Physics · Optics · Grade 11

Infrared, UV and X-rays

How does a thermal camera “see” a person in the dark, and an X-ray a bone?

The situation

At the entrance to an airport, passengers pass in front of a thermal imaging camera: on the screen each person is a coloured patch, and those with a fever “glow” brighter. A tourist who has walked for several hours in summer in Chimgan notices in the evening that his face is sunburnt, although the air was cool. In hospital an X-ray machine shows a broken bone, and a CT scanner “slices” the body layer by layer. All of these are electromagnetic waves invisible to the eye. How do they differ from light, and why is each suited to its own job?

Topic

Infrared, ultraviolet and X-rays. Thermal imager, sunburn and X-ray and CT in a hospital

Key ideas

Wien's law
X-ray spectrum
Computed tomography

Formulas

λ_{m a x} = \frac{b}{T}, b = 2.898 \cdot 10^{- 3} m \cdot K

Wien's displacement law: the warmer a body, the shorter the wavelength of its radiation peak. For skin (≈ 34 °C) it is ≈ 9.4 µm.

q = ε σ T^{4}

The Stefan–Boltzmann law: the power radiated by 1 m² of surface; $ε$ is the emissivity (skin ≈ 0.98, shiny metal ≈ 0.1).

λ_{m i n} = \frac{h c}{e U} \approx \frac{1.24}{U [kV]} nm

The Duane–Hunt law: if an electron gives all its energy $e U$ to a single photon, the shortest wavelength is produced.

2 d \sin θ = n λ

The Bragg condition: waves reflected from the planes of the crystal reinforce each other; $d$ is the spacing between planes and $θ$ is the glancing angle.

I = I_{0} e^{- μ x}, HU = 1000 \frac{μ - μ_{water}}{μ_{water}}

The attenuation of X-rays in matter and the Hounsfield scale in CT (water — 0, air — −1000).

Theory

One spectrum — different waves

Infrared (IR), ultraviolet (UV) and X-rays are electromagnetic waves of the same nature as light, only with a different wavelength: IR from 0.78 µm to 1 mm, UV 10–400 nm, X-rays roughly 0.01–10 nm. The photon energy is $E = h c / λ$ : the shorter the wave, the more “powerful” the photon. An IR photon merely makes molecules vibrate (heats them), a UV photon can break chemical bonds and damage the DNA of skin cells, and an X-ray photon ionises an atom and passes through tissue.

Thermal radiation and the thermal imaging camera

Every body emits thermal radiation corresponding to its temperature (the Planck curve). For bodies at about 300 K the peak is at 9–10 µm — which is why a thermal imaging camera works in the 8–14 µm band and sees even in the dark: it records not reflected light but the body's own radiation. The camera calculates temperature from the radiated power, and for this it needs to know the surface's emissivity $ε$ . Shiny metal ( $ε \approx 0.1$ ) radiates little and reflects the room like a mirror — a hot kettle looks “cold”. Ordinary glass does not transmit 8–14 µm radiation: the camera cannot see through a window. These laws are used in optical pyrometers (measuring the temperature of glowing metal from a distance) and in light sources: for an incandescent lamp at ≈ 2800 K the radiation peak is at ≈ 1 µm, so most of its energy goes into invisible IR.

Ultraviolet: sunburn, fluorescence, disinfection

The Sun's UV-C rays (< 280 nm) and most of the UV-B are absorbed by the ozone layer. The UV-B that reaches the Earth (280–315 nm) burns the skin: the skin's sensitivity (the erythemal spectrum) rises sharply at short wavelengths, so the “burning part” is concentrated around 300–320 nm. The UV index measures this effect: 1 unit = 25 mW/m². In a clear sky $U V I \approx 12.5 μ_{0}^{2.42} {(Ω / 300)}^{- 1.23}$ (the Madronich formula), where $μ_{0} = \sin h$ and $Ω$ is the amount of ozone (in Dobson units). In the mountains UV is stronger (≈ 10 % for every 1000 m), and fresh snow reflects up to 80 % of UV radiation. UV-A (315–400 nm) excites fluorescence: the security marks on banknotes and highlighter inks glow brightly under a UV lamp. 254 nm UV-C lamps destroy the DNA of microbes — they disinfect air and surfaces in hospitals and water at water-treatment plants.

