abtem.finite_difference

Module Contents

Classes

LaplaceOperator

Functions

conventional_operator	Split-step real-space multislice operator used in all higher-order expansions.
finite_difference_coefficients
full_series	Full Taylor series expansion of the MS Eq.(14) in Ultramicrscopy 134 (2013) 135-143. override_prefactor used in backscatter call, Eq. (13) in Micron 190 (2025) 103778.
multislice_step	Performs a single multislice step.
propagator_taylor_series	Taylor series expansion of the propagator term in the MS equation. Eq.(8) in Ultramicroscopy 134 (2013) 135-143.

Data

fd_coefficients

API

exception abtem.finite_difference.DivergedError(...)

Bases: Exception

class abtem.finite_difference.LaplaceOperator(...)

Initialization

Centered finite-difference laplacian operator.

Parameters:

accuracy (int) – centered finite-difference stencil accuracy

apply(...)

get_stencil(...) → Callable

Cached method to return finite-difference stencil using specified waves parameters, namely wavelength and sampling for the prefactor.

Parameters:

• waves (Waves) – Waves object stencil will ultimately be applied to

• device (str, optional) – Device to evaluate stencil on, “cpu” or “gpu”

Returns:

stencil – Cached stencil function with waves prefactor, on specified device

Return type:

Callable

exception abtem.finite_difference.NotConvergedError(...)

Bases: Exception

abtem.finite_difference.conventional_operator(...)

Split-step real-space multislice operator used in all higher-order expansions.

Parameters:

• waves (Waves) – Waves object to apply multislice operator on

• laplace (Callable) – Fast laplace operator stencil function

• transmission_function (ndarray,) – Scaled potential slice to multiply incoming waves with

• wavelength (float) – Waves wavelength

abtem.finite_difference.fd_coefficients

None

abtem.finite_difference.finite_difference_coefficients(...)

abtem.finite_difference.full_series(...)

Full Taylor series expansion of the MS Eq.(14) in Ultramicrscopy 134 (2013) 135-143. override_prefactor used in backscatter call, Eq. (13) in Micron 190 (2025) 103778.

abtem.finite_difference.multislice_step(...) → Waves | Sequence[Waves]

Performs a single multislice step.

Parameters:

• waves (Waves) – Waves object to apply multislice operator on

• potential_slice (PotentialArray) – PotentialArray of slice to be used in transmission operator

• next_slice (PotentialArray | None) – PotentialArray of next slice (used to ‘look ahead’ for backscattered waves)

• laplace (Callable) – Fast laplace operator stencil function

• tolerance (float) – Convergence tolerance for exponent Taylor series amplitude

• max_terms (int) – Maximum terms in exponent Taylor series

• order (int) – Multislice operator expansion order

• fully_corrected (bool) – If True, transmission and propagator operators are expanded to specified order. If next_slice is not None, the backscattered wave component is also computed.

abtem.finite_difference.propagator_taylor_series(...)

Taylor series expansion of the propagator term in the MS equation. Eq.(8) in Ultramicroscopy 134 (2013) 135-143.