abtem.waves

`abtem.waves`#

Module for describing wave functions of the electron beam and the exit wave.

Module Contents#

Classes#

`BaseWaves`	Base class of all wave functions.
`EnergyEnsemble`	Wraps electron energy for use inside the WavesBuilder ensemble machinery.
`PlaneWave`	Represents electron probe wave functions for simulating experiments with a plane- wave probe, such as HRTEM and SAED.
`Probe`	Represents electron-probe wave functions for simulating experiments with a convergent beam, such as CBED and STEM.
`Waves`	Waves define a batch of arbitrary 2D wave functions defined by a complex array.
`WavesBuilder`

Functions#

`reduce_ensemble`	Reduce an ensemble of wave functions or measurements by squeezing or averaging ensemble axes tagged for reduction with the “_squeeze” or “_ensemble_mean” attribute of the axis metadata.
`validate_energy`	Convert energy (float, list, distribution, or EnergyEnsemble) to EnergyEnsemble.

API#

class abtem.waves.BaseWaves[source]#

Bases: abtem.core.grid.HasGrid2DMixin, abtem.core.energy.HasAcceleratorMixin

Base class of all wave functions.

Documented in the subclasses.

property angular_sampling: tuple[float, float]#: Reciprocal-space sampling in units of scattering angles [mrad].

property antialias_cutoff_gpts: tuple[int, int]#: The number of grid points along the x and y direction in the simulation grid at the antialiasing cutoff scattering angle.

property antialias_valid_gpts: tuple[int, int]#: The number of grid points along the x and y direction in the simulation grid for the largest rectangle that fits within antialiasing cutoff scattering angle.

property base_axes_metadata: list[AxisMetadata]#: List of AxisMetadata for the base axes in real space.

property cutoff_angles: tuple[float, float]#: Scattering angles at the antialias cutoff [mrad].

property cutoff_frequencies: tuple[float, float]#: Spatial frequencies at the antialias cutoff [1/Å].

abstract property device: str#: The device where the waves are built or stored.

property dtype: dtype#: The datatype of waves.

property full_cutoff_angles: tuple[float, float]#: Scattering angles corresponding to the full wave function size [mrad].

abstract property metadata: dict#: Metadata stored as a dictionary.

property reciprocal_space_axes_metadata: list[AxisMetadata]#: List of AxisMetadata for base axes in reciprocal space.

property rectangle_cutoff_angles: tuple[float, float]#: Scattering angles corresponding to the sides of the largest rectangle within the antialias cutoff [mrad].

class abtem.waves.EnergyEnsemble(...)[source]#

Bases: abtem.distributions.EnsembleFromDistributions

Wraps electron energy for use inside the WavesBuilder ensemble machinery.

Accepts a scalar float, a list/array of floats, or a BaseDistribution. When a single value is given, the object behaves like a plain scalar. When multiple values are given, it acts as an ensemble axis and causes WavesBuilder subclasses to produce output with a leading EnergyAxis.

The energy property returns:

float — for a scalar energy or a single-element sequence.
BaseDistribution — for a genuine multi-energy ensemble.
None — if no energy has been set.

Initialization

property energy#

Return the energy value(s).

Returns:

float – The scalar energy [eV] if a single value was given.
BaseDistribution – The full distribution if multiple values were given.
None – If no energy has been set.

property ensemble_axes_metadata: list#

class abtem.waves.PlaneWave(...)[source]#

Bases: abtem.waves.WavesBuilder

Represents electron probe wave functions for simulating experiments with a plane- wave probe, such as HRTEM and SAED.

Parameters:

extent (two float, optional) – Lateral extent of the wave function [Å].
gpts (two int, optional) – Number of grid points describing the wave function.
sampling (two float, optional) – Lateral sampling of the wave functions [Å]. If ‘gpts’ is also given, will be ignored.
energy (float or list of float, optional) – Electron energy [eV]. A single float gives a standard single-energy simulation. A list or array of floats runs the simulation at each energy in turn and returns output with a leading EnergyAxis ensemble dimension. If not provided, the energy must be inferred from attached wave functions.
normalize (bool, optional) – If true, normalizes the wave function such that its reciprocal space intensity sums to one. If false, the wave function takes a value of one everywhere.
tilt (two float, optional) – Small-angle beam tilt [mrad] (default is (0., 0.)). Implemented by shifting the wave functions at every slice.
device (str, optional) – The wave functions are stored on this device (‘cpu’ or ‘gpu’). The default is determined by the user configuration.

