Polarimetry is a method for measuring the polarization state of light, used in astronomy and remote sensing.Polarimetry is a technique for measuring the polarization state of electromagnetic radiation. Light with a preferred orientation of the electric field is called polarized. The degree of polarization (from 0 to 1) and the angle of orientation provide information about the radiation sources and the propagation medium. Linear polarization arises from scattering by fine dust, reflection; circular polarization arises when passing through a medium with optical activity or anisotropic magnetic fields. In astronomical observations, polarizers and modulators, often with an analyzer, are used to construct polarization maps.
Étienne Malus in 1808 described the phenomenon he called polarization, observing reflected light through a calcite crystal. David Brewster discovered the law of the angle of complete polarization upon reflection (1815). Augustin Fresnel and Dominique Arago investigated the interference of polarized light. James Clerk Maxwell in 1865, while formulating Maxwell's equations, theoretically described electromagnetic waves and included polarization as a vector property. William Lawrence Bragg developed X-ray polarimetry. In astronomy, pioneers were Bernard Lyot (inventor of the polarizing filter for the coronagraph) and William Hiltner, who detected interstellar polarization in 1949.
Light passes through an optical path with polarization elements: first, phase-sensitive modulators (e.g., Pockels cell or rotating half-wave plate) change the polarization state, then an analyzer (polarizer) transmits the component along its axis, and a photodetector records the signal. Modulation allows separating the Stokes parameters by phase. In radio astronomy, polarization is measured by correlating orthogonally polarized channels. The degree of polarization p = sqrt(Q^2+U^2+V^2)/I. Key effects: electron scattering (linear polarization), synchrotron radiation (polarization direction perpendicular to the magnetic field), Zeeman effect (circular polarization in spectral lines), reflection from a surface (Brewster's angle). The principle of superposition and statistical signal processing are at the core.
In industry, polarimetry determines sugar concentration in solutions (saccharimetry). In astronomy, it reveals dust in exoplanet atmospheres and magnetic fields of stars.
Some scarab beetles see circular polarization of the sky, which helps them navigate even when the Sun is hidden by clouds.
| n_e(z') | variable | electron number density at redshift z' — electron number density per cubic metre |
| z | variable | source redshift — redshift |
| z' | variable | integration variable redshift — redshift |
| c | constant | speed of light in vacuum — speed of light = 299792458 metre per second |
| ∫ | operator | summation over redshift from 0 to z — integral operator |
| RM | variable | Rotation measure — rotation measure radian per metre squared |
| n_e | variable | Electron number density — number density per metre cubed |
| B_parallel | variable | Magnetic field component along line of sight — magnetic field tesla |
| s | variable | Path length along line of sight — length metre |
| L | variable | Total path length through plasma — length metre |
| e | constant | Charge of a single electron — elementary charge = 1.602176634e-19 coulomb |
| m_e | constant | Rest mass of an electron — electron mass = 9.1093837015e-31 kilogram |
| c | constant | Speed of light in vacuum — speed of light = 299792458 metre per second |
| ∫ | operator | Integration along the line of sight — integral operator |
| \mathbf{A} | variable | First vector — vector |
| \mathbf{B} | variable | Second vector — vector |
| \theta | variable | Angle between vectors — angle radian |
| \cdot | operator | Dot product of two vectors — dot product |
| \| \cdot \| | operator | Euclidean norm (magnitude) of a vector — euclidean norm |
| P | variable | Degree of linear polarization — polarization degree |
| Q | variable | Stokes parameter Q (linear polarization) — stokes parameter watt per square metre |
| U | variable | Stokes parameter U (linear polarization) — stokes parameter watt per square metre |
| I | variable | Total intensity (Stokes I) — intensity watt per square metre |
| √ | operator | Takes the square root of the sum of squares — square root |
| / | operator | Divides the polarized magnitude by total intensity — division |















