# 28.1.179 Voigt

## Function $y=y_0+A\frac{2\ln 2}{\pi ^{3/2}}\frac{W_L}{W_G^2}\int_{-\infty }^\infty \frac{e^{-t^2}}{\left( \sqrt{\ln 2}\frac{W_L}{W_G}\right) ^2+\left( \sqrt{4\ln 2}\frac{x-x_c}{W_G}-t\right) ^2}dt$

The convolution formula is: $y=y_0+(f_1 * f_2)(x)$

where $f_1\left(x \right)=\frac{2A}{\pi}\frac{w_{L}}{4\left(x-x_c \right )^2+w_{L}^{2}}$

and $f_2\left(x \right)=\sqrt{\frac{4\ln2}{\pi}}\frac{e^{-\frac{4\ln2}{w_{G}^{2}}*x^{2}}}{w_{G}}$

## Brief Description

Convolution of a Gaussian function (wG for FWHM) and a Lorentzian function.

## Sample Curve ## Parameters

Number: 5

Names: y0, xc, A, wG, wL

Meanings: y0 = offset, xc = center, A =area, wG = Gaussian FWHM, wL = Lorentzian FWHM

Lower Bounds: wG > 0.0, wL > 0.0

Upper Bounds: none

## Derived Parameters

Full Width at Half Maximum: FWHM = 0.5346 * wL + sqrt(0.2166 * wL * wL + wG * wG)

## Script Access

nlf_voigt(x,y0,xc,A,wG,wL)

## Function File

FITFUNC\VOIGT5.FDF

## Category

Origin Basic Functions, Peak Functions, PFW, Spectroscopy, Convolution