API reference#
This reference manual details the public modules, classes, and functions in kikuchipy, as generated from their docstrings. Many of the docstrings contain examples, however, see the user guide for how to use kikuchipy.
Caution
kikuchipy is in continuous development (alpha stage), so expect some breaking changes with each release.
The list of top modules and the load function:
Crystallographic computations not found (easily) elsewhere. 

Test data. 

An EBSD detector and related quantities. 

Creation of HyperSpy markers to add to signals and other tools. 

Pattern filters used on signals. 

Generate signals and simulations, sometimes from other signals. 

Tools for indexing of EBSD patterns by matching to a dictionary of simulated patterns. 

Read and write signals from and to file. 


Load an 
Single and chunk pattern processing used by signals. 

Various projections and transformations relevant to EBSD. 

Experimental and simulated diffraction patterns and virtual backscatter electron images. 

Simulations returned by a generator and handling of Kikuchi bands and zone axes. 
crystallography#
Crystallographic computations not found (easily) elsewhere.

[Deprecated] Direct structure matrix as defined in EMsoft. 

[Deprecated] Reciprocal metric tensor as defined in EMsoft. 

[Deprecated] Reciprocal structure matrix as defined in EMsoft. 
 kikuchipy.crystallography.get_direct_structure_matrix(lattice)[source]#
[Deprecated] Direct structure matrix as defined in EMsoft.
 Parameters:
lattice (
Lattice
) – Crystal structure lattice.
Notes
Deprecated since version 0.6: Function get_direct_structure_matrix() is deprecated and will be removed in version 0.7. Use diffpy.structure.Lattice.base instead.
 Return type:
 kikuchipy.crystallography.get_reciprocal_metric_tensor(lattice)[source]#
[Deprecated] Reciprocal metric tensor as defined in EMsoft.
 Parameters:
lattice (
Lattice
) – Crystal structure lattice. Return type:
Notes
Deprecated since version 0.6: Function get_reciprocal_metric_tensor() is deprecated and will be removed in version 0.7. Use diffpy.structure.Lattice.reciprocal().metrics instead.
 kikuchipy.crystallography.get_reciprocal_structure_matrix(lattice)[source]#
[Deprecated] Reciprocal structure matrix as defined in EMsoft.
 Parameters:
lattice (
Lattice
) – Crystal structure lattice. Return type:
Notes
Deprecated since version 0.6: Function get_reciprocal_structure_matrix() is deprecated and will be removed in version 0.7. Use diffpy.structure.Lattice.recbase instead.
data#

9 EBSD patterns in a (3, 3) navigation shape of (60, 60) detector pixels from Nickel, acquired on a NORDIF UF1100 detector [AHvHM19]. 

4125 EBSD patterns in a (55, 75) navigation shape of (60, 60) detector pixels from Nickel, acquired on a NORDIF UF1100 detector [AHvHM19]. 

(401, 401) uint8 square Lambert or stereographic projection of the northern and southern hemisphere of a Nickel master pattern at 20 keV accelerating voltage. 
One EBSD pattern of (480, 480) detector pixels from a single crystal Silicon sample, acquired on a NORDIF UF420 detector. 

One EBSD pattern of (480, 480) detector pixels from a single crystal Silicon sample, acquired on a NORDIF UF420 detector. 

One EBSD pattern of (480, 480) detector pixels from a single crystal Silicon sample, acquired on a NORDIF UF420 detector. 
Test data.
Some datasets must be downloaded from the web. For more test datasets, see open datasets.
Some datasets must be downloaded from the web. Datasets are placed in a local cache, in the location returned from pooch.os_cache(“kikuchipy”) by default. The location can be overwritten with a global KIKUCHIPY_DATA_DIR environment variable.
With every new version of kikuchipy, a new directory of datasets with the version name is added to the cache directory. Any old directories are not deleted automatically, and should then be deleted manually if desired.
 kikuchipy.data.nickel_ebsd_large(allow_download=False, progressbar=True, **kwargs)[source]#
4125 EBSD patterns in a (55, 75) navigation shape of (60, 60) detector pixels from Nickel, acquired on a NORDIF UF1100 detector [AHvHM19].
Carries a CC BY 4.0 license.
 Parameters:
allow_download (bool) – Whether to allow downloading the dataset from the kikuchipydata GitHub repository (https://github.com/pyxem/kikuchipydata) to the local cache with the pooch Python package. Default is
False
.progressbar (
bool
) – Whether to show a progressbar when downloading. Default isFalse
.kwargs – Keyword arguments passed to
load()
.
 Returns:
signal – EBSD signal.
 Return type:
Examples
>>> import kikuchipy as kp >>> s = kp.data.nickel_ebsd_large(allow_download=True) >>> s <EBSD, title: patterns Scan 1, dimensions: (75, 5560, 60)>
 kikuchipy.data.nickel_ebsd_master_pattern_small(**kwargs)[source]#
(401, 401) uint8 square Lambert or stereographic projection of the northern and southern hemisphere of a Nickel master pattern at 20 keV accelerating voltage.
Carries a CC BY 4.0 license.
 Parameters:
kwargs – Keyword arguments passed to
load()
. Returns:
signal – EBSD master pattern signal.
 Return type:
Notes
Initially generated using the EMsoft EMMCOpenCL and EMEBSDMaster programs. The included file was rewritten to disk with
h5py
, where the master patterns’ data type is converted from float32 to uint8 withrescale_intensity()
, all datasets were written withdict2h5ebsdgroup()
with keyword arguments compression=”gzip” and compression_opts=9. All other HDF5 groups and datasets are the same as in the original file.Examples
>>> import kikuchipy as kp >>> s = kp.data.nickel_ebsd_master_pattern_small() >>> s <EBSDMasterPattern, title: ni_mc_mp_20kv_uint8_gzip_opts9, dimensions: (401, 401)> >>> s.projection 'stereographic'
Import master pattern in the square Lambert projection
>>> s2 = kp.data.nickel_ebsd_master_pattern_small(projection="lambert") >>> s2.projection 'lambert'
 kikuchipy.data.nickel_ebsd_small(**kwargs)[source]#
9 EBSD patterns in a (3, 3) navigation shape of (60, 60) detector pixels from Nickel, acquired on a NORDIF UF1100 detector [AHvHM19].
Carries a CC BY 4.0 license.
 Parameters:
kwargs – Keyword arguments passed to
load()
. Returns:
signal – EBSD signal.
 Return type:
Examples
>>> import kikuchipy as kp >>> s = kp.data.nickel_ebsd_small() >>> s <EBSD, title: patterns My awes0m4 ..., dimensions: (3, 360, 60)>
 kikuchipy.data.silicon_ebsd_moving_screen_in(allow_download=False, progressbar=True, **kwargs)[source]#
One EBSD pattern of (480, 480) detector pixels from a single crystal Silicon sample, acquired on a NORDIF UF420 detector.
This pattern and two other patterns from the same sample position but with 5 mm and 10 mm greater samplescreendistances were acquired to test the movingscreen projection center estimation technique [HH91].
Carries a CC BY 4.0 license.
 Parameters:
allow_download (bool) – Whether to allow downloading the dataset from the kikuchipydata GitHub repository (https://github.com/pyxem/kikuchipydata) to the local cache with the pooch Python package. Default is
False
.progressbar (
bool
) – Whether to show a progressbar when downloading. Default isFalse
.kwargs – Keyword arguments passed to
load()
.
 Returns:
signal – EBSD signal.
 Return type:
Examples
>>> import kikuchipy as kp >>> s = kp.data.silicon_ebsd_moving_screen_in(allow_download=True) >>> s <EBSD, title: si_in Scan 1, dimensions: (480, 480)>
 kikuchipy.data.silicon_ebsd_moving_screen_out10mm(allow_download=False, progressbar=True, **kwargs)[source]#
One EBSD pattern of (480, 480) detector pixels from a single crystal Silicon sample, acquired on a NORDIF UF420 detector.
This pattern and two other patterns from the same sample position but with samplescreendistances 10 mm shorter (
silicon_ebsd_moving_screen_in()
) and 5 mm shorter (silicon_ebsd_moving_screen_out5mm()
) were acquired to test the movingscreen projection center estimation technique [HH91].Carries a CC BY 4.0 license.
 Parameters:
allow_download (bool) – Whether to allow downloading the dataset from the kikuchipydata GitHub repository (https://github.com/pyxem/kikuchipydata) to the local cache with the pooch Python package. Default is
False
.progressbar (
bool
) – Whether to show a progressbar when downloading. Default isFalse
.kwargs – Keyword arguments passed to
load()
.
 Returns:
signal – EBSD signal.
 Return type:
Examples
>>> import kikuchipy as kp >>> s = kp.data.silicon_ebsd_moving_screen_out10mm(allow_download=True) >>> s <EBSD, title: si_out10mm Scan 1, dimensions: (480, 480)>
 kikuchipy.data.silicon_ebsd_moving_screen_out5mm(allow_download=False, progressbar=True, **kwargs)[source]#
One EBSD pattern of (480, 480) detector pixels from a single crystal Silicon sample, acquired on a NORDIF UF420 detector.
This pattern and two other patterns from the same sample position but with samplescreendistances 5 mm shorter (
silicon_ebsd_moving_screen_in()
) and 5 mm greater (silicon_ebsd_moving_screen_out10mm()
) were acquired to test the movingscreen projection center estimation technique [HH91].Carries a CC BY 4.0 license.
 Parameters:
allow_download (bool) – Whether to allow downloading the dataset from the kikuchipydata GitHub repository (https://github.com/pyxem/kikuchipydata) to the local cache with the pooch Python package. Default is
False
.progressbar (
bool
) – Whether to show a progressbar when downloading. Default isFalse
.kwargs – Keyword arguments passed to
load()
.
 Returns:
signal – EBSD signal.
 Return type:
Examples
>>> import kikuchipy as kp >>> s = kp.data.silicon_ebsd_moving_screen_out5mm(allow_download=True) >>> s <EBSD, title: si_out5mm Scan 1, dimensions: (480, 480)>
detectors#
An EBSD detector and related quantities.

