Coherence length
L_c = c·τ_c ≈ λ²/Δλ, the path-length difference beyond which two parts of a light beam stop being able to interfere. Governs the maximum usable path difference in interferometers and holography.
Definition
The coherence length L_c is the maximum path-length difference over which two parts of a light beam still produce detectable interference fringes when recombined. Quantitatively, L_c = c · τ_c, where τ_c is the coherence time, and τ_c ≈ 1/Δν ≈ λ²/(c·Δλ) for a source with bandwidth Δν centred at wavelength λ. Coherence length is set by the monochromaticity of the source: a broadband white-light source has L_c ~ 1 μm; a filtered sodium lamp ~ 0.5 mm; a He–Ne laser with a 1 GHz linewidth ~ 30 cm; a stabilised He–Ne or single-mode diode laser with 1 kHz linewidth ~ 300 km.
The practical consequence is the maximum usable path-length difference in interferometry. Michelson interferometers for precision length measurement need the two arms matched to within L_c; Fourier-transform infrared (FTIR) spectrometers scan a mirror over the coherence length of the source to build up the autocorrelation function from which the spectrum is recovered. In holography, coherence length sets how deep an object can be in the recording volume — old He–Ne holography was limited to objects a few centimetres deep, while modern stabilised-laser systems hologram entire rooms. Coherence length is related but not identical to coherence area, the transverse extent over which the beam's phase is correlated; the two together characterise the full coherence volume of a light field.