Waves
Waves#
- class abtem.waves.Waves(array, energy, extent=None, sampling=None, reciprocal_space=False, ensemble_axes_metadata=None, metadata=None)[source]#
Bases:
abtem.waves.BaseWaves,abtem.array.ArrayObjectWaves 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 [1 / 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.
- __init__(array, energy, extent=None, sampling=None, reciprocal_space=False, ensemble_axes_metadata=None, metadata=None)[source]#
Methods
__init__(array, energy[, extent, sampling, ...])apply_ctf([ctf, max_batch])Apply the aberrations and apertures of a contrast transfer function to the wave functions.
apply_transform(transform[, max_batch])Transform the wave functions by a given transformation.
The complex array of the wave functions at the image plane.
compute([progress_bar, profiler, ...])Turn a lazy abTEM object into its in-memory equivalent.
convolve(kernel[, axes_metadata, out_space, ...])Convolve the wave-function array with a given array.
copy()Make a copy.
copy_to_device(device)Copy array to specified device.
diffraction_patterns([max_angle, ...])Calculate the intensity of the wave functions at the diffraction plane.
downsample([max_angle, gpts, normalization])Downsample the wave functions to a lower maximum scattering angle.
ensemble_blocks([chunks])Split the ensemble into an array of smaller ensembles.
ensure_lazy([chunks])Creates an equivalent lazy version of the array object.
ensure_real_space([overwrite_x])Transform to real space if the wave functions are represented in reciprocal space.
ensure_reciprocal_space([overwrite_x])Transform to reciprocal space if the wave functions are represented in real space.
expand_dims([axis, axis_metadata])Expand the shape of the array object.
from_array_and_metadata(array, axes_metadata)Creates wave functions from a given array and metadata.
from_zarr(url[, chunks])Read wave functions from a hdf5 file.
generate_blocks([chunks])Generate chunks of the ensemble.
generate_ensemble([keepdims])Generate every member of the ensemble.
get_items(items[, keepdims])Index the array and the corresponding axes metadata.
Calculate the intensity of the wave functions.
match_grid(other[, check_match])Match the grid to another object with a Grid.
max([axis, keepdims, split_every])Maximum of array object over one or more axes.
mean([axis, keepdims, split_every])Mean of array object over one or more axes.
min([axis, keepdims, split_every])Minmimum of array object over one or more axes.
multislice(potential[, detectors])Propagate and transmit wave function through the provided potential using the multislice algorithm.
Rechunk to remove chunks across the base dimensions.
normalize([space, in_place])Normalize the wave functions in real or reciprocal space.
phase_shift(amount)Shift the phase of the wave functions.
rechunk(chunks, **kwargs)Rechunk dask array.
select_block(index, chunks)Select a block from the ensemble.
set_ensemble_axes_metadata(axes_metadata, axis)Sets the axes metadata of an ensemble axis.
show([complex_images])Show the wave-function intensities.
squeeze([axis])Remove axes of length one from array object.
std([axis, keepdims, split_every])Standard deviation of array object over one or more axes.
sum([axis, keepdims, split_every])Sum of array object over one or more axes.
tile(repetitions[, renormalize])Tile the wave functions.
to_cpu()Move the array to the host memory from an arbitrary source array.
to_gpu([device])Move the array from the host memory to a gpu.
Convert measurement to a Hyperspy signal.
to_tiff(filename, **kwargs)Write data to a tiff file.
to_zarr(url[, compute, overwrite])Write data to a zarr file.
Attributes
Accelerator object describing the acceleration energy.
Reciprocal-space sampling in units of scattering angles [mrad].
The number of grid points along the x and y direction in the simulation grid at the antialiasing cutoff scattering angle.
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.
Underlying array describing the array object.
List of AxisMetadata.
List of AxisMetadata for the base axes in real space.
Number of base dimensions.
Shape of the base axes of the underlying array.
The base small-angle beam tilt (i.e.
Scattering angles at the antialias cutoff [mrad].
The device where the array is stored.
The datatype of waves.
Electron acceleration energy in electron volts.
List of AxisMetadata of the ensemble axes.
Number of ensemble dimensions.
Shape of the ensemble axes of the underlying array.
Extent of grid for each dimension in Ångstrom.
Scattering angles corresponding to the full wave function size [mrad].
Number of grid points for each dimension.
Simulation grid.
True if array is complex.
True if array is lazy.
Metadata stored as a dictionary.
True if the waves are represented in reciprocal space.
List of AxisMetadata for base axes in reciprocal space.
Reciprocal-space sampling in reciprocal Ångstrom.
Scattering angles corresponding to the sides of the largest rectangle within the antialias cutoff [mrad].