An EBSD detector class storing its shape, pixel size, binning factor, detector tilt, sample tilt and projection center (PC) per pattern. 

A class to perform and inspect the calibration of the EBSD projection center (PC) using the "moving screen" technique from [HH91]. 
EBSDDetector#

Return a deep copy using 
Return PC in the Bruker convention, defined in 


Return PC in the EMsoft convention. 
Return PC in the Oxford convention. 


Return PC in the EDAX TSL convention. 

Plot the detector screen. 
 class kikuchipy.detectors.EBSDDetector(shape=(1, 1), px_size=1, binning=1, tilt=0, azimuthal=0, sample_tilt=70, pc=(0.5, 0.5, 0.5), convention=None)[source]#
Bases:
object
An EBSD detector class storing its shape, pixel size, binning factor, detector tilt, sample tilt and projection center (PC) per pattern. Given one or multiple PCs, the detector’s gnomonic coordinates are calculated. Uses of these include projecting Kikuchi bands, given a unit cell, unit cell orientation and family of planes, onto the detector.
Calculation of gnomonic coordinates is based on the work by Aimo Winkelmann in the supplementary material to [BJG+16].
 __init__(shape=(1, 1), px_size=1, binning=1, tilt=0, azimuthal=0, sample_tilt=70, pc=(0.5, 0.5, 0.5), convention=None)[source]#
Create an EBSD detector with a shape, pixel size, binning, and projection/pattern center(s) (PC(s)).
 Parameters:
shape (
Tuple
[int
,int
]) – Number of detector rows and columns in pixels. Default is (1, 1).px_size (
float
) – Size of unbinned detector pixel in um, assuming a square pixel shape. Default is 1 um.binning (
int
) – Detector binning, i.e. how many pixels are binned into one. Default is 1, i.e. no binning.tilt (
float
) – Detector tilt from horizontal in degrees. Default is 0.azimuthal (
float
) – Sample tilt about the sample RD (downwards) axis. A positive angle means the sample normal moves towards the right looking from the sample to the detector. Default is 0.sample_tilt (
float
) – Sample tilt from horizontal in degrees. Default is 70.pc (
Union
[ndarray
,list
,tuple
]) – X, Y and Z coordinates of the projection/pattern centers (PCs), describing the location of the beam on the sample measured relative to the detection screen. See Notes for the definition and conversions between conventions. If multiple PCs are passed, they are assumed to be on the form [[x0, y0, z0], [x1, y1, z1], …]. Default is [[0.5, 0.5, 0.5]].convention (
Optional
[str
]) – PC convention. If None (default), Bruker’s convention is assumed. Options are “tsl”, “oxford”, “bruker”, “emsoft”, “emsoft4”, and “emsoft5”. “emsoft” and “emsoft5” is the same convention. See Notes for conversions between conventions.
Notes
The pattern on the detector is always viewed from the detector towards the sample. Pattern width and height is here given as $N_x$ and $N_y$ (possibly binned).
The Bruker PC coordinates $(x_B^*, y_B^*, z_B^*)$ are defined in fractions of $N_x$, $N_y$, and $N_y$, respectively, with $x_B^*$ and $y_B^*$ defined with respect to the upper left corner of the detector. These coordinates are used internally, called ($PC_x, PC_y, PC_z$) in the rest of the documentation when there is no reference to Bruker specifically.
The EDAX TSL PC coordinates $(x_T^*, y_T^*, z_T^*)$ and Oxford Instruments PC coordinates $(x_O^*, y_O^*, z_O^*)$ are identical and defined in fractions of $N_x$ with respect to the lower left corner of the detector.
The EMsoft PC coordinates $(x_{pc}, y_{pc})$ are defined as number of pixels (subpixel accuracy) with resepct to the center of the detector, with $x_{pc}$ towards the right and $y_{pc}$ upwards. The final PC coordinate $L$ is the detector distance in microns. Note that before EMsoft v5.0, $x_{pc}$ was defined towards the left.
Given these definitions, the following is the conversion from TSL/Oxford to Bruker
\[\begin{split}x_B^* &= x_T^*,\\ y_B^* &= 1  \frac{N_x}{N_y} y_T^*,\\ z_B^* &= \frac{N_x}{N_y} z_T^*.\end{split}\]The conversion from EMsoft to Bruker is given as
\[\begin{split}x_B^* &= \frac{1}{2}  \frac{x_{pc}}{N_x b},\\ y_B^* &= \frac{1}{2}  \frac{y_{pc}}{N_y b},\\ z_B^* &= \frac{L}{N_y b \delta},\end{split}\]where \(\delta\) is the unbinned detector pixel size in microns, and $b$ is the binning factor.
Examples
>>> import numpy as np >>> from kikuchipy.detectors import EBSDDetector >>> det = EBSDDetector( ... shape=(60, 60), ... pc=np.ones((149, 200, 3)) * (0.421, 0.779, 0.505), ... convention="tsl", ... px_size=70, ... binning=8, ... tilt=5, ... sample_tilt=70, ... ) >>> det EBSDDetector (60, 60), px_size 70 um, binning 8, tilt 5, azimuthal 0, pc (0.421, 0.221, 0.505) >>> det.navigation_shape # (nrows, ncols) (149, 200) >>> det.bounds array([ 0, 59, 0, 59]) >>> det.gnomonic_bounds[0, 0] array([0.83366337, 1.14653465, 0.83366337, 1.14653465]) >>> det.plot()
 deepcopy()[source]#
Return a deep copy using
copy.deepcopy()
.
 property gnomonic_bounds: ndarray#
Detector bounds [x0, x1, y0, y1] in gnomonic coordinates.
 Return type:
Number of navigation dimensions of the projection center array (a maximum of 2).
 Return type:
Navigation shape of the projection center array.
 Return type:
 pc_bruker()[source]#
Return PC in the Bruker convention, defined in
__init__()
. Return type:
 pc_emsoft(version=5)[source]#
Return PC in the EMsoft convention.
 Parameters:
version (
int
) – Which EMsoft PC convention to use. The direction of the x PC coordinate, $x_{pc}$, flipped in version 5.
Notes
The PC coordinate conventions of Bruker, EDAX TSL, Oxford Instruments and EMsoft are explained in
__init__()
. The PC is stored in the Bruker convention internally, so the conversion is\[\begin{split}x_{pc} &= N_x b \left(\frac{1}{2}  x_B^*\right),\\ y_{pc} &= N_y b \left(\frac{1}{2}  y_B^*\right),\\ L &= N_y b \delta z_B^*,\end{split}\]where $N_x$ and $N_y$ are number of detector columns and rows, $b$ is binning, \(\delta\) is the unbinned pixel size, $(x_B^*, y_B^*, z_B^*)$ are the Bruker PC coordinates, and $(x_{pc}, y_{pc}, L)$ are the returned EMsoft PC coordinates.
 Return type:
 pc_oxford()[source]#
Return PC in the Oxford convention.
Notes
The Oxford PC coordinates are identical to the TSL coordinates, see
pc_tsl()
. Return type:
 pc_tsl()[source]#
Return PC in the EDAX TSL convention.
Notes
The PC coordinate conventions of Bruker, EDAX TSL, Oxford Instruments and EMsoft are explained in
__init__()
. The PC is stored in the Bruker convention internally, so the conversion is\[\begin{split}x_T^* &= x_B^*,\\ y_T^* &= \frac{N_y}{N_x} (1  y_B^*),\\ z_T^* &= \frac{N_y}{N_x} z_B^*,\end{split}\]where $N_x$ and $N_y$ are number of detector columns and rows, $(x_B^*, y_B^*, z_B^*)$ are the Bruker PC coordinates, and $(x_T^*, y_T^*, z_T^*)$ are the returned EDAX TSL PC coordinates.
 Return type:
 plot(coordinates='detector', show_pc=True, pc_kwargs=None, pattern=None, pattern_kwargs=None, draw_gnomonic_circles=False, gnomonic_angles=None, gnomonic_circles_kwargs=None, zoom=1, return_fig_ax=False)[source]#
Plot the detector screen.
The plotting of gnomonic circles and general style is adapted from the supplementary material to [BJG+16] by Aimo Winkelmann.
 Parameters:
coordinates (
str
) – Which coordinates to use, “detector” (default) or “gnomonic”.show_pc (
bool
) – Show the average projection center in the Bruker convention. Default is True.pc_kwargs (
Optional
[dict
]) – A dictionary of keyword arguments passed tomatplotlib.axes.Axes.scatter()
.pattern (
Optional
[ndarray
]) – A pattern to put on the detector. If None (default), no pattern is displayed. The pattern array must have the same shape as the detector.pattern_kwargs (
Optional
[dict
]) – A dictionary of keyword arguments passed tomatplotlib.axes.Axes.imshow()
.draw_gnomonic_circles (
bool
) – Draw circles for angular distances from pattern. Default is False. Circle positions are only correct when coordinates=”gnomonic”.gnomonic_angles (
Union
[None
,list
,ndarray
]) – Which angular distances to plot if draw_gnomonic_circles is True. Default is from 10 to 80 in steps of 10.gnomonic_circles_kwargs (
Optional
[dict
]) – A dictionary of keyword arguments passed tomatplotlib.patches.Circle()
.zoom (
float
) – Whether to zoom in/out from the detector, e.g. to show the extent of the gnomonic projection circles. A zoom > 1 zooms out. Default is 1, i.e. no zoom.return_fig_ax (
bool
) – Whether to return the figure and axes object created. Default is False.
 Return type:
 Returns:
fig – Matplotlib figure object, if return_fig_ax is True.
ax – Matplotlib axes object, if return_fig_ax is True.
Examples
>>> import numpy as np >>> from kikuchipy.detectors import EBSDDetector >>> det = EBSDDetector( ... shape=(60, 60), ... pc=np.ones((149, 200, 3)) * (0.421, 0.779, 0.505), ... convention="tsl", ... sample_tilt=70, ... ) >>> det.plot() >>> det.plot( ... coordinates="gnomonic", ... draw_gnomonic_circles=True, ... gnomonic_circles_kwargs={"edgecolor": "b", "alpha": 0.3} ... ) >>> fig, ax = det.plot( ... pattern=np.ones(det.shape), ... show_pc=True, ... return_fig_ax=True, ... ) >>> fig.savefig("detector.png")
 property r_max: ndarray#
Maximum distance from PC to detector edge in gnomonic coordinates.
 Return type:
 property specimen_scintillator_distance: float#
Specimen to scintillator distance (SSD), known in EMsoft as L.
 Return type:
PCCalibrationMovingScreen#
Draw lines between all points within a pattern and populate self.lines. 


