Physics / A2 level
Connect imaging signals with interactions while respecting model limits.
Medical images are reconstructed from physical signals. X-ray intensity decreases as the beam interacts with matter; attenuation differences produce contrast. CT combines measurements from multiple directions to reconstruct sections. In an X-ray tube, accelerating electrons sets the maximum photon energy, eV.
Ultrasound uses echoes at acoustic-impedance boundaries, so echo time includes outward and return travel. A larger impedance mismatch gives stronger reflection. PET detects paired photons associated with positron annihilation. These methods involve different physics and risks; model exercises do not qualify a learner to select or interpret a clinical procedure.
In an X-ray tube, electrons accelerated through voltage V can transfer energy when interacting with the target. The greatest possible photon energy is eV, giving a minimum wavelength hc/(eV) in the ideal limit. A broad spectrum and characteristic lines can occur. X-ray intensity decreases through material; a simple uniform monoenergetic model gives I = I₀e^(−μx), while real beams and tissues are more complex.
Different attenuation produces differences in transmitted intensity. A projection overlaps structures along each ray, while computed tomography combines measurements from many directions to reconstruct sections. Greater image contrast is not automatically equivalent to better clinical information: resolution, noise, exposure and the question being investigated all matter. These notes explain physical mechanisms and cannot establish a patient-specific imaging choice or safe radiation exposure.
Acoustic impedance Z = ρc influences reflection at a boundary. At normal incidence in an ideal model, reflected intensity fraction is ((Z₂ − Z₁)/(Z₂ + Z₁))². Coupling gel reduces the problematic air gap between probe and skin. Echo time includes outward and return journeys, so depth = ct/2. Assuming one sound speed for different tissues introduces a modelling approximation, and strong reflection can obscure deeper structures.
A positron-emitting tracer produces positrons that can annihilate with electrons after slowing. Two photons are commonly emitted in approximately opposite directions, with about 511 keV each for annihilation at rest. Detectors registering suitable coincidences identify possible lines of emission, and many such events support reconstruction. The photons are detected, not a direct photograph of the positron’s path; timing, scattering and tracer behaviour influence the real system.
The recorded echo time includes travel from probe to reflector and back. ct gives that total path length, whereas the reflector’s depth is only the outward portion in the simple geometry.
Pulse–echo time includes both directions.
Ideal monoenergetic attenuation in a uniform material.
Acoustic impedance for density ρ and sound speed c.
Intensity reflection coefficient at normal incidence for an ideal boundary.
Minimum X-ray wavelength for ideal tube accelerating voltage V.
An ultrasound echo returns after 200 μs. If sound speed is 1540 m/s, what is the reflector depth?
Depth = 1540 × 200 × 10⁻⁶ / 2 = 0.154 m.
Use synthetic echo-time data to calculate depths and compare assumed sound speeds. No scanning of people or radiation source is needed.
These are related wave-interaction models, not clinical ultrasound, CT or PET scanners. Use them to discuss reflection and energy interaction only; they do not model diagnosis, tissue response or patient dose.
The pulse travels to the boundary and back.
Measured time covers a path of twice the depth.
0.154 m
Depth = 1540 × 200 × 10⁻⁶ / 2 = 0.154 m.
X-ray imaging
X-rays are ionising photons; ultrasound is mechanical.