hyperspy._components.pes_voigt module

class hyperspy._components.pes_voigt.PESVoigt

Bases: hyperspy.component.Component

Voigt component for photoemission spectroscopy data analysis.

Voigt profile component with support for shirley background, non_isochromaticity, transmission_function corrections and spin orbit splitting specially suited for photoemission spectroscopy data analysis.

$f(x) = G(x) \cdot L(x)$

where $G(x)$ is the Gaussian function and $L(x)$ is the Lorentzian function. This component uses an approximate formula by David (see Notes).

Parameters

area (Parameter) – Intensity below the peak.
centre (Parameter) – Location of the maximum of the peak.
FWHM (Parameter) – FWHM = $2 \sigma \sqrt{(2 \log(2))}$ of the Gaussian distribution.
gamma (Parameter) – $\gamma$ of the Lorentzian distribution.
resolution (Parameter) –
shirley_background (Parameter) –
non_isochromaticity (Parameter) –
transmission_function (Parameter) –
spin_orbit_splitting (Bool) –
spin_orbit_branching_ratio (float) –
spin_orbit_splitting_energy (float) –

Notes

Uses an approximate formula according to W.I.F. David, J. Appl. Cryst. (1986). 19, 63-64. doi:10.1107/S0021889886089999

estimate_parameters(signal, E1, E2, only_current=False)

Estimate the Voigt function by calculating the momenta of the Gaussian.

Parameters

signal (Signal1D instance) –
x1 (float) – Defines the left limit of the spectral range to use for the estimation.
x2 (float) – Defines the right limit of the spectral range to use for the estimation.
only_current (bool) – If False estimates the parameters for the full dataset.

Returns

Exit status required for the remove_background() function.

Return type

bool

Notes

Adapted from http://www.scipy.org/Cookbook/FittingData

Examples

>>> g = hs.model.components1D.PESVoigt()
>>> x = np.arange(-10, 10, 0.01)
>>> data = np.zeros((32, 32, 2000))
>>> data[:] = g.function(x).reshape((1, 1, 2000))
>>> s = hs.signals.Signal1D(data)
>>> s.axes_manager[-1].offset = -10
>>> s.axes_manager[-1].scale = 0.01
>>> g.estimate_parameters(s, -10, 10, False)

class hyperspy._components.pes_voigt.Voigt(legacy=True, **kwargs)

Bases: hyperspy.component.Component

This is the legacy Voigt profile component dedicated to photoemission spectroscopy data analysis that will renamed to PESVoigt in v2.0. To use the new Voigt lineshape component set legacy=False. See the documentation of hyperspy._components.voigt.Voigt() for details on the usage of the new Voigt component and hyperspy._components.pes_voigt.PESVoigt() for the legacy component.

$f(x) = G(x) \cdot L(x)$

where $G(x)$ is the Gaussian function and $L(x)$ is the Lorentzian function. This component uses an approximate formula by David (see Notes).

Notes

Uses an approximate formula according to W.I.F. David, J. Appl. Cryst. (1986). 19, 63-64. doi:10.1107/S0021889886089999

hyperspy._components.pes_voigt.voigt(x, FWHM=1, gamma=1, center=0, scale=1)

Voigt lineshape.

The voigt peak is the convolution of a Lorentz peak with a Gaussian peak:

$f(x) = G(x) \cdot L(x)$

where $G(x)$ is the Gaussian function and $L(x)$ is the Lorentzian function. In this case using an approximate formula by David (see Notes). This approximation improves on the pseudo-Voigt function (linear combination instead of convolution of the distributions) and is, to a very good approximation, equivalent to a Voigt function:

$z(x) &= \frac{x + i \gamma}{\sqrt{2} \sigma} \\ w(z) &= \frac{e^{-z^2} \text{erfc}(-i z)}{\sqrt{2 \pi} \sigma} \\ f(x) &= A \cdot \Re\left\{ w \left[ z(x - x_0) \right] \right\}$

Variable	Parameter
$x_0$	center
$A$	scale
$\gamma$	gamma
$\sigma$	sigma

Parameters

gamma (real) – The half-width half-maximum of the Lorentzian.
FWHM (real) – The FWHM = $2 \sigma \sqrt{(2 \log(2))}$ of the Gaussian.
center (real) – Location of the center of the peak.
scale (real) – Value at the highest point of the peak.

Notes

Ref: W.I.F. David, J. Appl. Cryst. (1986). 19, 63-64 doi:10.1107/S0021889886089999