Lorentz2D

Contents 1 Function 2 Brief Description 3 Sample Curve 4 Parameters 5 Derived Parameters 6 Script Access 7 Function File

Function

\[z=z_0+\frac A{\left[ 1+\left( \frac{x-x_c}{w_1}\right) ^2\right] \left[ 1+\left( \frac{y-y_c}{w_2}\right) ^2\right] }\]

Brief Description

Non-linear Sigmoid (Logistic Cumulative) Function

Sample Curve

Parameter

Number: 6

Name:	Meanings:	Lower Bounds:	Upper Bounds:
\[z_0\]	z offset
A	height
\[x_c\]	x center
\[w_1\]	x width	\[w_1>0\]
\[y_c\]	y center
\[w_2\]	y width	\[w_2>0\]

Derived Parameters

\[FWHM_x=2w_1\]

\[FWHM_y=2w_2\]

\[Volume=Aw_1w_2\pi^2\]

Script Access

Function File

fitfunc\Lorentz2D.fdf