magtomo.Reconstruction.Reconstruction#

class Reconstruction(magnetization, rotations, projections, pol=1j, iterations=10, mask=None, learning_parameter=10)#

Bases: Experiment

Performs a reconstruction from dichroic projections, inherits the properties that are specified by an magtomo.Experiment.Experiment.

Parameters:

magnetizationnp.ndarray: The initial guess for the magnetization.
rotationsnp.ndarray: Stack of rotation matrices describing the sample orientations that were measured; shaped (n, 3, 3).
projectionsnp.ndarray: Stack of projections obtained at the corresponding rot value.
polarray_like (optional): Single polarization used for all projections, stack of polarizations matching the number of projections or stack of polarization pairs. Linear polarization represented using values from 0 to 180 (in degrees). Circular left and right polarization represented using complex ±1j.
iterationsint (optional): Number of reconstruction iterations to perform.
masknp.ndarray (optional): Binary mask for the magnetization.
learning_parameterfloat (optional): The learning parameter for gradient descent.

Methods

`calc_error_norm`	Calculates a normalization factor (number of pixels in the projections) for scaling the error metric.
`calculate_sinogram`	Calculates the sinogram.
`configuration_error`	Computes the error between the current reconstruction and a provided reference.
`orientation_to_tensor`
`plot_sinogram`	Plots the calculated sinogram.
`reconstruct`	Performs the reconstructions and updates the magnetization.
`tensor_to_orientation`
`theta_error`	Computes the angular difference between the current reconstruction and a provided reference.

Attributes

`error_metric`	The error metric value at each iteration.
`iterations`	The number of reconstruction iterations.
`learning_parameter`	The learning parameter for gradient descent.
`magnetization`	The magnetic configuration of the sample.
`mask`	Binary mask for the magnetization.
`order`	The interpolation order for performing rotations.
`pol`	The polarization of the incident beam.
`projections`	The measured projections.
`rotations`	The stack of measured orientation described by rotation matrices.
`sinogram`	The calculated sinogram.

calc_error_norm()#

Calculates a normalization factor (number of pixels in the projections) for scaling the error metric.

Returns:

int: The normalization factor (number of pixels in the projections).

calculate_sinogram()#: Calculates the sinogram.

configuration_error(reference, axial=False)#

Computes the error between the current reconstruction and a provided reference.

Parameters:

referencenp.ndarray: Reference structure as a numpy array that will be compared with the current reconstruction.
axialbool (optional): Set to True if reconstructing orientation fields (e.g. linear dichroic projections).

Returns:

float: The configuration error.

Notes

The configuration error, \(\varepsilon_c\) is evaluated for directional (vector) and axial (orientation) fields using:

\[\begin{split}\varepsilon_c = \begin{cases} \vec{m}_r - \vec{m} & \text{directional} \\ \min\left(\left\lvert \vec{m}_r - \vec{m} \right\rvert, \left\lvert \vec{m}_r + \vec{m} \right\rvert\right) & \text{axial} \end{cases}\end{split}\]

where \(\vec{m}_r\) is the reconstruction and \(\vec{m}\) is the reference.

property error_metric#: The error metric value at each iteration.

property iterations#: The number of reconstruction iterations.

property learning_parameter#: The learning parameter for gradient descent.

property magnetization#: The magnetic configuration of the sample.

property mask#: Binary mask for the magnetization.

property order#: The interpolation order for performing rotations.

plot_sinogram(cmap='Spectral')#: Plots the calculated sinogram.

property pol#: The polarization of the incident beam.

property projections#: The measured projections.

reconstruct()#: Performs the reconstructions and updates the magnetization.

property rotations#: The stack of measured orientation described by rotation matrices.

property sinogram#: The calculated sinogram.

theta_error(reference, axial=False)#

Computes the angular difference between the current reconstruction and a provided reference.

Parameters:

referencenp.ndarray: Reference structure as a numpy array that will be compared with the current reconstruction.
axialbool (optional): Set to True if reconstructing orientation fields (e.g. linear dichroic projections).

Returns:

float: The angular error in radians.

Parameters:

reference (ndarray)
axial (bool)

Notes

The angular error, \(\varepsilon_\theta\) is evaluated for directional (vector) and axial (orientation) fields using:

\[\begin{split}\varepsilon_c = \begin{cases} \arccos\left( \frac{\vec{m_r} \cdot \vec{m}}{|\vec{m_r}||\vec{m}|} \right) & \text{directional} \\ \arccos\left( \frac{\left\lvert \vec{m_r} \cdot \vec{m} \right\rvert}{|\vec{m_r}| |\vec{m}|} \right) & \text{axial} \end{cases}\end{split}\]

where \(\vec{m}_r\) is the reconstruction and \(\vec{m}\) is the reference.