A convenience method of three images, the first two with the patterns with points and lines annotated, and the third with the calibration results. 
 class kikuchipy.detectors.PCCalibrationMovingScreen(pattern_in, pattern_out, points_in, points_out, delta_z=1, px_size=None, binning=1, convention='tsl')[source]#
Bases:
object
A class to perform and inspect the calibration of the EBSD projection center (PC) using the “moving screen” technique from [HH91].
The technique requires two patterns acquired with a stationary beam but with different detector distances (DDs) where the difference is known. First, the goal is to find the pattern region which does not shift between the two camera positions, (PCx, PCy). This point can be estimated by selecting the same pattern features in both patterns. Second, the DD (PCz) can be estimated in the same unit as the known camera distance difference. If also the detector pixel size is known, PCz can be given in the fraction of the detector screen height.
 __init__(pattern_in, pattern_out, points_in, points_out, delta_z=1, px_size=None, binning=1, convention='tsl')[source]#
Return a class instance storing the PC estimates, the average PC, and other parameters relevant for the estimation.
 Parameters:
pattern_in (
ndarray
) – Pattern acquired with the shortest detector distance (DD) in the “in” position.pattern_out (
ndarray
) – Pattern acquired with the longer DD in the “out” position, with the camera a known distance delta_z from the “in” position.points_in (
Union
[ndarray
,List
[Tuple
[float
]]]) – Set of \(n\) coordinates [(x1, y1), (x2, y2), …] of pattern features in pattern_in.points_out (
Union
[ndarray
,List
[Tuple
[float
]]]) – Set of \(n\) coordinates [(x1, y1), (x2, y2), …] of pattern features, the same as in points_in, in pattern_out. They must be in the same order as in points_in.delta_z (
float
) – Known distance between the “in” and “out” camera positions in which the pattern_in and pattern_out were acquired, respectively. Default is 1. The output PCz value will be in the same unit as this value, unless px_size is provided.px_size (
Optional
[float
]) – Known size of the detector pixels, in the same unit as delta_z. If this is None (default), the PCz will not be scaled to fractions of detector height.binning (
int
) – Detector pixel binning. Default is 1, meaning no binning. This is used together with px_size to scale PCz.convention (
str
) – Whether to present PCy as the value from bottom to top (TSL), or top to bottom (Bruker). Default is “tsl”.
 property lines: ndarray#
Start and end points of all possible lines between all points per pattern, of shape (2, n_lines, 4), where the last axis is (x1, y1, x2, y2).
 Return type:
 property lines_end: ndarray#
End points of lines within both patterns, of shape (2, n_lines, 2).
 Return type:
 property lines_out_in: ndarray#
Start (out) and end (in) points of the lines between corresponding points in the patterns, of shape (n_points, 4).
 Return type:
 property lines_out_in_end: ndarray#
End points of the lines between corresponding points in the patterns, of shape (n_points, 2).
 Return type:
 property lines_out_in_start: ndarray#
Starting points of the lines between corresponding points in the patterns, of shape (n_points, 2).
 Return type:
 property lines_start: ndarray#
Starting points of lines within the patterns, of shape (2, n_lines, 2).
 Return type:
 make_lines()[source]#
Draw lines between all points within a pattern and populate self.lines. Is first run upon initialization.
 property pcz_all: ndarray#
All estimates of PCz, scaled to fraction of detector height if px_size is not None.
 Return type:
 plot(pattern_kwargs={'cmap': 'gray'}, line_kwargs={'linewidth': 2, 'zorder': 1}, scatter_kwargs={'zorder': 2}, pc_kwargs={'edgecolor': 'k', 'facecolor': 'gold', 'marker': '*', 's': 300}, return_fig_ax=False, **kwargs)[source]#
A convenience method of three images, the first two with the patterns with points and lines annotated, and the third with the calibration results.
 Parameters:
pattern_kwargs (
dict
) – Keyword arguments passed tomatplotlib.axes.Axes.imshow()
.line_kwargs (
dict
) – Keyword arguments passed tomatplotlib.axes.Axes.axline()
.scatter_kwargs (
dict
) – Keyword arguments passed tomatplotlib.axes.Axes.scatter()
.pc_kwargs (
dict
) – Keyword arguments, along with scatter_kwargs, passed tomatplotlib.axes.Axes.scatter()
when plotting the PCs.return_fig_ax (
bool
) – Whether to return the figure and axes, default is False.kwargs (
dict
) – Keyword arguments passed tomatplotlib.pyplot.subplots()
.
 Return type:
 Returns:
fig – Figure, returned if return_fig_ax is True.
ax – Axes, returned if return_fig_ax is True.
 property pxy: float#
Average of intersections of the lines between corresponding points in the patterns.
 Return type:
 property pxy_all: ndarray#
Intersections of the lines between the corresponding points in the patterns, i.e. estimates of (PCx, PCy), of shape (n_points, 2).
 Return type:
draw#
Creation of HyperSpy markers to add to signals and other tools.
Color palettes for plotting Kikuchi bands. 


