Lineshapes

Lineshapes, in the context of spectroscopy and related fields, describe how the intensity of light near an optical transition varies as a function of frequency or wavelength. A spectral line is not infinitely sharp; its shape reflects the distribution of resonant frequencies for the transition and is influenced by several broadening mechanisms and instrumental effects.

The main broadening mechanisms include natural broadening from the finite lifetime of excited states, Doppler broadening from thermal motion of emitters or absorbers, collisional (pressure) broadening due to interactions with other particles, and instrumental broadening from the measurement apparatus. These mechanisms combine in different ways to produce characteristic line shapes.

Common line shapes are Gaussian, Lorentzian, and Voigt. Gaussian shapes arise mainly from Doppler broadening, Lorentzian shapes from natural and pressure broadening, and the Voigt profile is a convolution of Gaussian and Lorentzian components, representing systems with multiple broadening effects. In practice, line shapes are often approximated by a Gaussian, Lorentzian, or a pseudo-Voigt function, and more complex profiles may be used for blended or asymmetric lines.

Key parameters include the central frequency (or wavelength), the width of the line (often described by the full width at half maximum, FWHM), and the amplitude. Analyzing lineshapes through fitting allows extraction of physical quantities such as temperature, pressure, concentration, or velocity distributions, and helps separate intrinsic line properties from instrumental effects.

Lineshapes are fundamental in spectroscopy, astronomy, plasma diagnostics, and chemical analysis, where accurate peak characterization informs interpretation and modeling.