CTF#

class abtem.transfer.CTF(semiangle_cutoff=inf, soft=True, focal_spread=0.0, angular_spread=0.0, aberration_coefficients=None, energy=None, extent=None, gpts=None, sampling=None, flip_phase=False, wiener_snr=0.0, **kwargs)[source]#

Bases: abtem.transfer._HasAberrations, abtem.transfer.BaseAperture

The contrast transfer function (CTF) describes the aberrations of the objective lens in HRTEM and specifies how the condenser system shapes the probe in STEM.

abTEM implements phase aberrations up to 5th order using polar coefficients. See Eq. 2.22 in the reference 1.

Cartesian coefficients can be converted to polar using the utility function abtem.transfer.cartesian2polar.

Partial coherence is included as envelopes in the quasi-coherent approximation. See Chapter 3.2 in reference 1.

Parameters

semiangle_cutoff (float, optional) – The semiangle cutoff describes the sharp reciprocal-space cutoff due to the objective aperture [mrad] (default is no cutoff).
soft (bool, optional) – If True, the edge of the aperture is softened (default is True).
focal_spread (float, optional) – The standard deviation of the focal spread due to chromatic aberration and lens current instability [Å] (default is 0).
angular_spread (float, optional) – The standard deviation of the angular deviations due to source size [Å] (default is 0).
aberration_coefficients (dict, optional) – Mapping from aberration symbols to their corresponding values. All aberration magnitudes should be given in [Å] and angles should be given in [radian].
energy (float, optional) – Electron energy [eV]. If not provided, inferred from the wave functions.
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 [1 / Å]. If ‘gpts’ is also given, will be ignored.
flip_phase (bool, optional) – Changes the sign of all negative parts of the CTF to positive (following doi:10.1016/j.ultramic.2008.03.004) (default is False).
wiener_snr (float, optional) – Applies a Wiener filter to the CTF (following doi:10.1016/j.ultramic.2008.03.004) with a given SNR value. If no value is given, the default value of 0.0 means that no filter is applied.
kwargs (dict, optional) – Optionally provide the aberration coefficients as keyword arguments.

References

1(1,2): Kirkland, E. J. (2010). Advanced Computing in Electron Microscopy (2nd ed.). Springer.

__init__(semiangle_cutoff=inf, soft=True, focal_spread=0.0, angular_spread=0.0, aberration_coefficients=None, energy=None, extent=None, gpts=None, sampling=None, flip_phase=False, wiener_snr=0.0, **kwargs)[source]#

Methods

`__init__`([semiangle_cutoff, soft, ...])
`apply`(waves)	Apply the transform to the given waves.
`copy`()	Make a copy.
`ensemble_blocks`([chunks])	Split the ensemble into an array of smaller ensembles.
`generate_blocks`([chunks])	Generate chunks of the ensemble.
`match_grid`(other[, check_match])	Match the grid to another object with a Grid.
`profiles`([gpts, max_angle, phi])	Calculate radial line profiles for each included component (phase aberrations, aperture, temporal and spatial envelopes) of the contrast transfer function.
`select_block`(index, chunks)	Select a block from the ensemble.
`set_aberrations`(aberration_coefficients)	Set the phase of the phase aberration.
`show`(**kwargs)
`to_diffraction_patterns`([max_angle, gpts])
`to_point_spread_functions`(gpts, extent)

Attributes

`C10`
`C12`
`C21`
`C23`
`C30`
`C32`
`C34`
`C41`
`C43`
`C45`
`C5`
`C50`
`C52`
`C54`
`C56`
`Cs`
`aberration_coefficients`	The aberration coefficients as a dictionary.
`accelerator`	Accelerator object describing the acceleration energy.
`angular_sampling`	The sampling in scattering angles of the transfer function [mrad].
`angular_spread`	The standard deviation of the angular deviations due to source size [mrad].
`astigmatism`
`astigmatism_angle`
`axes_metadata`	List of AxisMetadata.
`base_axes_metadata`	List of AxisMetadata of the base axes.
`base_shape`	Shape of the base axes.
`coma`
`coma_angle`
`crossover_angle`	The first zero-crossing of the phase at Scherzer defocus [mrad].
`defocus`	Defocus equivalent to negative C10.
`distributions`
`energy`	Electron acceleration energy in electron volts.
`ensemble_axes_metadata`	Axes metadata describing the ensemble axes added to the waves when applying the transform.
`ensemble_shape`	The shape of the ensemble axes added to the waves when applying the transform.
`extent`	Extent of grid for each dimension in Ångstrom.
`flip_phase`	If true the signs of all negative parts of the CTF are changed to positive.
`focal_spread`	The standard deviation of the focal spread [Å].
`gpts`	Number of grid points for each dimension.
`grid`	Simulation grid.
`in_place`	The array representing the waves may be modified in-place.
`metadata`	Metadata added to the waves when applying the transform.
`nyquist_sampling`	Nyquist sampling corresponding to the semiangle cutoff of the aperture [Å].
`phi12`
`phi21`
`phi23`
`phi32`
`phi34`
`phi41`
`phi43`
`phi45`
`phi52`
`phi54`
`phi56`
`point_resolution`	The Scherzer point resolution [Å].
`reciprocal_space_sampling`	Reciprocal-space sampling in reciprocal Ångstrom.
`sampling`	Grid sampling for each dimension in Ångstrom per grid point.
`scherzer_defocus`	The Scherzer defocus [Å].
`semiangle_cutoff`	The semiangle cutoff [mrad].
`shape`	Shape of the ensemble.
`soft`	True if the aperture has a soft edge.
`wavelength`	Relativistic wavelength in Ångstrom.
`wiener_snr`	If true a Wiener filter is applied to the CTF.