Grid sampling for each dimension in Ångstrom per grid point.
Shape of the underlying array.
Relativistic wavelength in Ångstrom.
- property accelerator: abtem.core.energy.Accelerator#
Accelerator object describing the acceleration energy.
- Return type
Accelerator
- property angular_sampling: tuple[float, float]#
Reciprocal-space sampling in units of scattering angles [mrad].
- Return type
tuple[float,float]
- 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.
- Return type
tuple[int,int]
- 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.
- Return type
tuple[int,int]
- apply_ctf(ctf=None, max_batch='auto', **kwargs)[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
- apply_transform(transform, max_batch='auto')#
Transform the wave functions by a given transformation.
- Parameters
transform (ArrayObjectTransform) – The array object transformation to apply.
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”.
- Returns
transformed_array_object – The transformed array object.
- Return type
- property array: np.ndarray | da.core.Array#
Underlying array describing the array object.
- Return type
np.ndarray | da.core.Array
- property axes_metadata: abtem.core.axes.AxesMetadataList#
List of AxisMetadata.
- Return type
AxesMetadataList
- property base_axes_metadata: list[abtem.core.axes.AxisMetadata]#
List of AxisMetadata for the base axes in real space.
- Return type
list[AxisMetadata]
- property base_dims#
Number of base dimensions.
- property base_shape: tuple[int, ...]#
Shape of the base axes of the underlying array.
- Return type
tuple[int,...]
- property base_tilt#
The base small-angle beam tilt (i.e. the beam tilt not associated with an ensemble axis) applied to the Fresnel propagator [mrad].
- complex_images()[source]#
The complex array of the wave functions at the image plane.
- Returns
complex_images – The wave functions as a complex image.
- Return type
- compute(progress_bar=None, profiler=False, resource_profiler=False, **kwargs)#
Turn a lazy abTEM object into its in-memory equivalent.
- Parameters
progress_bar (bool) – Display a progress bar in the terminal or notebook during computation. The progress bar is only displayed with a local scheduler.
profiler (bool) – Return Profiler class used to profile Dask’s execution at the task level. Only execution with a local is profiled.
resource_profiler (bool) – Return ResourceProfiler class is used to profile Dask’s execution at the resource level.
kwargs – Additional keyword arguments passes to dask.compute.
- convolve(kernel, axes_metadata=None, out_space='in_space', in_place=False)[source]#
Convolve the wave-function array with a given array.
- Parameters
kernel (np.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
- copy()#
Make a copy.
- copy_to_device(device)#
Copy array to specified device.
- Parameters
device (str) –
- Returns
object_on_device
- Return type
T
- property cutoff_angles: tuple[float, float]#
Scattering angles at the antialias cutoff [mrad].
- Return type
tuple[float,float]
- property device: str#
The device where the array is stored.
- Return type
str
- diffraction_patterns(max_angle='cutoff', block_direct=False, fftshift=True, parity='odd', return_complex=False, renormalize=True)[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
- downsample(max_angle='cutoff', gpts=None, normalization='values')[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
- property dtype#
The datatype of waves.
- property energy#
Electron acceleration energy in electron volts.
- property ensemble_axes_metadata#
List of AxisMetadata of the ensemble axes.
- ensemble_blocks(chunks=None)#
Split the ensemble into an array of smaller ensembles.
- Parameters
chunks (iterable of tuples) – Block sizes along each dimension.
- Return type
Array
- property ensemble_dims#
Number of ensemble dimensions.
- property ensemble_shape: tuple[int, ...]#
Shape of the ensemble axes of the underlying array.
- Return type
tuple[int,...]
- ensure_lazy(chunks='auto')#
Creates an equivalent lazy version of the array object.
- Parameters
chunks (int or tuple or str) – How to chunk the array. See dask.array.from_array.
- Returns
lazy_array_object – Lazy version of the array object.
- Return type
ArrayObject or subclass of ArrayObject
- ensure_real_space(overwrite_x=False)[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
- ensure_reciprocal_space(overwrite_x=False)[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
- expand_dims(axis=None, axis_metadata=None)#
Expand the shape of the array object.
- Parameters
axis (int or tuple of ints) – Position in the expanded axes where the new axis (or axes) is placed.
axis_metadata (AxisMetadata or List of AxisMetadata, optional) – The axis metadata describing the expanded axes. Default is UnknownAxis.
- Returns
expanded – View of array object with the number of dimensions increased.
- Return type
ArrayObject or subclass of ArrayObject
- property extent: tuple[float] | tuple[float, float] | tuple[float, ...]#
Extent of grid for each dimension in Ångstrom.