Initialization

build(...) → Waves[source]#

Build plane-wave wave functions.

Parameters:

lazy (bool, optional) – If True, create the wave functions lazily, otherwise, calculate instantly. If not given, defaults to the setting in the user configuration file.
max_batch (int or str, optional) – The number of wave functions in each chunk of the Dask array. If ‘auto’ (default), the batch size is automatically chosen based on the abtem user configuration settings “dask.chunk-size” and “dask.chunk-size-gpu”.

Returns:

plane_waves – The wave functions.

Return type:

Waves

check_can_build()[source]#

property energy#

property metadata#

multislice(...) → BaseMeasurements | Waves | list[BaseMeasurements | Waves][source]#

Run the multislice algorithm, after building the plane-wave wave function as needed. The grid of the wave functions will be set to the grid of the potential.

Parameters:

potential (BasePotential, Atoms) – The potential through which to propagate the wave function. Optionally atoms can be directly given.
detectors (Detector, list of detectors, optional) – A detector or a list of detectors defining how the wave functions should be converted to measurements after running the multislice algorithm.
max_batch (int, optional) – The number of wave functions in each chunk of the Dask array. If ‘auto’ (default), the batch size is automatically chosen based on the abtem user configuration settings “dask.chunk-size” and “dask.chunk-size-gpu”.
lazy (bool, optional) – If True, create the wave functions lazily, otherwise, calculate instantly. If None, this defaults to the setting in the user configuration file.
potential_chunk_size (int or str, optional) – Number of potential slices to build and hold in memory at once. "auto" (default) selects a size based on the available memory budget. Smaller values reduce peak memory at the cost of more build overhead. Can be set globally via the potential.slice-chunk-size configuration key.
**multislice_func_kwargs – Additional keyword arguments passed to the multislice function.

Returns:

measurements (BaseMeasurements or ComputableList of BaseMeasurements) – The detected measurement (if detector(s) given).
exit_waves (Waves) – Wave functions at the exit plane(s) of the potential (if no detector(s) given).

property normalize#: True if the created waves are normalized in reciprocal space.

property tilt#: The small-angle tilt of applied to the Fresnel propagator [mrad].

class abtem.waves.Probe(...)[source]#

Bases: abtem.waves.WavesBuilder

Represents electron-probe wave functions for simulating experiments with a convergent beam, such as CBED and STEM.

Parameters:

semiangle_cutoff (float, optional) – The cutoff semiangle of the aperture [mrad]. Ignored if a custom aperture is given.
extent (float or two float, optional) – Lateral extent of wave functions [Å] in x and y directions. If a single float is given, both are set equal.
gpts (two ints, optional) – Number of grid points describing the wave functions.
sampling (two float, optional) – Lateral sampling of wave functions [Å]. If ‘gpts’ is also given, will be ignored.
energy (float or list of float, optional) – Electron energy [eV]. A single float gives a standard single-energy simulation. A list or array of floats runs the simulation at each energy in turn and returns output with a leading EnergyAxis ensemble dimension. If not provided, the energy must be inferred from attached wave functions.
soft (bool, optional) – If True, the edge of the default aperture is softened (default is True). Ignored if a custom aperture is given.
tilt (two float, two 1D BaseDistribution, 2D BaseDistribution,)
optional – Small-angle beam tilt [mrad]. This value should generally not exceed one degree.
device (str, optional) – The probe wave functions will be build and stored on this device (‘cpu’ or ‘gpu’). The default is determined by the user configuration.
aperture (BaseAperture, optional) – An optional custom aperture. The provided aperture should be a subtype of BaseAperture.
aberrations (dict or Aberrations) – The phase aberrations as a dictionary.
transforms (list of WaveTransform) – A list of additional wave function transforms which will be applied after creation of the probe wave functions.
kwargs – Provide the aberrations as keyword arguments, forwarded to the Aberrations.

