Voigt
Contents |
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
Voigt peak 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_voigt5(x,y0,xc,A,wG,wL)
Function File
FITFUNC\VOIGT5.FDF
Category
Origin Basic Functions, Peak Functions, PFW, Spectroscopy, Convolution