PolarMeasurements

class abtem.measurements.PolarMeasurements(array, radial_sampling, azimuthal_sampling, radial_offset=0.0, azimuthal_offset=0.0, ensemble_axes_metadata=None, metadata=None)

Bases: BaseMeasurements

Class describing polar measurements with a specified number of radial and azimuthal bins.

Each bin is a segment of an annulus and the bins are spaced equally in the radial and azimuthal directions. The bins may be rotated around the origin, and their center may be shifted from the origin.

Parameters:

• array (np.ndarray) – Array containing the measurement.

• radial_sampling (float) – Sampling of the radial bins [mrad].

• azimuthal_sampling (int) – Sampling of the azimuthal bins [rad].

• radial_offset (float, optional) – Offset of the bins from the origin [mrad] (default is 0.0).

• azimuthal_offset (float, optional) – Rotation of the bins around the origin [rad] (default is 0.0).

• ensemble_axes_metadata (list of AxisMetadata, optional) – List of metadata associated with the ensemble axes. The length and item order must match the ensemble axes.

• metadata (dict, optional) – A dictionary defining measurement metadata.

Returns:

polar_measurements – The polar measurements.

Return type:

PolarMeasurements

__init__(array, radial_sampling, azimuthal_sampling, radial_offset=0.0, azimuthal_offset=0.0, ensemble_axes_metadata=None, metadata=None)

Methods

__init__(array, radial_sampling, ...[, ...])
abs()	Calculates the absolute value of a complex-valued measurement.
apply_func(func, **kwargs)	rtype: TypeVar(T, bound= ArrayObject)
apply_transform(transform[, max_batch])	Transform the wave functions by a given transformation.
compute([progress_bar, profiler, ...])	Turn a lazy abTEM object into its in-memory equivalent.
copy()	Make a copy.
copy_to_device(device)	Copy array to specified device.
differentials(direction_1, direction_2[, ...])	Calculate the differential signal by subtracting the intensity of specified detector regions.
ensemble_blocks([chunks])	Split the ensemble into an array of smaller ensembles.
ensure_lazy([chunks])	Creates an equivalent lazy version of the array object.
expand_dims([axis, axis_metadata])	Expand the shape of the array object.
from_array_and_metadata(array, axes_metadata)	Creates polar measurements(s) from a given array and metadata.
from_zarr(url[, chunks])	Read wave functions from a hdf5 file.
gaussian_source_size(sigma)	Simulate the effect of a finite source size on diffraction pattern(s) using a Gaussian filter.
generate_blocks([chunks])	Generate chunks of the ensemble.
generate_ensemble([keepdims])	Generate every member of the ensemble.
get_from_metadata(name[, broadcastable])
get_items(items[, keepdims])	Index the array and the corresponding axes metadata.
imag()	Returns the imaginary part of a complex-valued measurement.
integrate([radial_limits, azimuthal_limits, ...])	Integrate polar regions to produce an image or line profiles.
integrate_radial(inner, outer)	Create images by integrating the polar measurements over an annulus defined by an inner and outer integration angle.
intensity()	Calculates the squared norm of a complex-valued measurement.
lazy([chunks])	rtype: TypeVar(T, bound= ArrayObject)
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.
no_base_chunks()	Rechunk to remove chunks across the base dimensions.
normalize_ensemble([scale, shift])	Normalize the ensemble by shifting ad scaling each member.
phase()	Calculates the phase of a complex-valued measurement.
poisson_noise([dose_per_area, total_dose, ...])	Add Poisson noise (i.e. shot noise) to a measurement corresponding to the provided 'total_dose' (per measurement if applied to an ensemble) or 'dose_per_area' (not applicable for single measurements).
real()	Returns the real part of a complex-valued measurement.
rechunk(chunks, **kwargs)	Rechunk dask array.
reduce_ensemble()	Calculates the mean of an ensemble measurement (e.g. of frozen phonon configurations).
relative_difference(other[, min_relative_tol])	Calculates the relative difference with respect to another compatible measurement.
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([ax, gpts, cbar, cmap, vmin, vmax, ...])	Show the image(s) using matplotlib.
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.
to_cpu()	Move the array to the host memory from an arbitrary source array.
to_data_array()	Convert ArrayObject to a xarray DataArray.
to_diffraction_patterns(gpts[, margin])	Convert the polar measurements to diffraction patterns by discretizing the polar bins on a regular grid.
to_gpu([device])	Move the array from the host memory to a gpu.
to_hyperspy()	Convert ArrayObject to a Hyperspy signal.
to_image_ensemble()	Convert the polar measurements to an ensemble of images, where the radial and azimuthal angles becomes ensemble axes.
to_measurement_ensemble()
to_tiff(filename, **kwargs)	Write data to a tiff file.
to_zarr(url[, compute, overwrite])	Write data to a zarr file.