Initialization

property aberrations: Aberrations#: Phase aberrations of the probe wave functions.

property aperture: BaseAperture#: Condenser or probe-forming aperture.

build(...) → Waves[source]#

Build probe wave functions at the provided positions.

Parameters:

scan (array of xy-positions or BaseScan, optional) – Positions of the probe wave functions. If not given, scans across the entire potential at Nyquist sampling.
max_batch (int, optional) – The number of wave functions in each chunk of the Dask array. If ‘auto’ (default), the batch size is automatically chosen based on the abtem user configuration settings “dask.chunk-size” and “dask.chunk-size-gpu”.
lazy (bool, optional) – If True, create the wave functions lazily, otherwise, calculate instantly. If not given, defaults to the setting in the user configuration file.

Returns:

probe_wave_functions – The built probe wave functions.

Return type:

Waves

check_can_build()[source]#

property ctf#: Contrast transfer function describing the probe.

property energy#

property metadata: dict#: Metadata describing the probe wave functions.

multislice(...) → Waves | BaseMeasurements | list[Waves | BaseMeasurements][source]#

Run the multislice algorithm for probe wave functions at the provided positions.

Parameters:

potential (BasePotential or Atoms) – The scattering potential. Optionally atoms can be directly given.
scan (array of xy-positions or BaseScan, optional) – Positions of the probe wave functions. If not given, scans across the entire potential at Nyquist sampling.
detectors (BaseDetector or list of BaseDetector, optional) – A detector or a list of detectors defining how the wave functions should be converted to measurements after running the multislice algorithm. If not given, defaults to the flexible annular detector.
max_batch (int, optional) – The number of wave functions in each chunk of the Dask array. If ‘auto’ (default), the batch size is automatically chosen based on the abtem user configuration settings “dask.chunk-size” and “dask.chunk-size-gpu”.
lazy (bool, optional) – If True, create the wave functions lazily, otherwise, calculate instantly. If None, this defaults to the setting in the user configuration file.
**multislice_func_kwargs – Additional keyword arguments passed to the multislice function.

Returns:

measurements

Return type:

BaseMeasurements or Waves or list of BaseMeasurements

profiles(...) → RealSpaceLineProfiles[source]#

Create a line profile through the center of the probe.

Parameters:: angle (float, optional) – Angle with respect to the x-axis of the line profile [degree].

scan(...) → BaseMeasurements | Waves | list[BaseMeasurements | Waves][source]#

Run the multislice algorithm from probe wave functions over the provided scan.

Parameters:

potential (BasePotential or Atoms) – The scattering potential.
scan (BaseScan) – Positions of the probe wave functions. If not given, scans across the entire potential at Nyquist sampling.
detectors (BaseDetector, list of BaseDetector, optional) – A detector or a list of detectors defining how the wave functions should be converted to measurements after running the multislice algorithm. See abtem.measurements.detect for a list of implemented detectors.
max_batch (int, optional) – The number of wave functions in each chunk of the Dask array. If ‘auto’ (default), the batch size is automatically chosen based on the abtem user configuration settings “dask.chunk-size” and “dask.chunk-size-gpu”.
lazy (bool, optional) – If True, create the measurements lazily, otherwise, calculate instantly. If None, this defaults to the value set in the configuration file.
**multislice_func_kwargs – Additional keyword arguments passed to the multislice function.

Returns:

detected_waves (BaseMeasurements or list of BaseMeasurements) – The detected measurement (if detector(s) given).
exit_waves (Waves) – Wave functions at the exit plane(s) of the potential (if no detector(s) given).

property scan_positions: BaseScan#: The position(s) of the probe.

property semiangle_cutoff#: The semiangle cutoff [mrad].

show(...) → abtem.visualize.Visualization[source]#

Show the intensity of the probe wave function.

Parameters:

complex_images (bool) – If true shows complex images using domain-coloring instead of the intensity.
kwargs (Keyword arguments for the Images.show() function.)

property soft#: True if the aperture has a soft edge.

transition_potential_scan(...) → Waves | BaseMeasurements | list[Waves | BaseMeasurements][source]#

Run the inelastic multislice algorithm for probe wave functions over the provided scan, using transition potentials to model core-loss excitations.