Create an RGB navigator signal which is suitable to pass to 
Creation of lists of HyperSpy markers. 
Create an RGB navigator signal which is suitable to pass to
plot()
as the navigator parameter. Parameters:
image (numpy.ndarray) – RGB color image of shape (n rows, n columns, 3).
dtype (numpy.dtype) – Which data type to cast the signal data to, either uint16 (default) or uint8.
 Returns:
signal – Signal with an (n columns, n rows) signal shape and no navigation shape, of data type either rgb8 or rgb16.
 Return type:
hyperspy.signals.Signal2D
markers#
Creation of lists of HyperSpy markers.

Return a list of line segment markers. 

Return a list of point markers. 

Return a list of text markers. 
 kikuchipy.draw.markers.get_line_segment_list(lines, **kwargs)[source]#
Return a list of line segment markers.
 Parameters:
lines (
Union
[list
,ndarray
]) – On the form [[x00, y00, x01, y01], [x10, y10, x11, y11], …].kwargs – Keyword arguments allowed by
matplotlib.pyplot.axvline()
.
 Returns:
marker_list – List of
hyperspy.drawing._markers.line_segment.LineSegment
. Return type:
 kikuchipy.draw.markers.get_point_list(points, **kwargs)[source]#
Return a list of point markers.
 Parameters:
points (
Union
[list
,ndarray
]) – On the form [[x0, y0], [x1, y1], …].kwargs – Keyword arguments allowed by
matplotlib.pyplot.scatter()
.
 Returns:
marker_list – List of
hyperspy.drawing._markers.point.Point
. Return type:
colors#
Color palettes for plotting Kikuchi bands.
filters#
Pattern filters used on signals.

Return the distance to the window origin in pixels. 

Return a frequency domain highpass filter transfer function in 2D. 

Return a frequency domain lowpass filter transfer function in 2D. 

Return a 1D modified Hann window with the maximum value normalized to 1. 

A window/kernel/mask/filter of a given shape with some values. 
 kikuchipy.filters.distance_to_origin(shape, origin=None)[source]#
Return the distance to the window origin in pixels.
 kikuchipy.filters.highpass_fft_filter(shape, cutoff, cutoff_width=None)[source]#
Return a frequency domain highpass filter transfer function in 2D.
Used in [WMD06].
 Parameters:
 Returns:
w – 2D transfer function.
 Return type:
Notes
The highpass filter transfer function is defined as
\[\begin{split}w(r) = e^{\left(\frac{c  r}{\sqrt{2}w_c/2}\right)^2}, w(r) = \begin{cases} 0, & r < c  2w_c\\ 1, & r > c, \end{cases}\end{split}\]where \(r\) is the radial distance to the window centre, \(c\) is the cutoff frequency, and \(w_c\) is the width of the cutoff region.
Examples
>>> import numpy as np >>> import kikuchipy as kp >>> w1 = kp.filters.Window( ... "highpass", cutoff=1, cutoff_width=0.5, shape=(96, 96) ... ) >>> w2 = kp.filters.highpass_fft_filter( ... shape=(96, 96), cutoff=1, cutoff_width=0.5 ... ) >>> np.allclose(w1, w2) True
 kikuchipy.filters.lowpass_fft_filter(shape, cutoff, cutoff_width=None)[source]#
Return a frequency domain lowpass filter transfer function in 2D.
Used in [WMD06].
 Parameters:
 Returns:
2D transfer function.
 Return type:
w
Notes
The lowpass filter transfer function is defined as
\[\begin{split}w(r) = e^{\left(\frac{r  c}{\sqrt{2}w_c/2}\right)^2}, w(r) = \begin{cases} 0, & r > c + 2w_c \\ 1, & r < c, \end{cases}\end{split}\]where \(r\) is the radial distance to the window centre, \(c\) is the cutoff frequency, and \(w_c\) is the width of the cutoff region.
Examples
>>> import numpy as np >>> import kikuchipy as kp >>> w1 = kp.filters.Window( ... "lowpass", cutoff=30, cutoff_width=15, shape=(96, 96) ... ) >>> w2 = kp.filters.lowpass_fft_filter( ... shape=(96, 96), cutoff=30, cutoff_width=15 ... ) >>> np.allclose(w1, w2) True
 kikuchipy.filters.modified_hann(Nx)[source]#
Return a 1D modified Hann window with the maximum value normalized to 1.
Used in [WMD06].
 Parameters:
Nx (
int
) – Number of points in the window. Returns:
1D Hann window.
 Return type:
w
Notes
The modified Hann window is defined as
\[w(x) = \cos\left(\frac{\pi x}{N_x}\right),\]with \(x\) relative to the window centre.
Examples
>>> import numpy as np >>> import kikuchipy as kp >>> w1 = kp.filters.modified_hann(Nx=30) >>> w2 = kp.filters.Window("modified_hann", shape=(30,)) >>> np.allclose(w1, w2) True
Window#

Return whether the window is in a valid state. 
Make window circular. 


Plot window values with indices relative to the origin. 