Attributes

array	Underlying array describing the array object.
axes_metadata	List of AxisMetadata.
azimuthal_offset	Rotation of the bins around the origin [rad].
azimuthal_sampling	Sampling of the azimuthal bins [rad].
base_axes_metadata	List of AxisMetadata of the base axes.
base_dims	Number of base dimensions.
base_shape	Shape of the base axes of the underlying array.
device	The device where the array is stored.
dtype	Datatype of array.
ensemble_axes_metadata	List of AxisMetadata of the ensemble axes.
ensemble_dims	Number of ensemble dimensions.
ensemble_shape	Shape of the ensemble axes of the underlying array.
is_complex	True if array is complex.
is_lazy	True if array is lazy.
metadata	Metadata describing the measurement.
outer_angle	The outer angle of the outermost radial bin [mrad].
radial_offset	Offset of the bins from the origin [mrad].
radial_sampling	Sampling of the radial bins [mrad].
shape	Shape of the underlying array.

abs()

Calculates the absolute value of a complex-valued measurement.

Return type:

TypeVar(T, bound= BaseMeasurements)

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:

ArrayObjectTransform

property array: np.ndarray | da.core.Array

Underlying array describing the array object.

property axes_metadata: AxesMetadataList

List of AxisMetadata.

property azimuthal_offset: float

Rotation of the bins around the origin [rad].

property azimuthal_sampling: float

Sampling of the azimuthal bins [rad].

property base_axes_metadata: list[AxisMetadata]

List of AxisMetadata of the base axes.

property base_dims

Number of base dimensions.

property base_shape: tuple[int, ...]

Shape of the base axes of the underlying array.

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.

copy()

Make a copy.

copy_to_device(device)

Copy array to specified device.

Parameters:

device (str)

Returns:

object_on_device

Return type:

T

property device: str

The device where the array is stored.

differentials(direction_1, direction_2, return_complex=True)

Calculate the differential signal by subtracting the intensity of specified detector regions.

Parameters:

• direction_1 (tuple of int or tuple of tuple of int) – The detector regions used for calculating the differential signal for the first direction. The first item is the detector region(s) contributing to the positive term and the second item is the detector region(s) contributing to the negative terms.

• direction_2 (tuple of int or tuple of tuple of int) – The detector regions used for calculating the differential signal for the second direction. The first item is the detector region(s) contributing to the positive term and the second item is the detector region(s) contributing to the negative terms.

• return_complex (bool, optional) – If True, return a complex image where the real and imaginary part represents direction_1 and direction_2. If False, return images with an ensemble dimension for the directions.

Returns:

differential_image – The (complex) differential image(s).

Return type:

Images

property dtype

Datatype of array.

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.

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

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

classmethod from_array_and_metadata(array, axes_metadata, metadata=None)

Creates polar measurements(s) from a given array and metadata.

Parameters:

• array (array) – Complex array defining one or more polar measurements. The second-to-last and last dimensions are the measurement y- and x-axis.

• 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 (dict) – A dictionary defining the measurement metadata.

Returns:

polar_measurements – Polar measurement(s) from the array and metadata.

Return type:

PolarMeasurements

classmethod from_zarr(url, chunks='auto')

Read wave functions from a hdf5 file.

Return type:

TypeVar(T, bound= ArrayObject)

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.

gaussian_source_size(sigma)

Simulate the effect of a finite source size on diffraction pattern(s) using a Gaussian filter.

The filter is not applied to diffraction pattern individually, but the intensity of diffraction patterns are mixed across scan axes. Applying this filter requires two linear scan axes.

Applying this filter before integrating the diffraction patterns will produce the same image as integrating the diffraction patterns first then applying a Gaussian filter.

Parameters:

sigma (float or two float) – Standard deviation of Gaussian kernel in the x and y-direction. If given as a single number, the standard deviation is equal for both axes.

Returns:

filtered_diffraction_patterns – The filtered diffraction pattern(s).

Return type:

DiffractionPatterns

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

imag()

Returns the imaginary part of a complex-valued measurement.

Return type:

TypeVar(T, bound= BaseMeasurements)

integrate(radial_limits=None, azimuthal_limits=None, detector_regions=None)

Integrate polar regions to produce an image or line profiles.

Parameters:

• radial_limits (tuple of float) – Inner and outer radial angles of the integration limits [mrad].

• azimuthal_limits (tuple of float) – Lower and upper azimuthal angles of the integration limits [rad].

• detector_regions (int or sequence of int) – The explicit detector regions to integrate over.

Returns:

integrated_images

Return type:

Images or RealSpaceLineProfiles

integrate_radial(inner, outer)

Create images by integrating the polar measurements over an annulus defined by an inner and outer integration angle.

Parameters:

• inner (float) – Inner integration limit [mrad].

• outer (float) – Outer integration limit [mrad].

Return type:

Images | RealSpaceLineProfiles

Returns:

• integrated_images (Images) – The integrated images.

• real_space_line_profiles (RealSpaceLineProfiles) – Integrated line profiles (returned if there is only one scan axis).

intensity()

Calculates the squared norm of a complex-valued measurement.

Return type:

TypeVar(T, bound= BaseMeasurements)

property is_complex: bool

True if array is complex.

property is_lazy: bool

True if array is lazy.

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 describing the measurement.

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

no_base_chunks()

Rechunk to remove chunks across the base dimensions.

normalize_ensemble(scale='max', shift='mean')

Normalize the ensemble by shifting ad scaling each member.

