Measurement

Module to describe the detection of scattered electron waves.

class abtem.measure.Calibration(offset, sampling, units, name='', endpoint=True, adjustable=True)[source]

Calibration object

The calibration object represents the sampling of a uniformly sampled Measurement.

Parameters:

  • offset (float) – The lower bound of the sampling points.

  • sampling (float) – The distance between sampling points.

  • units (str) – The units of the calibration shown in plots.

  • name (str) – The name of this calibration to be shown in plots.

copy()[source]

Make a copy.

class abtem.measure.Measurement(array, calibrations=None, units='', name='', base_dimensions=2)[source]

Measurement object.

The measurement object is used for representing the output of a TEM simulation. For example a line profile, an image or a collection of diffraction patterns.

Parameters:

  • array (ndarray) – The array representing the measurements. The array can be any dimension.

  • calibrations (list of Calibration objects) – The calibration for each dimension of the measurement array.

  • units (str) – The units of the array values to be displayed in plots.

  • name (str) – The name of the array values to be displayed in plots.

property array

Array of measurements.

Return type:

ndarray

property calibrations

The measurement calibrations.

Return type:

Tuple[Optional[Calibration]]

copy()[source]

Make a copy.

Return type:

Measurement

diffractograms(axes=None, energy=None)[source]

Calculate the diffractograms of this measurement.

Parameters:

axes (list of int) – The axes to Fourier transform.

Returns:

Return type:

Measurement

property dimensions

The measurement dimensions.

Return type:

int

gaussian_filter(sigma, padding_mode='wrap')[source]

Apply gaussian filter to measurement.

Parameters:

  • sigma (float or sequence of float) – Standard deviation for Gaussian kernel. The standard deviations of the Gaussian filter are given for each axis as a sequence, or as a single number, in which case it is equal for all axes.

  • padding_mode (str) – The padding_mode parameter determines how the input array is padded at the border. Different modes can be specified along each axis. Default value is ‘wrap’.

Returns:

Blurred measurement.

Return type:

Measurement

integrate(start, end, axis=- 1, interactive=False)[source]

Perform 1d integration measurement from e.g. the FlexibleAnnularDetector

Parameters:

  • start (float) – Lower limit of integral in units of the calibration of the given axis.

  • end (float) – Upper limit of integral in units of the calibration of the given axis.

  • axis (int) – The

Returns:

Integrated measurement.

Return type:

Measurement

interpolate(new_sampling=None, new_gpts=None, padding='wrap', kind=None, axes=None)[source]

Interpolate a 2d measurement.

Parameters:

  • new_sampling (one or two float, optional) – Target measurement sampling. Same units as measurement calibrations.

  • new_gpts (one or two int, optional) – Target measurement gpts.

  • padding (str, optional) – The padding mode as used by numpy.pad.

  • kind (str, optional) – The kind of spline interpolation to use. Default is ‘quintic’.

Returns:

Interpolated measurement

Return type:

Measurement object

interpolate_line(start, end=None, angle=0.0, gpts=None, sampling=None, width=None, margin=0.0, endpoint=True, interpolation_method='splinef2d')[source]

Interpolate 2d measurement along a line.

Parameters:

  • start (two float, Atom) – Start point on line [Å].

  • end (two float, Atom, optional) – End point on line [Å].

  • angle (float, optional) – The angle of the line. This is only used when an “end” is not give.

  • gpts (int) – Number of grid points along line.

  • sampling (float) – Sampling rate of grid points along line [1 / Å].

  • width (float, optional) – The interpolation will be averaged across line of this width.

  • margin (float, optional) – The line will be extended by this amount at both ends.

  • interpolation_method (str, optional) – The interpolation method.

Returns:

Line profile measurement.

Return type:

Measurement

mean(axis)[source]

Mean of measurement elements over a given axis.

Parameters:

axis (int or tuple of ints) – Axis or axes along which a sum is performed. If axis is negative it counts from the last to the first axis.

Returns:

A measurement with the same shape, but with the specified axis removed.

Return type:

Measurement object

property name

The name of the array values to be displayed in plots.

Return type:

str

classmethod read(path)[source]

Read measurement from a hdf5 file.

path: str

The path to read the file.

Return type:

Measurement

save_as_image(path)[source]

Write the measurement array to an image file. The array will be normalized and converted to 16-bit integers.

path: str

The path to write the file.

property shape

The shape of the measurement array.

Return type:

Tuple[int]

show(ax=None, interact=False, **kwargs)[source]

Show the measurement.

Parameters:

kwargs – Additional keyword arguments for the abtem.plot.show_image function.

squeeze()[source]

Remove dimensions of length one from measurement.

Returns:

Return type:

Measurement

sum(axis)[source]

Sum of measurement elements over a given axis.

Parameters:

axis (int or tuple of ints) – Axis or axes along which a sum is performed. If axis is negative it counts from the last to the first axis.

