
Lidar uses laser light to detect and measure properties of distant objects through backscattered light.Lidar (Light Detection and Ranging) is a remote sensing technology that fires laser pulses at a target and measures the time and properties of the light that bounces back. By analyzing the backscattered signal, lidar can map distances, velocities, and even the composition of distant objects. It is the optical analogue of radar, but uses much shorter wavelengths, allowing for far finer spatial resolution.
The concept dates back to the 1930s, but the first practical lidar systems were developed in the 1960s shortly after the invention of the laser. Early work by the MIT Lincoln Laboratory and NASA laid the groundwork for atmospheric and topographic mapping.
A lidar system emits a short laser pulse. The pulse travels to the target, scatters off it, and a fraction of the light returns to a detector. The round-trip time gives the distance. By scanning the beam, a 3D map is built. More advanced lidar uses the polarization, spectral shift, or intensity of the return signal to infer material properties — for example, distinguishing water droplets from ice crystals in clouds by their different backscattering and depolarization signatures. Recent developments include using the 'glint' or mirror-like reflection from oriented ice crystals to improve cloud phase discrimination.
Lidar is used in autonomous vehicles for obstacle detection, in atmospheric science for cloud and aerosol profiling, in archaeology for mapping forest-covered ruins, and in planetary exploration (e.g., Mars orbiter laser altimetry).
Lidar can measure wind speed and turbulence by analyzing the Doppler shift of the backscattered light from tiny aerosol particles moving with the air.
| C^ell | variable | Angular power spectrum at multipole ell — angular power spectrum |
| z | variable | Redshift — redshift |
| H(z) | variable | Hubble parameter at redshift z — hubble parameter kilometre per second per megaparsec |
| chi(z) | variable | Comoving distance to redshift z — comoving distance metre |
| W(z) | variable | Window function (selection function) at redshift z — window function |
| P(k,z) | variable | Three-dimensional power spectrum at wavenumber k and redshift z — power spectrum cubic metre |
| k | variable | Wavenumber — wavenumber reciprocal metre |
| ell | variable | Multipole moment — multipole moment |
| c | constant | Fundamental constant relating distance and time in relativity — speed of light = 299792458 metre per second |
| ∫ dz | operator | Sum over all redshifts along the line of sight — integral operator |