Return whether window shape is compatible with a data shape. 
 class kikuchipy.filters.Window(window: Union[None, str, ndarray, Array] = None, shape: Optional[Sequence[int]] = None, **kwargs)[source]#
Bases:
ndarray
A window/kernel/mask/filter of a given shape with some values.
This class is a subclass of
numpy.ndarray
with some additional convenience methods.It can be used to create a transfer function for filtering in the frequency domain, create an averaging window for averaging patterns with their nearest neighbours, and so on.
 Parameters:
window ("circular", "rectangular", "gaussian", str, numpy.ndarray, or dask.array.Array, optional) – Window type to create. Available types are listed in
scipy.signal.windows.get_window()
and includes “rectangular” and “gaussian”, in addition to a “circular” window (default) filled with ones in which corner data are set to zero, a “modified_hann” window and “lowpass” and “highpass” FFT windows. A window element is considered to be in a corner if its radial distance to the origin (window centre) is shorter or equal to the half width of the windows’s longest axis. A 1D or 2Dnumpy.ndarray
ordask.array.Array
can also be passed.shape (sequence of int, optional) – Shape of the window. Not used if a custom window is passed to window. This can be either 1D or 2D, and can be asymmetrical. Default is (3, 3).
**kwargs – Required keyword arguments passed to the window type.
Examples
>>> import numpy as np >>> import kikuchipy as kp
The following passed parameters are the default
>>> w = kp.filters.Window(window="circular", shape=(3, 3)) >>> w Window (3, 3) circular [[0. 1. 0.] [1. 1. 1.] [0. 1. 0.]]
A window can be made circular
>>> w = kp.filters.Window(window="rectangular") >>> w Window (3, 3) rectangular [[1. 1. 1.] [1. 1. 1.] [1. 1. 1.]] >>> w.make_circular() >>> w Window (3, 3) circular [[0. 1. 0.] [1. 1. 1.] [0. 1. 0.]]
A custom window can be created
>>> w = kp.filters.Window(np.arange(6).reshape(3, 2)) >>> w Window (3, 2) custom [[0 1] [2 3] [4 5]]
To create a Gaussian window with a standard deviation of 2, obtained from
scipy.signal.windows.gaussian()
>>> w = kp.filters.Window(window="gaussian", std=2) >>> w Window (3, 3) gaussian [[0.7788 0.8825 0.7788] [0.8825 1. 0.8825] [0.7788 0.8825 0.7788]]
See also
 __init__()#
 make_circular()[source]#
Make window circular.
The data of window elements who’s radial distance to the window origin is shorter or equal to the half width of the window’s longest axis are set to zero. This has no effect if the window has only one axis.
 property n_neighbours: tuple#
Maximum number of nearest neighbours in each navigation axis to the origin.
 Return type:
 plot(grid=True, show_values=True, textcolors=None, cmap='viridis', cmap_label='Value', colorbar=True, return_figure=False)[source]#
Plot window values with indices relative to the origin.
 Parameters:
grid (
bool
) – Whether to separate each value with a white spacing in a grid. Default is True.show_values (
bool
) – Whether to show values as text in centre of element. Default is True.textcolors (
Optional
[List
[str
]]) – A list of two color specifications. The first is used for values below a threshold, the second for those above. If None (default), this is set to [“white”, “black”].cmap (
str
) – A color map to color data with, available inmatplotlib.colors.ListedColormap
. Default is “viridis”.cmap_label (
str
) – Color map label. Default is “Value”.colorbar (
bool
) – Whether to show the colorbar. Default is True.return_figure (
bool
) – Whether to return the figure or not. Default is False.
 Return type:
fig
Examples
A plot of window data with indices relative to the origin, showing element values and x/y ticks, can be produced and written to file
>>> import kikuchipy as kp >>> w = kp.filters.Window() >>> fig = w.plot(return_figure=True) >>> fig.savefig('my_kernel.png')
If getting the figure axes, image array or colorbar is necessary
>>> ax = fig.axes[0] >>> im = ax.get_images()[0] >>> arr = im.get_array() >>> cbar = im.colorbar
generators#
Generate signals and simulations, sometimes from other signals.

[Deprecated] A generator storing necessary parameters to simulate geometrical EBSD patterns. 

Generates virtual backscatter electron (BSE) images for a specified electron backscatter diffraction (EBSD) signal and a set of EBSD detector areas. 

Return an RGB image from three numpy arrays, with a potential alpha channel. 
Normalize an image's intensities to a mean of 0 and a standard deviation of 1, with the possibility to also scale by a contrast factor and shift the brightness values. 
EBSDSimulationGenerator#

Project a set of Kikuchi bands and zone axes onto the detector, one set for each rotation of the unit cell. 
 class kikuchipy.generators.EBSDSimulationGenerator(detector, phase, rotations)[source]#
Bases:
object
[Deprecated] A generator storing necessary parameters to simulate geometrical EBSD patterns.
Notes
Deprecated since version 0.6: Class
EBSDSimulationGenerator
is deprecated and will be removed in version 0.7. UseKikuchiPatternSimulator
instead. __init__(detector, phase, rotations)[source]#
A generator storing necessary parameters to simulate geometrical EBSD patterns.
 Parameters:
detector (
EBSDDetector
) – Detector describing the detectorsample geometry.phase (
Phase
) – A phase container with a crystal structure and a space and point group describing the allowed symmetry operations.rotations (
Rotation
) – Unit cell rotations to simulate patterns for. The navigation shape of the resulting simulation is determined from the rotations’ shape, with a maximum dimension of 2.
Examples
>>> from orix import crystal_map, quaternion >>> import kikuchipy as kp >>> det = kp.detectors.EBSDDetector( ... shape=(60, 60), sample_tilt=70, pc=[0.5,] * 3 ... ) >>> p = crystal_map.Phase(name="ni", space_group=225) >>> p.structure.lattice.setLatPar(3.52, 3.52, 3.52, 90, 90, 90) >>> simgen = kp.generators.EBSDSimulationGenerator( ... detector=det, ... phase=p, ... rotations=Rotation.from_euler([1.57, 0, 1.57]) ... ) >>> simgen EBSDSimulationGenerator (1,) EBSDDetector (60, 60), px_size 1 um, binning 1, tilt 0, azimuthal 0, pc (0.5, 0.5, 0.5) <name: ni. space group: Fm3m. point group: m3m. proper point group: 432. color: tab:blue> Rotation (1,)
 geometrical_simulation(reciprocal_lattice_point=None)[source]#
Project a set of Kikuchi bands and zone axes onto the detector, one set for each rotation of the unit cell.
The zone axes are calculated from the Kikuchi bands.
 Parameters:
reciprocal_lattice_point (
Optional
[ReciprocalLatticePoint
]) – Crystal planes to project onto the detector. If None, and the generator has a phase with a unit cell with a point group, a set of planes with minimum distance of 1 Å and their symmetrically equivalent planes are used. Return type:
Examples
>>> from diffsims.crystallography import ReciprocalLatticePoint >>> from orix import crystal_map, quaternion >>> import kikuchipy as kp >>> det = kp.detectors.EBSDDetector( ... shape=(60, 60), sample_tilt=70, pc=[0.5,] * 3 ... ) >>> p = crystal_map.Phase(name="ni", space_group=225) >>> p.structure.lattice.setLatPar(3.52, 3.52, 3.52, 90, 90, 90) >>> simgen = kp.generators.EBSDSimulationGenerator( ... detector=det, ... phase=p, ... rotations=quaternion.Rotation.from_euler([0, 0, 0]) ... ) >>> sim1 = simgen.geometrical_simulation() >>> sim1.bands.size 94 >>> rlp = ReciprocalLatticePoint( ... phase=p, hkl=[[1, 1, 1], [2, 0, 0]] ... ).symmetrise() >>> sim2 = simgen.geometrical_simulation(rlp) >>> sim2.bands.size 7
Number of navigation dimensions (a maximum of 2).
 Return type:
Navigation shape of the rotations and detector projection center array (maximum of 2).
 Return type:
VirtualBSEGenerator#

Return an inmemory signal with a stack of virtual backscatter electron (BSE) images by integrating the intensities within regions of interest (ROI) defined by the detector grid_shape. 

Return an inmemory RGB virtual BSE image from three regions of interest (ROIs) on the EBSD detector, with a potential "alpha channel" in which all three arrays are multiplied by a fourth. 

Plot a pattern with the detector grid superimposed, potentially coloring the edges of three grid tiles red, green and blue. 

