hyperspy._components.voigt module

class hyperspy._components.voigt.Voigt(centre=10.0, area=1.0, gamma=0.2, sigma=0.1, module=['numpy', 'scipy'], **kwargs)

Bases: Expression

Voigt component.

Symmetric peak shape based on the convolution of a Lorentzian and Normal (Gaussian) distribution:

\[f(x) = G(x) \cdot L(x)\]

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:

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

Variable

Parameter

\(x_0\)

centre

\(A\)

area

\(\gamma\)

gamma

\(\sigma\)

sigma
Parameters:

  • centre (float) – Location of the maximum of the peak.

  • area (float) – Intensity below the peak.

  • gamma (float) – \(\gamma\) = HWHM of the Lorentzian distribution.

  • sigma (float) – \(2 \sigma \sqrt{(2 \log(2))}\) = FWHM of the Gaussian distribution.

  • **kwargs – Extra keyword arguments are passed to the Expression component.

Notes

For convenience the gwidth and lwidth attributes can also be used to set and get the FWHM of the Gaussian and Lorentzian parts of the distribution, respectively. For backwards compatability, FWHM is another alias for the Gaussian width.

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

estimate_parameters(signal, x1, x2, 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 https://scipy-cookbook.readthedocs.io/items/FittingData.html

Examples

>>> g = hs.model.components1D.Voigt(legacy=False)
>>> 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)