2.2. fakecbed.shapes

For creating undistorted geometric shapes.

This module contains classes that represent the intensity patterns of different undistorted geometric shapes that can be combined to construct intensity patterns that imitate convergent beam diffraction beam (CBED) patterns. As a shorthand, we refer to these intensity patterns that imitate CBED patterns as “fake CBED patterns”.

Users can create images of fake CBED patterns using the fakecbed.discretized module. An image of a fake CBED pattern is formed by specifying a series of parameters, with the most important parameters being: the set of intensity patterns of undistorted shapes that determine the undistorted noiseless non-blurred uncorrupted fake CBED pattern; and a distortion model which transforms the undistorted noiseless non-blurred uncorrupted fake CBED pattern into a distorted noiseless non-blurred uncorrupted fake CBED pattern. The remaining parameters determine whether additional images effects are applied, like e.g. shot noise or blur effects. Note that in the case of the aforementioned shapes, we expand the notion of intensity patterns to mean a 2D real-valued function, i.e. it can be negative. To be clear, we do not apply this generalized notion of intensity patterns to the fake CBED patterns: in such cases intensity patterns mean 2D real-valued functions that are strictly nonnegative.

Let \(u_{x}\) and \(u_{y}\) be the fractional horizontal and vertical coordinates, respectively, of a point in an undistorted image, where \(\left(u_{x},u_{y}\right)=\left(0,0\right)\) is the bottom left corner of the image. Secondly, let \(q_{x}\) and \(q_{y}\) be the fractional horizontal and vertical coordinates, respectively, of a point in a distorted image, where \(\left(q_{x},q_{y}\right)=\left(0,0\right)\) is the bottom left corner of the image. When users specify a distortion model, represented by an distoptica.DistortionModel object, they also specify a coordinate transformation which maps a given coordinate pair \(\left(u_{x},u_{y}\right)\) to a corresponding coordinate pair \(\left(q_{x},q_{y}\right)\), and implicitly a right-inverse to said coordinate transformation that maps a coordinate pair \(\left(q_{x},q_{y}\right)\) to a corresponding coordinate pair \(\left(u_{x},u_{y}\right)\), when such a relationship exists for \(\left(q_{x},q_{y}\right)\).

Classes

Arc	The intensity pattern of a circular arc.
Band	The intensity pattern of a band.
BaseShape	The intensity pattern of an undistorted geometric shape.
Circle	The intensity pattern of a circle.
Ellipse	The intensity pattern of a ellipse.
GenericBlob	The intensity pattern of a generic blob.
Lune	The intensity pattern of a lune.
NonuniformBoundedShape	The intensity pattern of a nonuniform bounded shape.
Orbital	The intensity pattern of a hydrogen-like atomic orbital.
Peak	The intensity pattern of a peak.
PlaneWave	The intensity pattern of a plane wave.