Parameters:

potential (BasePotential or Atoms) – The scattering potential through which to propagate the probe.
transition_potentials (BaseTransitionPotential or list of BaseTransitionPotential) – The transition potential(s) describing the core-loss excitation(s).
scan (array of xy-positions or BaseScan, optional) – Positions of the probe wave functions. If not given, scans across the entire potential at Nyquist sampling.
detectors (BaseDetector or list of BaseDetector, optional) – A detector or list of detectors defining how the wave functions are converted to measurements. If not given, defaults to FlexibleAnnularDetector. See abtem.measurements for the implemented detectors.
sites (SliceIndexedAtoms or Atoms, optional) – The sites at which inelastic scattering events are evaluated. If not given, all atoms of the species matching the transition potential are used.
max_batch (int or str, optional) – The number of probe wave functions in each chunk of the Dask array. If ‘auto’ (default), the batch size is chosen from the abtem configuration (dask.chunk-size / dask.chunk-size-gpu).
lazy (bool, optional) – If True, build measurements lazily; otherwise compute eagerly. Defaults to the value set in the user configuration file.
**multislice_func_kwargs – Additional keyword arguments forwarded to the inelastic multislice function (e.g. double_channel, threshold).

Returns:

measurements – The detected measurements for each scan position. If multiple transition potentials are given, an additional ensemble axis distinguishes them.

Return type:

BaseMeasurements or Waves or list of BaseMeasurements

class abtem.waves.Waves(...)[source]#

Bases: abtem.waves.BaseWaves, abtem.array.ArrayObject

Waves define a batch of arbitrary 2D wave functions defined by a complex array.

Parameters:

array (array) – Complex array defining one or more 2D wave functions. The second-to-last and last dimensions are the wave function y- and x-axes, respectively.
energy (float) – Electron energy [eV].
extent (one or two float) – Extent of wave functions in x and y [Å].
sampling (one or two float) – Sampling of wave functions in x and y [Å].
reciprocal_space (bool, optional) – If True, the wave functions are assumed to be represented in reciprocal space instead of real space (default is False).
ensemble_axes_metadata (list of AxesMetadata) – Axis metadata for each ensemble axis. The axis metadata must be compatible with the shape of the array.
metadata (dict) – A dictionary defining wave function metadata. All items will be added to the metadata of measurements derived from the waves.

Initialization

property angular_sampling: tuple[float, float]#

Reciprocal-space sampling in units of scattering angles [mrad].

For a single-energy object the exact energy is used. For an indexed member of an energy ensemble the per-member energy stored in metadata["energy"] is used. For the full multi-member ensemble the maximum energy (shortest wavelength) is used so that the grid is conservative — it covers all members without aliasing.

apply_ctf(...) → Waves[source]#

Apply the aberrations and apertures of a contrast transfer function to the wave functions.

Parameters:

ctf (CTF, optional) – Contrast transfer function to be applied.
max_batch (int, optional) – The number of wave functions in each chunk of the Dask array. If ‘auto’ (default), the batch size is automatically chosen based on the abtem user configuration settings “dask.chunk-size” and “dask.chunk-size-gpu”.
kwargs – Provide the parameters of the contrast transfer function as keyword arguments (see CTF).

Returns:

aberrated_waves – The wave functions with the contrast transfer function applied.

Return type:

Waves

property base_tilt: tuple[float, float]#: The base small-angle beam tilt (i.e. the beam tilt not associated with an ensemble axis) applied to the Fresnel propagator [mrad].

convolve(...) → Waves[source]#

Convolve the wave-function array with a given array.

Parameters:

kernel (ndarray) – Array to be convolved with.
axes_metadata (list of AxisMetadata, optional) – Metadata for the resulting convolved array. Needed only if the given array has more than two dimensions.
out_space (str, optional) – Space in which the convolved array is represented. Options are ‘reciprocal_space’ and ‘real_space’ (default is the space of the wave functions).
in_place (bool, optional) – If True, the array representing the waves may be modified in-place.

Returns:

convolved – The convolved wave functions.

Return type:

Waves

depth_profile(...) → Images[source]#

Create a depth profile by projecting wave functions along a spatial axis.

Requires wave functions with a thickness dimension, i.e. from a multislice simulation with exit_planes.

