This tech is cool. Photons (light particles) from a warm body tend to be maximally random. Very simple math proves that "maximally random" is when more photons are at one wavelength than another. It is the most probable spectrum. The shape of this spectrum tells temperature! /1
2/ It might seem weird that the "maximally random" spectrum does not have an equal number of photons at every wavelength. For comparison, if you roll 6 million dice, you will get one million 1's, one million 2's, etc, an equal number in each possible state. Why not for photons?
3/ Becoz different wavelength photons carry different amounts of energy. The higher the wavelength, the more energy the photon carries from your body. If you were radiating as many high wavelength photons (x rays) from your body as low wavelength (IR), you would instantly freeze.
4/ So "maximally random" must meet the constraint of conserving energy. What is the most random distribution of photon wavelengths subject to a conserved energy? This can be calculated using simple math, almost as simple as counting 6 sides of dice to divide the probability by 6.
5/ This distribution is called the Planck Spectrum, or the Black-body Spectrum. It has different shape depending how much energy is in it (i.e., what it's temperature is). So if you measure it's shape, how many photons at each wavelength, you can figure out the temperature.
6/ But you don't really need to measure the entire shape. These spectrums can't be any possible shape. They are always the maximally possible shape, and they only have two variables: the overall brightness, and the temperature encoded into it. Only two unknowns.
7/7 So in principle (simplified), to solve 2 unknowns you need only 2 measurements. By measuring the amount of infrared at just two wavelengths, calculating their ratio, you know temperature of the object that emitted them. (But measuring more wavelengths gives more accuracy.)
*maximally random, not "maximally possible" 😣
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