Return a rectangular region of interest (ROI) on the EBSD detector from one or multiple generator grid tile indices as row(s) and column(s). 
 class kikuchipy.generators.VirtualBSEGenerator(signal)[source]#
Bases:
object
Generates virtual backscatter electron (BSE) images for a specified electron backscatter diffraction (EBSD) signal and a set of EBSD detector areas.
 signal#
 Type:
 get_images_from_grid(dtype_out=<class 'numpy.float32'>)[source]#
Return an inmemory signal with a stack of virtual backscatter electron (BSE) images by integrating the intensities within regions of interest (ROI) defined by the detector grid_shape.
 Parameters:
dtype_out (
dtype
) – Output data type, default is float32. Returns:
vbse_images – Inmemory signal with virtual BSE images.
 Return type:
Examples
>>> import kikuchipy as kp >>> s = kp.data.nickel_ebsd_small() >>> s <EBSD, title: patterns My awes0m4 ..., dimensions: (3, 360, 60)> >>> vbse_gen = kp.generators.VirtualBSEGenerator(s) >>> vbse_gen.grid_shape = (5, 5) >>> vbse = vbse_gen.get_images_from_grid() >>> vbse <VirtualBSEImage, title: , dimensions: (5, 53, 3)>
 get_rgb_image(r, g, b, percentiles=None, normalize=True, alpha=None, dtype_out=<class 'numpy.uint8'>, **kwargs)[source]#
Return an inmemory RGB virtual BSE image from three regions of interest (ROIs) on the EBSD detector, with a potential “alpha channel” in which all three arrays are multiplied by a fourth.
 Parameters:
r (
Union
[BaseInteractiveROI
,Tuple
,List
[BaseInteractiveROI
],List
[Tuple
]]) – One ROI or a list of ROIs, or one tuple or a list of tuples with detector grid indices specifying one or more ROI(s). Intensities within the specified ROI(s) are summed up to form the red color channel.g (
Union
[BaseInteractiveROI
,Tuple
,List
[BaseInteractiveROI
],List
[Tuple
]]) – One ROI or a list of ROIs, or one tuple or a list of tuples with detector grid indices specifying one or more ROI(s). Intensities within the specified ROI(s) are summed up to form the green color channel.b (
Union
[BaseInteractiveROI
,Tuple
,List
[BaseInteractiveROI
],List
[Tuple
]]) – One ROI or a list of ROIs, or one tuple or a list of tuples with detector grid indices specifying one or more ROI(s). Intensities within the specified ROI(s) are summed up to form the blue color channel.normalize (
bool
) – Whether to normalize the individual images (channels) before RGB image creation.alpha (
Union
[None
,ndarray
,VirtualBSEImage
]) – “Alpha channel”. If None (default), no “alpha channel” is added to the image.percentiles (
Optional
[Tuple
]) – Whether to apply contrast stretching with a given percentile tuple with percentages, e.g. (0.5, 99.5), after creating the RGB image. If None (default), no contrast stretching is performed.dtype_out (
Union
[uint8
,uint16
]) – Output data type, either np.uint16 or np.uint8 (default).kwargs – Keyword arguments passed to
get_rgb_image()
.
 Returns:
vbse_rgb_image – Virtual RGB image in memory.
 Return type:
Notes
HyperSpy only allows for RGB signal dimensions with data types unsigned 8 or 16 bit.
 plot_grid(pattern_idx=None, rgb_channels=None, visible_indices=True, **kwargs)[source]#
Plot a pattern with the detector grid superimposed, potentially coloring the edges of three grid tiles red, green and blue.
 Parameters:
pattern_idx (
Optional
[Tuple
[int
,...
]]) – A tuple of integers defining the pattern to superimpose the grid on. If None (default), the first pattern is used.rgb_channels (
Union
[None
,List
[Tuple
],List
[List
[Tuple
]]]) – A list of tuple indices defining three or more detector grid tiles which edges to color red, green and blue. If None (default), no tiles’ edges are colored.visible_indices (
bool
) – Whether to show grid indices. Default is True.kwargs – Keyword arguments passed to
matplotlib.pyplot.axhline()
and axvline, used by HyperSpy to draw lines.
 Returns:
pattern – A single pattern with the markers added.
 Return type:
 roi_from_grid(index)[source]#
Return a rectangular region of interest (ROI) on the EBSD detector from one or multiple generator grid tile indices as row(s) and column(s).
Other functions#
 kikuchipy.generators.virtual_bse_generator.get_rgb_image(channels, percentiles=None, normalize=True, alpha=None, dtype_out=<class 'numpy.uint8'>, **kwargs)[source]#
Return an RGB image from three numpy arrays, with a potential alpha channel.
 Parameters:
channels (
List
[ndarray
]) – A list of np.ndarray for the red, green and blue channel, respectively.normalize (
bool
) – Whether to normalize the individual channels before RGB image creation.alpha (
Optional
[ndarray
]) – Potential alpha channel. If None (default), no alpha channel is added to the image.percentiles (
Optional
[Tuple
]) – Whether to apply contrast stretching with a given percentile tuple with percentages, e.g. (0.5, 99.5), after creating the RGB image. If None (default), no contrast stretching is performed.dtype_out (
Union
[uint8
,uint16
]) – Output data type, either np.uint16 or np.uint8 (default).kwargs – Keyword arguments passed to
normalize_image()
.
 Returns:
rgb_image – RGB image.
 Return type:
np.ndarray
 kikuchipy.generators.virtual_bse_generator.normalize_image(image, add_bright=0, contrast=1.0, dtype_out=<class 'numpy.uint8'>)[source]#
Normalize an image’s intensities to a mean of 0 and a standard deviation of 1, with the possibility to also scale by a contrast factor and shift the brightness values.
Clips intensities to uint8 data type range, [0, 255].
Adapted from the aloe/xcdskd package.
indexing#
Tools for indexing of EBSD patterns by matching to a dictionary of simulated patterns.
The EBSD method dictionary_indexing()
uses
some of these tools for dictionary indexing.

Compute the results from 
Compute the results from 

Compute the results from 


Compute an orientation similarity map where the ranked list of the dictionary indices of the best matching simulated patterns in one point is compared to the corresponding lists in the nearest neighbour points [MDeGraefS+17]. 

Merge a list of at least two single phase 
Similarity metrics for comparing grayscale patterns. 
 kikuchipy.indexing.compute_refine_orientation_results(results, xmap, master_pattern)[source]#
Compute the results from
refine_orientation()
and return theCrystalMap
. Parameters:
results (
Array
) – The dask array returned from refine_orientation().xmap (
CrystalMap
) – Crystal map passed to refine_orientation() to obtain results.master_pattern (EBSDMasterPattern) – Master pattern passed to refine_orientation() to obtain results.
 Returns:
Crystal map with refined orientations and scores.
 Return type:
refined_xmap
 kikuchipy.indexing.compute_refine_orientation_projection_center_results(results, detector, xmap, master_pattern)[source]#
Compute the results from
refine_orientation_projection_center()
and return theCrystalMap
andEBSDDetector
. Parameters:
results (
Array
) – The dask array returned from refine_orientation_projection_center().detector (EBSDDetector) – Detector passed to refine_orientation_projection_center() to obtain results.
xmap (
CrystalMap
) – Crystal map passed to refine_orientation_projection_center() to obtain results.master_pattern (EBSDMasterPattern) – Master pattern passed to refine_orientation_projection_center() to obtain results.
 Returns:
xmap_refined (
CrystalMap
) – Crystal map with refined orientations and scores.new_detector (
EBSDDetector
) – EBSD detector with refined projection center parameters.
 kikuchipy.indexing.compute_refine_projection_center_results(results, detector, xmap)[source]#
Compute the results from
refine_projection_center()
and return the score array andEBSDDetector
. Parameters:
results (
Array
) – The dask array returned from refine_projection_center().detector (EBSDDetector) – Detector passed to refine_projection_center() to obtain results.
xmap (
CrystalMap
) – Crystal map passed to refine_projection_center() to obtain results.
 Returns:
new_scores (
numpy.ndarray
) – Score array.new_detector (
EBSDDetector
) – EBSD detector with refined projection center parameters.
 kikuchipy.indexing.orientation_similarity_map(xmap, n_best=None, simulation_indices_prop='simulation_indices', normalize=False, from_n_best=None, footprint=None, center_index=2)[source]#
Compute an orientation similarity map where the ranked list of the dictionary indices of the best matching simulated patterns in one point is compared to the corresponding lists in the nearest neighbour points [MDeGraefS+17].
 Parameters:
xmap (
CrystalMap
) – A crystal map with a ranked list of the array indices of the best matching simulated patterns among its properties.n_best (
Optional
[int
]) – Number of ranked indices to compare. If None (default), all indices are compared.simulation_indices_prop (
str
) – Name of simulated indices array in the crystal maps’ properties. Default is “simulation_indices”.normalize (
bool
) – Whether to normalize the number of equal indices to the range [0, 1], by default False.from_n_best (
Optional
[int
]) – Return an OSM for each n in the range [from_n_best, n_best]. If None (default), only the OSM for n_best indices is returned.footprint (
Optional
[ndarray
]) – Boolean 2D array specifying which neighbouring points to compare lists with, by default the four nearest neighbours.center_index (
int
) – Flat index of central navigation point in the truthy values of footprint, by default 2.
 Returns:
osm – Orientation similarity map(s). If from_n_best is not None, the returned array has three dimensions, where n_best is at array[:, :, 0] and from_n_best at array[:, :, 1].
 Return type:
Notes
If the set \(S_{r,c}\) is the ranked list of best matching indices for a given point \((r,c)\), then the orientation similarity index \(\eta_{r,c}\) is the average value of the cardinalities (#) of the intersections with the neighbouring sets
\[\eta_{r,c} = \frac{1}{4} \left( \#(S_{r,c} \cap S_{r1,c}) + \#(S_{r,c} \cap S_{r+1,c}) + \#(S_{r,c} \cap S_{r,c1}) + \#(S_{r,c} \cap S_{r,c+1}) \right).\]Changed in version 0.5: Default value of normalize changed to False.
 kikuchipy.indexing.merge_crystal_maps(crystal_maps, mean_n_best=1, greater_is_better=None, scores_prop='scores', simulation_indices_prop=None)[source]#
Merge a list of at least two single phase
CrystalMap
with a 1D or 2D navigation shape into one multi phase map.It is required that all maps have the same number of rotations and scores (and simulation indices if applicable) per point.
 Parameters:
crystal_maps (
List
[CrystalMap
]) – A list of crystal maps with simulated indices and scores among their properties.mean_n_best (
int
) – Number of best metric results to take the mean of before comparing. Default is 1. If given with a negative sign and greater_is_better is not given, the n lowest valued metric results are chosen.greater_is_better (
Optional
[int
]) – True if a higher score means a better match. Default is None, in which case the sign of mean_n_best is used, with a positive sign meaning True.scores_prop (
str
) – Name of scores array in the crystal maps’ properties. Default is “scores”.simulation_indices_prop (
Optional
[str
]) – Name of simulated indices array in the crystal maps’ properties. If None (default), the merged crystal map will not contain an array of merged simulation indices from the input crystal maps’ properties. If a string, there must be as many simulation indices per point as there are scores.
 Returns:
merged_xmap – A crystal map where the rotation of the phase with the best matching score(s) is assigned to each point. The best matching scores, merge sorted, are added to its properties with a name equal to whatever passed to scores_prop with “merged” as a suffix. If simulation_indices_prop is passed, the best matching simulation indices are added in the same way as the scores.
 Return type:
Notes
Changed in version 0.5: The greater_is_better parameter replaced metric.
similarity_metrics#
Similarity metrics for comparing grayscale patterns.