Parameters:

projection_axis (str) – Spatial axis to project (sum) along. "y" (default) produces an x–z cross-section; "x" produces a y–z cross-section.
depth (float, optional) – If given, project only over a finite slab of this thickness [Å], centered on the midpoint of the projected axis. The number of grid points is rounded to the nearest integer. If None, the full extent is projected.
convert_complex (str) – How to convert the complex wave function before projecting. One of "intensity" (default), "phase", "real", or "imag".

Returns:

depth_profile – 2D image(s) with the depth (z) as the first base axis and the remaining spatial axis as the second. Any additional ensemble axes (e.g. scan positions) are preserved.

Return type:

Images

property device: str#: The device where the array is stored.

diffraction_patterns(...) → DiffractionPatterns[source]#

Calculate the intensity of the wave functions at the diffraction plane.

Parameters:

max_angle ({'cutoff', 'valid', 'full'} or float) –
Control the maximum scattering angle of the diffraction patterns.

cutoff :
Downsample to the antialias cutoff scattering angle (default).

valid :
Downsample to the largest rectangle that fits inside the circle with a radius defined by the antialias cutoff scattering angle.

full :
The diffraction patterns are not cropped, and hence the antialiased region is included.

float :
Downsample to a maximum scattering angle specified by a float [mrad].
block_direct (bool or float, optional) – If True the direct beam is masked (default is False). If given as a float, masks up to that scattering angle [mrad].
fftshift (bool, optional) – If False, do not shift the direct beam to the center of the diffraction patterns (default is True).
parity ({'same', 'even', 'odd', 'none'}) – The parity of the shape of the diffraction patterns. Default is ‘odd’, so that the shape of the diffraction pattern is odd with the zero at the middle.
renormalize (bool, optional) – If true and the wave function intensities were normalized to sum to the number of pixels in real space, i.e. the default normalization of a plane wave, the intensities are to sum to one in reciprocal space.
return_complex (bool) – If True, return complex-valued diffraction patterns (i.e. the wave function in reciprocal space) (default is False).

Returns:

diffraction_patterns – The diffraction pattern(s).

Return type:

DiffractionPatterns

downsample(...) → Waves[source]#

Downsample the wave functions to a lower maximum scattering angle.

Parameters:

max_angle ({'cutoff', 'valid'} or float, optional) –
Controls the downsampling of the wave functions.

cutoff :
Downsample to the antialias cutoff scattering angle (default).

valid :
Downsample to the largest rectangle that fits inside the circle with a radius defined by the antialias cutoff scattering angle.

float :
Downsample to a maximum scattering angle specified by a float [mrad].
gpts (two int, optional) – Number of grid points of the wave functions after downsampling. If given, max_angle is not used.
normalization ({'values', 'amplitude'}) –
The normalization parameter determines the preserved quantity after normalization.

values :
The pixel-wise values of the wave function are preserved (default).

amplitude :
The total amplitude of the wave function is preserved.

Returns:

downsampled_waves – The downsampled wave functions.

Return type:

Waves

ensure_real_space(...) → Waves[source]#

Transform to real space if the wave functions are represented in reciprocal space.

Parameters:: overwrite_x (bool, optional) – If True, modify the array in place; otherwise a copy is created (default is False).
Returns:: waves_in_real_space – The wave functions in real space.
Return type:: Waves

ensure_reciprocal_space(...) → Waves[source]#

Transform to reciprocal space if the wave functions are represented in real space.

Parameters:: overwrite_x (bool, optional) – If True, modify the array in place; otherwise a copy is created (default is False).
Returns:: waves_in_reciprocal_space – The wave functions in reciprocal space.
Return type:: Waves

classmethod from_array_and_metadata(...) → Waves[source]#

Creates wave functions from a given array and metadata.

Parameters:

array (array) – Complex array defining one or more 2D wave functions. The second-to-last and last dimensions are the wave function y- and x-axis, respectively.
axes_metadata (list of AxesMetadata) – Axis metadata for each axis. The axis metadata must be compatible with the shape of the array. The last two axes must be RealSpaceAxis.
metadata – A dictionary defining wave function metadata. All items will be added to the metadata of measurements derived from the waves. The metadata must contain the electron energy [eV].