Returns:

A measurement with the same shape, but with the specified axis removed.

Return type:

Measurement

tile(multiples)[source]

Construct a measurement by repeating the measurement number of times given by multiples.

Parameters:

multiples (sequence of int) – The number of repetitions of the measurement along each axis.

Returns:

The tiled potential.

Return type:

Measurement object

to_hyperspy(signal_type=None)[source]

Changes the Measurement object to a hyperspy.BaseSignal Object or a defined signal type.

signal_type: str

The signal type alias for some signal type

property units

The units of the array values to be displayed in plots.

Return type:

str

write(path, mode='w', format='hdf5', **kwargs)[source]

Write measurement to a hdf5 file.

path: str

The path to write the file.

format: str

One of [“hdf5”, “hspy”]

kwargs:

Any of the additional parameters for saving a hyperspy dataset

abtem.measure.bandlimit(measurement, cutoff, taper=0.1, band_type='lowpass')[source]

Bandlimit a collection of diffraction patterns.

Parameters:

  • measurement (Measurement) – Collection of diffraction patterns.

  • cutoff (float) – The cutoff radius in mrad.

  • taper (float) – Taper the bandlimiting window to avoid a sharp cutoff.

Returns:

Bandlimited measurement.

Return type:

Measurement

abtem.measure.block_zeroth_order_spot(diffraction_pattern, angular_radius=1)[source]

Set the zero’th order spot of a diffraction pattern to zero.

Parameters:

  • diffraction_pattern (Measurement) – Measurement representing one or more diffraction patterns.

  • angular_radius (float) – The radius of the disk-shaped region set to zero.

Returns:

Return type:

Measurement

abtem.measure.calculate_fwhm(probe_profile)[source]

Calculate the full width at half maximum of a 1d measurement, typically a probe profile.

Parameters:

probe_profile (Measurement) – Probe profile measurement.

Returns:

Return type:

float

abtem.measure.calibrations_from_grid(gpts, sampling, names=None, units=None, fourier_space=False, scale_factor=1.0)[source]

Returns the spatial calibrations for a given computational grid and sampling.

Parameters:

  • gpts (list of int) – Number of grid points in the x and y directions.

  • sampling (list of float) – Sampling of the potential in Å.

  • names (list of str, optional) – The name of this calibration.

  • units (str, optional) – Units for the calibration.

  • fourier_space (bool, optional) – Setting for calibrating either in the reciprocal or real space. Default is False.

  • scale_factor (float, optional) – Scaling factor for the calibration. Default is 1.0.

Returns:

calibrations

Return type:

Tuple of Calibrations

abtem.measure.center_of_mass(measurement, return_magnitude=False, return_icom=False)[source]

Calculate the center of mass of a measurement.

Parameters:

  • measurement (Measurement) – A collection of diffraction patterns.

  • return_icom (bool) – If true, return the integrated center of mass.

Returns:

Return type:

Measurement

abtem.measure.fourier_space_offset(n, d)[source]

Calculate the calibration offset of a Fourier space measurement.

Parameters:

  • n (int) – Number of sampling points.

  • d (float) – Real space sampling density.

abtem.measure.integrate_disc(image, position, radius, return_mean=True, border='wrap', interpolate=0.01)[source]

Integrate the values of a 2d measurement on a disc-shaped region.

Parameters:

  • position (two floats) – Center of disc-shaped integration region

  • measurement (2d measurement) – The measurement to integrate

  • radius (float) – Radius of disc-shaped integration region

  • return_mean (bool) – If true return the mean, otherwise return the sum.

  • border (str) –

    Specify how to treat integration regions that cross the image border. The valid values and their behaviour is: ‘wrap’

    The measurement is extended by wrapping around to the opposite edge.

    ’raise’

    Raise an error if the integration region crosses the measurement border.

  • interpolate (float or False) – The image will be interpolated to this sampling. Units of Angstrom.

Returns:

Integral value

Return type:

float

abtem.measure.intgrad2d(gradient, sampling=None)[source]

Perform Fourier-space integration of gradient.

Parameters:

  • gradient (two np.ndarrays) – The x- and y-components of the gradient.

  • sampling (two float) – Lateral sampling of the gradients. Default is 1.0.

Returns:

Integrated center of mass measurement

Return type:

np.ndarray

abtem.measure.probe_profile(probe_measurement, angle=0.0)[source]

Return the profile of a probe given a 2d measurement of that probe.

Parameters:

  • probe_measurement (Measurement) – 2d measurement of the centered intensity of an electron probe.

  • angle (float) – The angle at which to interpolate the profile.

Returns:

1d measurement of the probe profile.

Return type:

Measurement

abtem.measure.rotational_average(measurement)[source]

Calculate the rotational average of a measurement.

Parameters:

measurement (Measurement) – 2d measurement of calculate the rotational average from.

Returns:

1d rotational average of a 2d measurement.

Return type:

Measurement