|
, ~~~z=\frac }} In spectroscopy, the Voigt profile (named after Woldemar Voigt) is a line profile resulting from the convolution of two broadening mechanisms, one of which alone would produce a Gaussian profile (usually, as a result of the Doppler broadening), and the other would produce a Lorentzian profile. Voigt profiles are common in many branches of spectroscopy and diffraction. Due to the computational expense of the convolution operation, the Voigt profile is often approximated using a pseudo-Voigt profile. All normalized line profiles can be considered to be probability distributions. The Gaussian profile is equivalent to a Gaussian or normal distribution and a Lorentzian profile is equivalent to a Lorentz or Cauchy distribution. Without loss of generality, we can consider only centered profiles which peak at zero. The Voigt profile is then a convolution of a Lorentz profile and a Gaussian profile: : where ''x'' is frequency from line center, is the centered Gaussian profile: : and is the centered Lorentzian profile: : The defining integral can be evaluated as: : ==Properties== The Voigt profile is normalized: : since it is the convolution of normalized profiles. The Lorentzian profile has no moments (other than the zeroth) and so the moment-generating function for the characteristic function for the Cauchy distribution is well defined, as is the characteristic function for the normal distribution. The characteristic function (probability theory) 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Voigt profile」の詳細全文を読む スポンサード リンク
|