Returns:

wave_functions – The created wave functions.

Return type:

Waves

imag() → Images[source]#

Calculate the imaginary part of the wave functions.

Returns:: imaginary_images – The imaginary part of the wave functions.
Return type:: Images

intensity() → Images[source]#

Calculate the intensity of the wave functions.

Returns:: intensity_images – The intensity of the wave functions.
Return type:: Images

property metadata: dict#

multislice(...) → Waves | BaseMeasurements | list[Waves | BaseMeasurements][source]#

Propagate and transmit wave function through the provided potential using the multislice algorithm. When detector(s) are given, output will be the corresponding measurement.

Parameters:

potential (BasePotential or ASE.Atoms) – The potential through which to propagate the wave function. Optionally atoms can be directly given.
detectors (BaseDetector or list of BaseDetector, optional) – A detector or a list of detectors defining how the wave functions should be converted to measurements after running the multislice algorithm. See abtem.measurements.detect for a list of implemented detectors. If not given, returns the wave functions themselves.
potential_chunk_size (int or str, optional) – Number of potential slices to build and hold in memory at once. "auto" (default) selects a size based on the available memory budget. Smaller values reduce peak memory at the cost of more build overhead. Can be set globally via the potential.slice-chunk-size configuration key.
**multislice_func_kwargs – Additional keyword arguments passed to the multislice function.

Returns:

detected_waves (BaseMeasurements or list of BaseMeasurements) – The detected measurement (if detector(s) given).
exit_waves (Waves) – Wave functions at the exit plane(s) of the potential (if no detector(s) given).

normalize(...) → Waves[source]#

Normalize the wave functions in real or reciprocal space.

Parameters:

space (str) – Should be one of ‘real’ or ‘reciprocal’ (default is ‘reciprocal’). Defines whether the wave function should be normalized such that the intensity sums to one in real or reciprocal space.
in_place (bool, optional) – If True, the array representing the waves may be modified in-place.

Returns:

normalized_waves – The normalized wave functions.

Return type:

Waves

phase() → Images[source]#

Calculate the phase of the wave functions.

Returns:: phase_images – The phase of the wave functions.
Return type:: Images

phase_shift(...) → Waves[source]#

Shift the phase of the wave functions.

Parameters:: amount (float) – Amount of phase shift [rad].
Returns:: phase_shifted_waves – The shifted wave functions.
Return type:: Waves

phonon_loss_diffraction_patterns(...)[source]#: Compute inelastic (TDS) diffraction patterns from energy-resolved frozen-phonon exit waves. See abtem.measurements.phonon_loss_diffraction_patterns() for full documentation.

real() → Images[source]#

Calculate the real part of the wave functions.

Returns:: real_images – The real part of the wave functions.
Return type:: Images

property reciprocal_space: bool#: True if the waves are represented in reciprocal space.

scan(...) → Waves | BaseMeasurements | list[Waves | BaseMeasurements][source]#

Run the multislice algorithm from probe wave functions over the provided scan.

Parameters:

potential (BasePotential or Atoms) – The scattering potential.
scan (BaseScan) – Positions of the probe wave functions. If not given, scans across the entire potential at Nyquist sampling.
detectors (BaseDetector, list of BaseDetector, optional) – A detector or a list of detectors defining how the wave functions should be converted to measurements after running the multislice algorithm. See abtem.measurements.detect for a list of implemented detectors.
max_batch (int, optional) – The number of wave functions in each chunk of the Dask array. If ‘auto’ (default), the batch size is automatically chosen based on the abtem user configuration settings “dask.chunk-size” and “dask.chunk-size-gpu”.
**multislice_func_kwargs – Additional keyword arguments passed to the multislice function.

Returns:

detected_waves (BaseMeasurements or list of BaseMeasurements) – The detected measurement (if detector(s) given).
exit_waves (Waves) – Wave functions at the exit plane(s) of the potential (if no detector(s) given).

show(...) → abtem.visualize.Visualization[source]#

Show the wave-function intensities.

kwargs :: Keyword arguments for abtem.measurements.Images.show.

show_depth_profile(...) → abtem.visualize.Visualization[source]#

Show a depth propagation profile of the wave functions.