The X-ray tube: bremsstrahlung and characteristic radiation

Electrons emitted from a heated cathode are accelerated by the voltage $U$ and strike the anode with energy $e U$ . An electron that decelerates sharply near the anode's atoms emits bremsstrahlung (braking radiation) — the spectrum is continuous because the electron can give up any part of its energy. If all the energy passes to a single photon, the shortest wavelength $λ_{m i n} = h c / (e U)$ is produced; it does not depend on the anode material. Bremsstrahlung is proportional to the anode's atomic number $Z$ — so a heavy ( $Z = 74$ ) and high-melting (3422 °C) metal, tungsten, is chosen for the anode. If $e U$ is enough to knock out a K-shell electron, an electron from the L shell (Kα) or the M shell (Kβ) drops into the vacancy and characteristic lines appear; their frequency obeys Moseley's law: $\sqrt{ν} \propto Z - 1$ . Only ≈ 1 % of the electrons' energy becomes X-rays; the rest heats the anode. The radiation of a charged particle as it slows down in matter is radiative braking; if a fast particle travels through a medium faster than the speed of light in that medium, Cherenkov (Vavilov–Cherenkov) radiation appears (the blue glow in the water of a reactor).

The Bragg condition and X-ray diffraction

The wavelength of X-rays is close to the distance between atoms in a crystal (≈ 0.1 nm), so a crystal acts as a diffraction grating for X-rays. Waves reflected from parallel atomic planes reinforce each other only when the path difference $2 d \sin θ$ equals a whole number of wavelengths. In a Bragg spectrometer the crystal is turned through $θ$ and the counter through $2 θ$ : at each angle one wavelength (and, in order $n = 2$ , half of it) is measured — this is how the spectrum is recorded. Conversely, if the wavelength is known, $d$ can be found and the structure of the crystal determined (the Laue and Bragg methods). The kind and arrangement of the atoms in a plane determine the strength of the reflected beam (the structure factor): some orders may vanish completely. Electrons and neutrons also have wave properties and diffract in the same way.

The X-ray image and computed tomography

X-rays are attenuated in matter according to $I = I_{0} e^{- μ x}$ . Because of the photoelectric effect, $μ$ depends strongly on atomic number: bone, which contains calcium, absorbs several times more than soft tissue — so bone looks white on an X-ray image. But in an ordinary image (a topogram) all the organs along the path of the beam are superimposed. In CT the tube and detectors rotate around the patient and take projections from hundreds of angles (a sinogram). Each projection is filtered and “back-projected”, and a map $μ (x, y)$ of the slice is reconstructed; as the table moves, the slices are assembled into a 3D image. CT values are given in Hounsfield units (HU). Besides being absorbed, X-rays are also scattered in matter (by electrons — the Compton effect, covered in a separate experiment). In agriculture, internal damage to seeds and how well filled they are can be checked on an X-ray image. Model: an average $μ$ at about 70 keV; the organs are simplified to ellipsoids; IR, UV and X-rays are drawn in the scene in conventional colours.

Did you know?

Wilhelm Röntgen discovered new rays in November 1895 and called them “X-rays”. In 1901 he received the first Nobel Prize in Physics.
In 1800 William Herschel measured the spectrum from a prism with thermometers and found that beyond the red — where the eye sees nothing — the thermometer warmed up even more. This is how infrared rays were discovered.

Inside the experiment

The experiment starts from a real-life situation: you predict the result, change the controls, run the experiment and draw a conclusion. Inside are missions, theory, a quiz and a guided tour in which the camera moves and explains the key points.

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Interference and diffraction — Grade 11
Polarisation of light — Grade 11
Laser physics and holography — Grade 11
Luminous flux and illuminance — Grade 11
Scattering of light — Year 1
Crystal optics — Year 1
Interferometers and LIGO — Year 1
Resolving power — Year 1
Nonlinear optics: the green laser — Year 2