- Return type
tuple[float] | tuple[float, float] | tuple[float, …]
- classmethod from_array_and_metadata(array, axes_metadata, metadata=None)[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 (
Optional[dict]) – 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
- classmethod from_zarr(url, chunks='auto')#
Read wave functions from a hdf5 file.
- urlstr
Location of the data, typically a path to a local file. A URL can also include a protocol specifier like s3:// for remote data.
- chunkstuple of ints or tuples of ints
Passed to dask.array.from_array(), allows setting the chunks on initialisation, if the chunking scheme in the on-disc dataset is not optimal for the calculations to follow.
- Return type
TypeVar(T, bound= ArrayObject)
- property full_cutoff_angles: tuple[float, float]#
Scattering angles corresponding to the full wave function size [mrad].
- Return type
tuple[float,float]
- generate_blocks(chunks=1)#
Generate chunks of the ensemble.
- Parameters
chunks (iterable of tuples) – Block sizes along each dimension.
- generate_ensemble(keepdims=False)#
Generate every member of the ensemble.
- Parameters
keepdims (bool, opptional) – If True, all ensemble axes are left in the result as dimensions with size one. Default is False.
- Yields
ArrayObject or subclass of ArrayObject – Member of the ensemble.
- get_items(items, keepdims=False)#
Index the array and the corresponding axes metadata. Only ensemble axes can be indexed.
- Parameters
items (int or tuple of int or slice) – The array is indexed according to this.
keepdims (bool, optional) – If True, all ensemble axes are left in the result as dimensions with size one. Default is False.
- Returns
indexed_array – The indexed array object.
- Return type
ArrayObject or subclass of ArrayObject
- property gpts: tuple[int] | tuple[int, int] | tuple[int, ...]#
Number of grid points for each dimension.
- Return type
tuple[int] | tuple[int, int] | tuple[int, …]
- property grid: abtem.core.grid.Grid#
Simulation grid.
- Return type
Grid
- intensity()[source]#
Calculate the intensity of the wave functions.
- Returns
intensity_images – The intensity of the wave functions.
- Return type
- property is_complex: bool#
True if array is complex.
- Return type
bool
- property is_lazy: bool#
True if array is lazy.
- Return type
bool
- match_grid(other, check_match=False)#
Match the grid to another object with a Grid.
- max(axis=None, keepdims=False, split_every=2)#
Maximum of array object over one or more axes. Only ensemble axes can be reduced.
- Parameters
axis (int or tuple of ints, optional) – Axis or axes along which a maxima are calculated. The default is to compute the mean of the flattened array. If this is a tuple of ints, the maxima are calculated over multiple axes. The indicated axes must be ensemble axes.
keepdims (bool, optional) – If True, the reduced axes are left in the result as dimensions with size one. Default is False.
split_every (int) – Only used for lazy arrays. See dask.array.reductions.
- Returns
reduced_array – The reduced array object.
- Return type
ArrayObject or subclass of ArrayObject
- mean(axis=None, keepdims=False, split_every=2)#
Mean of array object over one or more axes. Only ensemble axes can be reduced.
- Parameters
axis (int or tuple of ints, optional) – Axis or axes along which a means are calculated. The default is to compute the mean of the flattened array. If this is a tuple of ints, the mean is calculated over multiple axes. The indicated axes must be ensemble axes.
keepdims (bool, optional) – If True, the reduced axes are left in the result as dimensions with size one. Default is False.
split_every (int) – Only used for lazy arrays. See dask.array.reductions.
- Returns
reduced_array – The reduced array object.
- Return type
ArrayObject or subclass of ArrayObject
- property metadata: dict#
Metadata stored as a dictionary.
- Return type
dict
- min(axis=None, keepdims=False, split_every=2)#
Minmimum of array object over one or more axes. Only ensemble axes can be reduced.
- Parameters
axis (int or tuple of ints, optional) – Axis or axes along which a minima are calculated. The default is to compute the mean of the flattened array. If this is a tuple of ints, the minima are calculated over multiple axes. The indicated axes must be ensemble axes.
keepdims (bool, optional) – If True, the reduced axes are left in the result as dimensions with size one. Default is False.
split_every (int) – Only used for lazy arrays. See dask.array.reductions.
- Returns
reduced_array – The reduced array object.
- Return type
ArrayObject or subclass of ArrayObject
- multislice(potential, detectors=None)[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.
- Return type
- Returns
detected_waves (BaseMeasurements or list of BaseMeasurement) – 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).
- no_base_chunks()#
Rechunk to remove chunks across the base dimensions.
