\(\renewcommand\AA{\unicode{x212B}}\)

Gaussian¶

Description¶

A Gaussian function (also referred to as a normal distribution) is defined as:

\[\mbox{Height}*\exp \left( -0.5*\frac{(x-\mbox{PeakCentre})^2}{\mbox{Sigma}^2} \right)\]

where

Height - height of peak
PeakCentre - centre of peak
Sigma - Gaussian width parameter

Note that the FWHM (Full Width Half Maximum) of a Gaussian equals \(2\sqrt{2\ln 2}*\mbox{Sigma}\).

The integrated peak intensity for the Gaussian is given by \(\mbox{height} * \mbox{sigma} * \sqrt{2\pi}\).

The uncertainty for the intensity is: \(\mbox{intensity} * \sqrt{\left(\frac{\delta \mbox{height}}{\mbox{height}}\right)^2 + \left(\frac{\delta \mbox{sigma}}{\mbox{sigma}}\right)^2}\).

The figure below illustrate this symmetric peakshape function fitted to a TOF peak:

Properties (fitting parameters)¶

Name	Default	Description
Height	0.0	Height of peak
PeakCentre	0.0	Centre of peak
Sigma	0.0	Width parameter

Categories: FitFunctions | Peak

Source¶

C++ header: Gaussian.h (last modified: 2021-05-26)

C++ source: Gaussian.cpp (last modified: 2021-05-26)