property aberration_coefficients#: The aberration coefficients as a dictionary.

property accelerator: abtem.core.energy.Accelerator#

Accelerator object describing the acceleration energy.

Return type: Accelerator

property angular_sampling: tuple[float, float]#

The sampling in scattering angles of the transfer function [mrad].

Return type: tuple[float, float]

property angular_spread: float | BaseDistribution#

The standard deviation of the angular deviations due to source size [mrad].

Return type: float | BaseDistribution

apply(waves)#

Apply the transform to the given waves.

Parameters: array_object (ArrayObject) – The array object to transform.
Returns: transformed_array_object
Return type: ArrayObject

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 of the base axes.

Return type: list[AxisMetadata]

property base_shape: tuple[int, ...]#

Shape of the base axes.

Return type: tuple[int, ...]

copy()#: Make a copy.

property crossover_angle#: The first zero-crossing of the phase at Scherzer defocus [mrad].

property defocus: float | BaseDistribution#

Defocus equivalent to negative C10.

Return type: float | BaseDistribution

property energy#: Electron acceleration energy in electron volts.

property ensemble_axes_metadata#: Axes metadata describing the ensemble axes added to the waves when applying the transform.

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_shape#: The shape of the ensemble axes added to the waves when applying the transform.

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, …]

property flip_phase: bool#

If true the signs of all negative parts of the CTF are changed to positive.

Return type: bool

property focal_spread: float | BaseDistribution#

The standard deviation of the focal spread [Å].

Return type: float | BaseDistribution

generate_blocks(chunks=1)#

Generate chunks of the ensemble.

Parameters: chunks (iterable of tuples) – Block sizes along each dimension.

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

property in_place: bool#

The array representing the waves may be modified in-place.

Return type: bool

match_grid(other, check_match=False)#: Match the grid to another object with a Grid.

property metadata#: Metadata added to the waves when applying the transform.

property nyquist_sampling: float#

Nyquist sampling corresponding to the semiangle cutoff of the aperture [Å].

Return type: float

property point_resolution#: The Scherzer point resolution [Å].

profiles(gpts=1000, max_angle=None, phi=0.0)[source]#

Calculate radial line profiles for each included component (phase aberrations, aperture, temporal and spatial envelopes) of the contrast transfer function.

Parameters

gpts (int) – Number of grid points along the line profiles.
max_angle (float) – The maximum scattering angle included in the radial line profiles [mrad]. The default is 1.5 times the semiangle cutoff or 50 mrad if no semiangle cutoff is set.
phi (float) – The azimuthal angle of the radial line profiles [rad]. Default is 0.

Returns

ctf_profiles – Ensemble of reciprocal space line profiles. The first ensemble dimension represents the different

Return type

ReciprocalSpaceLineProfiles

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 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, …]

property scherzer_defocus#: The Scherzer defocus [Å].

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.

property semiangle_cutoff: float | BaseDistribution#

The semiangle cutoff [mrad].

Return type: float | BaseDistribution

set_aberrations(aberration_coefficients)#

Set the phase of the phase aberration.

Parameters: aberration_coefficients (dict) – Mapping from aberration symbols to their corresponding values.

property shape#: Shape of the ensemble.

property soft: float#

True if the aperture has a soft edge.

Return type: float

property wavelength#: Relativistic wavelength in Ångstrom.

property wiener_snr: float#

If true a Wiener filter is applied to the CTF.

Return type: float