
Spectroscopy techniques for measuring temperature in gases, plasmas, and astronomical objects.Temperature measurement spectroscopy is a set of techniques that use the light emitted, absorbed, or scattered by a substance to determine its temperature without direct contact. Instead of a thermometer, scientists analyze the spectrum of light — its intensity at different wavelengths — to infer how hot a gas, plasma, or distant star is. This is essential in environments where a physical probe is impossible, such as the interior of a fusion reactor, the atmosphere of a star, or the early universe.
The foundations were laid in the 19th century with the work of Gustav Kirchhoff and Robert Bunsen, who linked spectral lines to chemical elements and temperature. The quantitative use of spectral line ratios for temperature measurement developed in the early 20th century with the advent of quantum theory.
The key principle is that atoms and molecules emit or absorb light at specific wavelengths, and the relative strength of these spectral lines depends on temperature. For example, in a hot gas, more atoms are in excited states, so absorption lines from those states become stronger. By comparing the intensities of different lines, or by fitting the overall shape of a continuous spectrum (blackbody radiation), scientists can extract a precise temperature. In some advanced methods, like frequency-comb spectroscopy, a laser with a spectrum of equally spaced lines is used to measure absorption with extreme accuracy, allowing temperature mapping in gases and flames.
Used in astrophysics to determine stellar temperatures, in plasma physics to monitor fusion experiments, and in combustion research to map flame temperatures in engines and turbines.
The cosmic microwave background radiation, which fills the universe, is a perfect blackbody spectrum with a temperature of 2.725 Kelvin — measured so precisely that it reveals tiny variations of a few microkelvin, which are the seeds of galaxies.
| S_a^{1/2} | variable | Spectral density of acceleration noise (square root) — acceleration noise spectral density metre per second squared per root hertz |
| T | variable | Temperature — temperature kelvin |
| k | variable | Spring constant of the resonator — spring constant newton per metre |
| m | variable | Mass of the resonator — mass kilogram |
| ω | variable | Angular resonance frequency — angular frequency radian per second |
| Q | variable | Quality factor of the resonator — quality factor |
| k_B | constant | Boltzmann constant, relates thermal energy to temperature — boltzmann constant = 1.380649e-23 joule per kelvin |
| T_B | variable | brightness temperature — brightness temperature kelvin |
| F_ν | variable | spectral flux density — spectral flux density watt per metre squared per hertz |
| ν | variable | frequency — frequency hertz |
| Ω | variable | solid angle of the source — solid angle steradian |
| c | constant | speed of light in vacuum — speed of light = 299792458 metre per second |
| k_B | constant | relates energy to temperature — boltzmann constant = 1.380649e-23 joule per kelvin |
| \Delta\lambda | variable | Line broadening (full width at half maximum) — line width metre |
| \lambda | variable | Central wavelength of the spectral line — wavelength metre |
| T | variable | Temperature of the emitting/absorbing gas — temperature kelvin |
| m | variable | Mass of the emitting/absorbing particle — mass kilogram |
| c | constant | Speed of light in vacuum — speed of light = 299792458 metre per second |
| k_B | constant | Relates thermal energy to temperature — boltzmann constant = 1.380649e-23 joule per kelvin |
| \sqrt{} | operator | Takes the square root of the argument — square root |