Abstract class implementing a similarity metric to match experimental and simulated EBSD patterns in a dictionary. 
Similarity metric implementing the normalized crosscorrelation, or Pearson Correlation Coefficient [GW17] 


Similarity metric implementing the normalized dot product [CPW+15] 
 class kikuchipy.indexing.similarity_metrics.SimilarityMetric(n_experimental_patterns=None, n_dictionary_patterns=None, signal_mask=None, dtype=<class 'numpy.float32'>, rechunk=False)[source]#
Abstract class implementing a similarity metric to match experimental and simulated EBSD patterns in a dictionary.
For use in
dictionary_indexing()
or directly on pattern arrays if a__call__()
method is implemented. Note that dictionary_indexing() will always reshape the dictionary pattern array to 2D (1 navigation dimension, 1 signal dimension) before callingprepare_dictionary()
andmatch()
.Take a look at the implementation of
NormalizedCrossCorrelationMetric
for how to write a concrete custom metric.When writing a custom similarity metric class, the methods listed as abstract below must be implemented. Any number of custom parameters can be passed. Also listed are the attributes available to the methods if set properly during initialization or after.
 allowed_dtypes#
List of allowed array data types used during matching.
 Type:
list of numpy.dtype
 dtype#
Which data type to cast the patterns to before matching. Must be listed in allowed_dtypes.
 Type:
 n_dictionary_patterns#
Number of dictionary patterns to match. This information might be necessary when reshaping the dictionary array in
prepare_dictionary()
. Type:
int or None
 n_experimental_patterns#
Number of experimental patterns to match. This information might be necessary when reshaping the dictionary array in
prepare_experimental()
. Type:
int or None
 sign#
+1 if a greater match is better, 1 if a lower match is better. This must be set in the inheriting class.
 Type:
int or None
 signal_mask#
A boolean mask equal to the experimental patterns’ detector shape (n rows, n columns), where only pixels equal to False are matched.
 Type:
numpy.ndarray or None
 __init__(n_experimental_patterns=None, n_dictionary_patterns=None, signal_mask=None, dtype=<class 'numpy.float32'>, rechunk=False)[source]#
Create a similarity metric matching experimental and simulated EBSD patterns in a dictionary.
 Parameters:
n_experimental_patterns (
Optional
[int
]) – Number of experimental patterns. If not given, this is set to None and must be set later. Must be at least 1.n_dictionary_patterns (
Optional
[int
]) – Number of dictionary patterns. If not given, this is set to None and must be set later. Must be at least 1.signal_mask (
Optional
[ndarray
]) – A boolean mask equal to the experimental patterns’ detector shape (n rows, n columns), where only pixels equal to False are matched. If not given, all pixels are used.dtype (
type
) – Which data type to cast the patterns to before matching to.rechunk (
bool
) – Whether to allow rechunking of arrays before matching. Default is False.
 abstract match(*args, **kwargs)[source]#
Match all experimental patterns to all dictionary patterns and return their similarities.
 abstract prepare_dictionary(*args, **kwargs)[source]#
Prepare dictionary patterns before matching to experimental patterns in
match()
.
 class kikuchipy.indexing.similarity_metrics.NormalizedCrossCorrelationMetric(n_experimental_patterns=None, n_dictionary_patterns=None, signal_mask=None, dtype=<class 'numpy.float32'>, rechunk=False)[source]#
Bases:
SimilarityMetric
Similarity metric implementing the normalized crosscorrelation, or Pearson Correlation Coefficient [GW17]
\[r = \frac {\sum^n_{i=1}(x_i  \bar{x})(y_i  \bar{y})} { \sqrt{\sum ^n _{i=1}(x_i  \bar{x})^2} \sqrt{\sum ^n _{i=1}(y_i  \bar{y})^2} },\]where experimental patterns \(x\) and simulated patterns \(y\) are centered by subtracting out the mean of each pattern, and the sum of crossproducts of the centered patterns is accumulated. The denominator adjusts the scales of the patterns to have equal units.
Equivalent results are obtained with
dask.array.tensordot()
withaxes=([2, 3], [1, 2]))
for 4D and 3D experimental and simulated data sets, respectively.See
SimilarityMetric
for remaining attributes. allowed_dtypes#
float32
andfloat64
.
 sign#
+1, meaning greater is better.
 __call__(experimental, dictionary)[source]#
Compute the similarities between experimental patterns and simulated dictionary patterns.
Before calling
match()
, this method callsprepare_experimental()
, reshapes the dictionary patterns to 1 navigation dimension and 1 signal dimension, and callsprepare_dictionary()
.
 match(experimental, dictionary)[source]#
Match all experimental patterns to all dictionary patterns and return their similarities.
 Return type:
 class kikuchipy.indexing.similarity_metrics.NormalizedDotProductMetric(n_experimental_patterns=None, n_dictionary_patterns=None, signal_mask=None, dtype=<class 'numpy.float32'>, rechunk=False)[source]#
Bases:
SimilarityMetric
Similarity metric implementing the normalized dot product [CPW+15]
\[\rho = \frac {\langle \mathbf{X}, \mathbf{Y} \rangle} {\mathbf{X} \cdot \mathbf{Y}},\]where \({\langle \mathbf{X}, \mathbf{Y} \rangle}\) is the dot (inner) product of the pattern vectors \(\mathbf{X}\) and \(\mathbf{Y}\).
See
SimilarityMetric
for remaining attributes. allowed_dtypes#
float32
andfloat64
.
 sign#
+1, meaning greater is better.
 __call__(experimental, dictionary)[source]#
Compute the similarities between experimental patterns and simulated dictionary patterns.
Before calling
match()
, this method callsprepare_experimental()
, reshapes the dictionary patterns to 1 navigation dimension and 1 signal dimension, and callsprepare_dictionary()
.
 match(experimental, dictionary)[source]#
Match all experimental patterns to all dictionary patterns and return their similarities.
 Return type:
io#
Read and write signals from and to file.