Requires wave functions with a thickness dimension, i.e. from a multislice simulation with exit_planes.

Parameters:

projection_axis (str) – Spatial axis to project (sum) along. "y" (default) produces an x–z cross-section; "x" produces a y–z cross-section.
depth (float, optional) – If given, project only over a finite slab of this thickness [Å], centered on the midpoint of the projected axis. The number of grid points is rounded to the nearest integer. If None, the full extent is projected.
convert_complex (str) – How to convert the complex wave function before projecting. One of "intensity" (default), "phase", "real", or "imag".
z_scale (float) – Scaling factor for the z-axis relative to the spatial axis. Values less than 1 compress the z-axis, making panels of thick specimens more compact. Default is 1.0 (equal scaling).
slice_lines (bool) – If True, draw horizontal lines at slice boundaries. Default is False.
ax (matplotlib.axes.Axes, optional) – If given the plot is added to the axis.
cbar (bool, optional) – Add a colorbar to the plot. Default is False.
cmap (str, optional) – Matplotlib colormap name.
vmin (float, optional) – Minimum of the intensity color scale.
vmax (float, optional) – Maximum of the intensity color scale.
power (float) – Show image on a power scale.
common_color_scale (bool, optional) – If True, all images in a grid share the same color scale.
explode (bool or sequence of int, optional) – If True, create a grid of images for ensemble items.
figsize (two int, optional) – Figure size as (width, height) in inches.
title (bool or str, optional) – Column title for the images.
**kwargs – Additional keyword arguments passed to the show method.

Returns:

visualization

Return type:

Visualization

tile(...) → Waves[source]#

Tile the wave functions. Can only be applied in real space.

Parameters:

repetitions (two int) – The number of repetitions of the wave functions along the x- and y-axes.
renormalize (bool, optional) – If True, preserve the total intensity of the wave function (default is False).

Returns:

tiled_wave_functions – The tiled wave functions.

Return type:

Waves

to_images(...) → Images[source]#

The complex array of the wave functions at the image plane.

Returns:: images – The wave functions as an image.
Return type:: Images

transition_potential_multislice(...) → Waves | BaseMeasurements[source]#

property wavelength: float#

Relativistic electron wavelength [Å].

Resolves the per-member energy (metadata["energy"] or a single-value EnergyAxis) for an indexed energy-ensemble member, mirroring angular_sampling. A full multi-energy ensemble has no single wavelength and raises EnergyUndefinedError.

class abtem.waves.WavesBuilder(...)[source]#

Bases: abtem.waves.BaseWaves, abtem.core.ensemble.Ensemble, abtem.core.utils.CopyMixin, abtem.core.utils.EqualityMixin

apply_transform(...)[source]#

property axes_metadata: AxesMetadataList#: List of AxisMetadata.

property base_shape: tuple[int, int]#: Shape of the base axes of the waves.

abstract build(...) → Waves[source]#

check_can_build()[source]#: Check whether the wave functions can be built.

property device: str#: The device where the waves are created.

property ensemble_axes_metadata: list[AxisMetadata]#: List of AxisMetadata of the ensemble axes.

property ensemble_shape#: Shape of the ensemble axes of the waves.

property shape: tuple[int, ...]#: Shape of the waves.

property tilt#: The small-angle tilt of applied to the Fresnel propagator [mrad].

abtem.waves.reduce_ensemble(...) → Waves | BaseMeasurements | list[Waves | BaseMeasurements][source]#

Reduce an ensemble of wave functions or measurements by squeezing or averaging ensemble axes tagged for reduction with the “_squeeze” or “_ensemble_mean” attribute of the axis metadata.

Parameters:: ensemble (Waves, BaseMeasurements, list[Waves | BaseMeasurements]) – The ensemble to reduce.
Returns:: reduced_output – The reduced ensemble.
Return type:: Waves, BaseMeasurements, list[Waves | BaseMeasurements]

abtem.waves.validate_energy(...) → EnergyEnsemble[source]#: Convert energy (float, list, distribution, or EnergyEnsemble) to EnergyEnsemble.

abtem.waves

Contents

abtem.waves#

Module Contents#

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Functions#

API#

`abtem.waves`#