects ultrasound pulses.
- Use the pulse-echo technique and d = ct/2 to locate a boundary in tissue.
- Use acoustic impedance Z = ρc to explain reflection at boundaries and the need for coupling gel.
Open the full revision checklist to track your progress across the whole unit.
No animated video for this topic yet; these notes stand alone. InkPhysics on YouTube.