extrapolate_pc#

Return a new detector with projection centers (PCs) in a 2D map extrapolated from an average PC.

The average PC \(\bar{PC}\) is calculated from pc, possibly excluding some PCs based on the is_outlier mask. The sample position having this PC, \((\bar{x}, \bar{y})\), is assumed to be the one obtained by averaging pc_indices. All other PCs \((PC_x, PC_y, PC_z)\) in positions \((x, y)\) are then extrapolated based on the following equations given in appendix A in [Singh et al., 2017]:

\[\begin{split}PC_x &= \bar{PC_x} + (\bar{x} - x) \cdot \Delta x / (\delta \cdot N_x \cdot b),\\ PC_y &= \bar{PC_y} + (\bar{y} - y) \cdot \Delta y \cdot \cos{\alpha} / (\delta \cdot N_y \cdot b),\\ PC_z &= \bar{PC_z} - (\bar{y} - y) \cdot \Delta y \cdot \sin{\alpha} / (\delta \cdot N_y \cdot b),\\\end{split}\]

where \((\Delta y, \Delta x)\) are the vertical and horizontal step sizes, respectively, \((N_y, N_x)\) are the number of binned detector rows and columns, respectively, the angle \(\alpha = 90^{\circ} - \sigma + \theta\), where \(\sigma\) is the sample tilt and \(\theta\) is the detector tilt, \(\delta\) is the unbinned detector pixel size and \(b\) is the binning factor.

Parameters:

pc_indices: 2D map pixel coordinates (row, column) of each pc, possibly outside navigation_shape. Must be a flattened array of shape (2,) + navigation_size.
navigation_shape: Shape of the output PC array (n rows, n columns).
step_sizes: Vertical and horizontal step sizes (dy, dx).
shape: Detector (signal) shape (n rows, n columns). If not given, (nrows, ncols) is used.
px_size: Unbinned detector pixel size. If not given, px_size is used.
binning: Detector binning factor. If not given, binning is used.
is_outlier: Boolean array with True for PCs to not include in the fit. If not given, all PCs are used. Must be of navigation_shape.

Returns:

new_detector: Detector with navigation_shape given by input navigation_shape.

Examples using `EBSDDetector.extrapolate_pc`#

Fit a plane to selected projection centers

Estimate tilt about the detector x axis

Estimate tilts about the detector x and z axis

extrapolate_pc#

Examples using EBSDDetector.extrapolate_pc#

Examples using `EBSDDetector.extrapolate_pc`#