Parameters:

• scale ({'max', 'min', 'sum', 'mean', 'ptp'})

• shift ({'max', 'min', 'sum', 'mean', 'ptp'})

Returns:

normalized_measurements

Return type:

BaseMeasurements or subclass of _BaseMeasurement

property outer_angle: float

The outer angle of the outermost radial bin [mrad].

phase()

Calculates the phase of a complex-valued measurement.

Return type:

TypeVar(T, bound= BaseMeasurements)

poisson_noise(dose_per_area=None, total_dose=None, samples=1, seed=None)

Add Poisson noise (i.e. shot noise) to a measurement corresponding to the provided ‘total_dose’ (per measurement if applied to an ensemble) or ‘dose_per_area’ (not applicable for single measurements).

Parameters:

• dose_per_area (float, optional) – The irradiation dose [electrons per Å:sup:2].

• total_dose (float, optional) – The irradiation dose per diffraction pattern.

• samples (int, optional) – The number of samples to draw from a Poisson distribution. If this is greater than 1, an additional ensemble axis will be added to the measurement.

• seed (int, optional) – Seed the random number generator.

Returns:

noisy_measurement – The noisy measurement.

Return type:

BaseMeasurements or subclass of _BaseMeasurement

property radial_offset: float

Offset of the bins from the origin [mrad].

property radial_sampling: float

Sampling of the radial bins [mrad].

real()

Returns the real part of a complex-valued measurement.

Return type:

TypeVar(T, bound= BaseMeasurements)

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.

reduce_ensemble()

Calculates the mean of an ensemble measurement (e.g. of frozen phonon configurations).

Return type:

TypeVar(T, bound= BaseMeasurements)

relative_difference(other, min_relative_tol=0.0)

Calculates the relative difference with respect to another compatible measurement.

Parameters:

• other (BaseMeasurements) – Measurement to which the difference is calculated.

• min_relative_tol (float) – Avoids division by zero errors by defining a minimum value of the divisor in the relative difference.

Returns:

difference – The relative difference as a measurement of the same type.

Return type:

BaseMeasurements

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.

show(ax=None, gpts=(512, 512), cbar=False, cmap=None, vmin=None, vmax=None, power=1.0, common_color_scale=False, explode=(), overlay=(), figsize=None, title=True, units=None, interact=False, display=True)

Show the image(s) using matplotlib.

Parameters:

• gpts (int or tuple of int, optional)

• ax (matplotlib.axes.Axes, optional) – If given the plots are added to the axis. This is not available for exploded plots.

• cbar (bool, optional) – Add colorbar(s) to the image(s). The size and padding of the colorbars may be adjusted using the set_cbar_size and set_cbar_padding methods.

• cmap (str, optional) – Matplotlib colormap name used to map scalar data to colors. If the measurement is complex the colormap must be one of ‘hsv’ or ‘hsluv’.

• vmin (float, optional) – Minimum of the intensity color scale. Default is the minimum of the array values.

• vmax (float, optional) – Maximum of the intensity color scale. Default is the maximum of the array values.

• power (float) – Show image on a power scale.

• common_color_scale (bool, optional) – If True all images in an image grid are shown on the same colorscale, and a single colorbar is created (if it is requested). Default is False.

• explode (bool, optional) – If True, a grid of images is created for all the items of the last two ensemble axes. If False, the first ensemble item is shown. May be given as a sequence of axis indices to create a grid of images from the specified axes. The default is determined by the axis metadata.

• figsize (two int, optional) – The figure size given as width and height in inches, passed to matplotlib.pyplot.figure.

• title (bool or str, optional) – Set the column title of the images. If True is given instead of a string the title will be given by the value corresponding to the “name” key of the axes metadata dictionary, if this item exists.

• units (str) – The units used for the x and y axes. The given units must be compatible with the axes of the images.

• interact (bool) – If True, create an interactive visualization. This requires enabling the ipympl Matplotlib backend.

• display (bool, optional) – If True (default) the figure is displayed immediately.

Returns:

measurement_visualization_2d

Return type:

MeasurementVisualizationImshow

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

to_cpu()

Move the array to the host memory from an arbitrary source array.

Return type:

TypeVar(T, bound= ArrayObject)

to_data_array()

Convert ArrayObject to a xarray DataArray.

to_diffraction_patterns(gpts, margin=0.1)

Convert the polar measurements to diffraction patterns by discretizing the polar bins on a regular grid.

Parameters:

• gpts (int or two int) – Number of grid points describing the diffraction patterns.

• margin (float or two float, optional) – The margin as a fraction of the outer angle of the polar measurements to add to the maximum angle of the diffraction patterns.

Returns:

diffraction_patterns

Return type:

DiffractionPatterns

to_gpu(device='gpu')

Move the array from the host memory to a gpu.

Return type:

TypeVar(T, bound= ArrayObject)

to_hyperspy()

Convert ArrayObject to a Hyperspy signal.

to_image_ensemble()

Convert the polar measurements to an ensemble of images, where the radial and azimuthal angles becomes ensemble axes.

Returns:

image_ensemble

Return type:

Images

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.