Thermal cameras, which we frequently see in action movies or military documentaries, showing people, animals, and running engines in bright colors even in pitch darkness, seem almost like magic. However, behind this technology lies not magic, but Wien's Displacement Law, one of the cornerstones of quantum physics and thermodynamics. Let's take a journey into physics to understand how thermal imaging systems, which capture light our eyes cannot see, work and the secrets of infrared radiation.
Blackbody Radiation and Invisible Light
Every object in the universe with a temperature above absolute zero (0 Kelvin or $-273.15^\circ\text{C}$) emits thermal radiation into its surroundings. This includes you, the chair you are sitting on, the tree in the garden, and the Sun in the sky. This radiation occurs in the form of electromagnetic waves.
However, the color (wavelength) of the light emitted by an object depends on the object's temperature. Very hot objects (like the Sun or a burning lamp filament) emit visible light; objects at room temperature emit infrared (IR) rays, which have lower energy and longer wavelengths. The human eye has biologically evolved to see only a very narrow range of wavelengths (between approximately 400 nm and 700 nm). Therefore, we cannot see the infrared light emitted by ourselves or the objects around us.
What Do Thermal Cameras "See"?
Standard cameras (or the human eye) create images by detecting visible light reflected from objects. In pitch darkness, since there is no light to reflect, no image is formed.
Thermal cameras, on the other hand, are concerned not with the light reflected by objects, but directly with the thermal radiation emitted by objects due to their own temperatures. The special microbolometer sensors inside a thermal camera are sensitive to infrared wavelengths (usually between 8 and 14 micrometers). Infrared photons hitting the sensor cause it to heat up and its electrical resistance to change. The camera's processor processes these electrical signals to create a "false-color" image (thermogram) where different colors (e.g., red/white for hot, blue/black for cold) are used to represent different temperatures.
The Human Body and Wien's Displacement Law
So how do the engineers who produce thermal cameras know exactly which wavelength to make the sensors sensitive to? This is where Wien's Displacement Law, formulated in 1893, comes into play.
Wien's law states that the peak wavelength ($\lambda_{\text{max}}$) at which the spectral radiance emitted by a body is most intense is inversely proportional to the absolute temperature ($T$) of the body:
$$\lambda_{\text{max}} = \frac{b}{T}$$
In this formula, $b$ is Wien's constant, which has a value of approximately $2.898 \times 10^{-3} \text{ m}\cdot\text{K}$.
Now, let's consider the human body, one of the most common targets for thermal cameras. The outer skin temperature of an average healthy human body is between approximately $30^\circ\text{C}$ and $34^\circ\text{C}$. If we take an average value of $33^\circ\text{C}$, the absolute temperature ($T = 33 + 273.15$) is approximately $306 \text{ K}$.
Let's use Wien's law to find at which wavelength the human body radiates the most:
$$\lambda_{\text{max}} = \frac{2.898 \times 10^{-3} \text{ m}\cdot\text{K}}{306 \text{ K}} \approx 9.47 \times 10^{-6} \text{ m} = 9.47 \text{ \mu m} \text{ (micrometers)}$$
The value of approximately $9.5 \text{ \mu m}$ we obtained as a result of the calculation falls exactly in the long-wave infrared (LWIR) region. For this reason, most thermal cameras (for example, FLIR systems) are designed to be most sensitive to wavelengths between $8 \text{ \mu m}$ and $14 \text{ \mu m}$. If the sensors were tuned to visible light (0.5 µm) or near-infrared (1-2 µm), it would be impossible for them to detect our body heat in the dark.
Using the Wien's Displacement Law Calculator
If you want to calculate the range to which thermal sensors should be calibrated for different applications, you can use the Wien's Displacement Law Calculator tool on our site.
Example Scenario: You are designing an industrial furnace, and the average internal temperature of the furnace is $800^\circ\text{C}$ ($1073.15 \text{ K}$). You are going to choose a pyrometer or thermal camera to measure the heat emitted by the walls of this furnace.
When you enter the value $1073.15 \text{ K}$ into our calculator, the tool will instantly give you the peak wavelength:
$\lambda_{\text{max}} \approx 2700 \text{ nm}$ or $2.7 \text{ \mu m}$.
This result tells the engineer: For targets at $800^\circ\text{C}$, instead of standard thermal cameras measuring the human body (8-14 µm), using sensors that measure in the short-wave infrared (SWIR) or mid-wave infrared (MWIR) region (e.g., 3-5 µm) will yield much more efficient and accurate results.
The Impact of Thermal Imaging in Medicine and Healthcare
Thanks to the sensitivity adjusted by Wien's law, thermal cameras have revolutionary applications in the field of healthcare and medical screening. With this method, known in medicine as thermography, regional temperature differences in the human body can be detected quickly and without contact.
For example, when there is an infection, inflammation, or an abnormal increase in blood flow in the body, the temperature of that region shows a very slight increase (perhaps between 0.5 and 1 Kelvin) compared to the surrounding tissues. This tiny temperature difference between $33^\circ\text{C}$ and $34^\circ\text{C}$ causes a very small shift in the emitted infrared wavelength, which can again be calculated using Wien's formula. High-quality thermal sensors (concentrating in the 8-14 µm range) convert these small radiation differences into a highly sensitive color (temperature) map. Especially during pandemics for detecting people with fever in crowds, or for early diagnosis of foot circulation disorders in diabetic patients, the role of thermal cameras, which allow us to understand invisible infrared light, is immense.
Warning: Wien's law alone is not enough when making thermal measurements. Real materials (metal, plastic, skin) have different "emissivity" values. While the emissivity value of an ideal blackbody is 1, the emissivity of real objects is between 0 and 1. Shiny metals (low emissivity) reflect heat well and emit little, while matte surfaces reveal their temperatures more accurately on a thermal camera. However, Wien's law is a perfect engineering compass for determining the wavelength of peak radiation.
