A spectrometer is an instrument that measures properties of light or particles, such as temperature or spin, often miniaturized.A spectrometer is an instrument for measuring the distribution of electromagnetic radiation by wavelength or frequency. Main components: an entrance slit, a dispersive element (prism or diffraction grating), focusing optics, and a detector (CCD array, photomultiplier). Spectrometers are distinguished by range: ultraviolet, visible, infrared, X-ray, etc. A spectrograph is an instrument that records the entire spectrum simultaneously. Key characteristics are spectral resolution and light throughput.
The history of the spectrometer began with the experiments of Isaac Newton in 1666, who decomposed sunlight with a prism. Newton introduced the term “spectrum,” calling the colored stripe a “ghost” (spectrum). In 1814, Joseph von Fraunhofer, replacing the prism with a diffraction grating of his own making, discovered dark lines in the solar spectrum (Fraunhofer lines) and measured their wavelengths. This laid the foundation for astrospectroscopy. In 1859, Gustav Kirchhoff and Robert Bunsen created the first spectroscope with a gas burner and prism, linking spectral lines to chemical elements. In the 20th century, the development of electronics led to photoelectric registration. Today, space observatories are equipped with spectrometers operating from X-ray to infrared ranges (for example, the STIS instrument on the Hubble telescope).
The principle of an optical spectrometer: the radiation under study passes through an entrance slit to a collimator, which forms a parallel beam. Then the beam hits a dispersing element—for example, a reflective diffraction grating with rules. According to the diffraction condition d(sin α ± sin β) = mλ, where d is the grating period, α and β are the angles of incidence and diffraction, m is the order, light of different wavelengths is deflected at different angles. Then a focusing mirror forms images of the slit in monochromatic light on the detector (CCD line or array). The signal intensity from each pixel is proportional to the photon flux of the corresponding wavelength. Calibration converts pixel number into wavelength. An alternative type is the Fourier spectrometer: it uses a Michelson interferometer, where the interferogram (intensity dependence on path difference) is measured, and the spectrum is recovered by Fourier transformation. The advantage is high resolution and light throughput.
In medicine, mass spectrometers detect traces of drugs in blood, while optical spectrometers test water quality by identifying contaminants.
Every chemical element leaves a unique “fingerprint” in the spectrum—a set of bright lines. This is how astronomers determined that the Sun and other stars are composed mainly of hydrogen and helium.
| n_s | variable | scalar spectral index — scalar spectral index |
| P_R | variable | power spectrum of curvature perturbations — power spectrum |
| k | variable | wavenumber — wavenumber reciprocal metre |
| d/d ln k | operator | derivative with respect to natural logarithm of wavenumber — logarithmic derivative |
| A(ω) | variable | spectral function value at energy ω — spectral function |
| ω | variable | energy variable (frequency) — energy joule |
| n | variable | index labeling excited eigenstates |
| |n⟩ | variable | excited eigenstate of the system — quantum state |
| |0⟩ | variable | ground state of the system — quantum state |
| O | variable | operator whose excitations are probed — operator |
| E_n | variable | energy of excited state n — energy joule |
| E_0 | variable | energy of ground state — energy joule |
| ⟨n|O|0⟩ | operator | inner product of states with operator applied — matrix element |
| δ(...) | operator | selects only contributions at exact energy difference — dirac delta |
| ∑_n | operator | adds contributions from all possible excitations — summation |


