- normalize(space='reciprocal', in_place=False)[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
- phase_shift(amount)[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
- rechunk(chunks, **kwargs)#
Rechunk dask array.
- chunksint or tuple or str
How to rechunk the array. See dask.array.rechunk.
- kwargs :
Additional keyword arguments passes to dask.array.rechunk.
- property reciprocal_space#
True if the waves are represented in reciprocal space.
- property reciprocal_space_axes_metadata: list[abtem.core.axes.AxisMetadata]#
List of AxisMetadata for base axes in reciprocal space.
- Return type
list[AxisMetadata]
- property reciprocal_space_sampling: tuple[float] | tuple[float, float] | tuple[float, ...]#
Reciprocal-space sampling in reciprocal Ångstrom.
- Return type
tuple[float] | tuple[float, float] | tuple[float, …]
- property rectangle_cutoff_angles: tuple[float, float]#
Scattering angles corresponding to the sides of the largest rectangle within the antialias cutoff [mrad].
- Return type
tuple[float,float]
- property sampling: tuple[float] | tuple[float, float] | tuple[float, ...]#
Grid sampling for each dimension in Ångstrom per grid point.
- Return type
tuple[float] | tuple[float, float] | tuple[float, …]
- select_block(index, chunks)#
Select a block from the ensemble.
- Parameters
index (tuple of ints) – Index of selected block.
chunks (iterable of tuples) – Block sizes along each dimension.
- set_ensemble_axes_metadata(axes_metadata, axis)#
Sets the axes metadata of an ensemble axis.
- Parameters
axes_metadata (AxisMetadata) – The new axis metadata.
axis (int) – The axis to set.
- property shape: tuple[int, ...]#
Shape of the underlying array.
- Return type
tuple[int,...]
- show(complex_images=False, **kwargs)[source]#
Show the wave-function intensities.
- kwargs :
Keyword arguments for abtem.measurements.Images.show.
- squeeze(axis=None)#
Remove axes of length one from array object.
- Parameters
axis (int or tuple of ints, optional) – Selects a subset of the entries of length one in the shape.
- Returns
squeezed – The input array object, but with all or a subset of the dimensions of length 1 removed.
- Return type
ArrayObject or subclass of ArrayObject
- std(axis=None, keepdims=False, split_every=2)#
Standard deviation of array object over one or more axes. Only ensemble axes can be reduced.
- Parameters
axis (int or tuple of ints, optional) – Axis or axes along which a standard deviations are calculated. The default is to compute the mean of the flattened array. If this is a tuple of ints, the standard deviations are calculated over multiple axes. The indicated axes must be ensemble axes.
keepdims (bool, optional) – If True, the reduced axes are left in the result as dimensions with size one. Default is False.
split_every (int) – Only used for lazy arrays. See dask.array.reductions.
- Returns
reduced_array – The reduced array object.
- Return type
ArrayObject or subclass of ArrayObject
- sum(axis=None, keepdims=False, split_every=2)#
Sum of array object over one or more axes. Only ensemble axes can be reduced.
- Parameters
axis (int or tuple of ints, optional) – Axis or axes along which a sums are performed. The default is to compute the mean of the flattened array. If this is a tuple of ints, the sum is performed over multiple axes. The indicated axes must be ensemble axes.
keepdims (bool, optional) – If True, the reduced axes are left in the result as dimensions with size one. Default is False.
split_every (int) – Only used for lazy arrays. See dask.array.reductions.
- Returns
reduced_array – The reduced array object.
- Return type
ArrayObject or subclass of ArrayObject
- tile(repetitions, renormalize=False)[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
- to_cpu()#
Move the array to the host memory from an arbitrary source array.
- Return type
TypeVar(T, bound= ArrayObject)
- to_gpu(device='gpu')#
Move the array from the host memory to a gpu.
- Return type
TypeVar(T, bound= ArrayObject)
- to_hyperspy()#
Convert measurement to a Hyperspy signal.
- to_tiff(filename, **kwargs)#
Write data to a tiff file.
- Parameters
filename (str) – The filename of the file to write.
kwargs – Keyword arguments passed to tifffile.imwrite.
- to_zarr(url, compute=True, overwrite=False, **kwargs)#
Write data to a zarr file.
- Parameters
url (str) – Location of the data, typically a path to a local file. A URL can also include a protocol specifier like s3:// for remote data.
compute (bool) – If true compute immediately; return dask.delayed.Delayed otherwise.
overwrite (bool) – If given array already exists, overwrite=False will cause an error, where overwrite=True will replace the existing data.
kwargs – Keyword arguments passed to dask.array.to_zarr.
- property wavelength#
Relativistic wavelength in Ångstrom.