Load an 
Input/output plugins. 
 kikuchipy.io._io.load(filename, lazy=False, **kwargs)[source]#
Load an
EBSD
orEBSDMasterPattern
object from a supported file format.This function is a modified version of
hyperspy.io.load()
. Parameters:
filename (
str
) – Name of file to load.lazy (
bool
) – Open the data lazily without actually reading the data from disk until required. Allows opening arbitrary sized datasets. Default is False.kwargs – Keyword arguments passed to the corresponding kikuchipy reader. See their individual documentation for available options.
 Return type:
kikuchipy.signals.EBSD, kikuchipy.signals.EBSDMasterPattern, list of kikuchipy.signals.EBSD or list of kikuchipy.signals.EBSDMasterPattern
Examples
Import nine patterns from an HDF5 file in a directory DATA_DIR
>>> import kikuchipy as kp >>> s = kp.load(DATA_DIR + "/patterns.h5") >>> s <EBSD, title: patterns My awes0m4 ..., dimensions: (3, 360, 60)>
plugins#
Input/output plugins.
Read support for simulated EBSD patterns in EMsoft's HDF5 format. 

Read support for simulated EBSD master patterns in EMsoft's HDF5 format. 

Read/write support for EBSD patterns in some HDF5 file formats. 

Read/write support for EBSD patterns in NORDIF's binary format. 

Read support for NORDIF's calibration patterns. 

Read support for uncompressed EBSD patterns in Oxford Instruments' binary .ebsp file format. 
The plugins import patterns and parameters from file formats into
EBSD
or EBSDMasterPattern
(or
LazyEBSD
or
LazyEBSDMasterPattern
if loading lazily) objects.
emsoft_ebsd#
Read support for simulated EBSD patterns in EMsoft’s HDF5 format.
 kikuchipy.io.plugins.emsoft_ebsd.file_reader(filename, scan_size=None, lazy=False, **kwargs)[source]#
Read dynamically simulated electron backscatter diffraction patterns from EMsoft’s format produced by their EMEBSD.f90 program.
 Parameters:
filename (
str
) – Full file path of the HDF file.scan_size (
Union
[None
,int
,Tuple
[int
,...
]]) – Scan size in number of patterns in width and height.lazy (
bool
) – Open the data lazily without actually reading the data from disk until requested. Allows opening datasets larger than available memory. Default is False.kwargs – Keyword arguments passed to h5py.File.
 Returns:
signal_dict_list – Data, axes, metadata and original metadata.
 Return type:
list of dicts
emsoft_ebsd_master_pattern#
Read support for simulated EBSD master patterns in EMsoft’s HDF5 format.
 kikuchipy.io.plugins.emsoft_ebsd_master_pattern.file_reader(filename, energy=None, projection='stereographic', hemisphere='upper', lazy=False, **kwargs)[source]#
Read electron backscatter diffraction master patterns from EMsoft’s HDF5 file format [CDeGraef13].
 Parameters:
filename (
str
) – Full file path of the HDF file.energy (
Optional
[range
]) – Desired beam energy or energy range. If None is passed (default), all available energies are read.projection (
str
) – Projection(s) to read. Options are"stereographic"
(default) or"lambert"
.hemisphere (
str
) – Projection hemisphere(s) to read. Options are"upper"
(default),"lower"
or"both"
. If"both"
, these will be stacked in the vertical navigation axis.lazy (
bool
) – Open the data lazily without actually reading the data from disk until requested. Allows opening datasets larger than available memory. Default isFalse
.kwargs – Keyword arguments passed to h5py.File.
 Returns:
signal_dict_list – Data, axes, metadata and original metadata.
 Return type:
list of dicts
h5ebsd#
Read/write support for EBSD patterns in some HDF5 file formats.
 kikuchipy.io.plugins.h5ebsd.brukerheader2dicts(scan_group, md)[source]#
Return scan metadata dictionaries from a Bruker h5ebsd file.
 Parameters:
scan_group (h5py:Group) – HDF group of scan data and header.
md (hyperspy.misc.utils.DictionaryTreeBrowser) – Dictionary with empty fields from kikuchipy’s metadata.
 Return type:
Tuple
[DictionaryTreeBrowser
,DictionaryTreeBrowser
,DictionaryTreeBrowser
] Returns:
md – kikuchipy
metadata
elements available in Bruker file.omd – All metadata available in Bruker file.
scan_size – Scan, image, step and detector pixel size available in Bruker file.
 kikuchipy.io.plugins.h5ebsd.check_h5ebsd(file)[source]#
Check if HDF file is an h5ebsd file by searching for datasets containing manufacturer, version and scans in the top group.
 Parameters:
file (h5py:File) – File where manufacturer, version and scan datasets should reside in the top group.
 kikuchipy.io.plugins.h5ebsd.dict2h5ebsdgroup(dictionary, group, **kwargs)[source]#
Write a dictionary from
metadata
to datasets in a new group in an opened HDF file in the h5ebsd format. Parameters:
dictionary (
dict
) –Metadata
, with keys as dataset names.group (h5py:Group) – HDF group to write dictionary to.
kwargs – Keyword arguments passed to
h5py:Group.require_dataset()
.
 kikuchipy.io.plugins.h5ebsd.edaxheader2dicts(scan_group, md)[source]#
Return scan metadata dictionaries from an EDAX TSL h5ebsd file.
 Parameters:
scan_group (h5py:Group) – HDF group of scan data and header.
md (
DictionaryTreeBrowser
) – Dictionary with empty fields from kikuchipy’s metadata.
 Return type:
Tuple
[DictionaryTreeBrowser
,DictionaryTreeBrowser
,DictionaryTreeBrowser
] Returns:
md – kikuchipy
metadata
elements available in EDAX file.omd – All metadata available in EDAX file.
scan_size – Scan, image, step and detector pixel size available in EDAX file.
 kikuchipy.io.plugins.h5ebsd.file_reader(filename, scan_group_names=None, lazy=False, **kwargs)[source]#
Read electron backscatter diffraction patterns from an h5ebsd file [Jackson2014]. A valid h5ebsd file has at least one top group with the subgroup ‘EBSD’ with the subgroups ‘Data’ (patterns etc.) and ‘Header’ (
metadata
etc.). Parameters:
filename (
str
) – Full file path of the HDF file.scan_group_names (
Union
[None
,str
,List
[str
]]) – Name or a list of names of HDF5 top group(s) containing the scan(s) to return. If None, the first scan in the file is returned.lazy (
bool
) – Open the data lazily without actually reading the data from disk until required. Allows opening arbitrary sized datasets. Default is False.kwargs – Key word arguments passed to
h5py:File
.
 Returns:
scan_dict_list – Data, axes, metadata and original metadata.
 Return type:
list of dicts
References
[Jackson2014]M. A. Jackson, M. A. Groeber, M. D. Uchic, D. J. Rowenhorst and M. De Graef, “h5ebsd: an archival data format for electron backscatter diffraction data sets,” Integrating Materials and Manufacturing Innovation 3 (2014), doi: https://doi.org/10.1186/2193977234.
 kikuchipy.io.plugins.h5ebsd.file_writer(filename, signal, add_scan=None, scan_number=1, **kwargs)[source]#
Write an
EBSD
orLazyEBSD
signal to an existing, but not open, or new h5ebsd file.Only writing to kikuchipy’s h5ebsd format is supported.
 Parameters:
filename (
str
) – Full path of HDF file.signal (kikuchipy.signals.EBSD or kikuchipy.signals.LazyEBSD) – Signal instance.
add_scan (
Optional
[bool
]) – Add signal to an existing, but not open, h5ebsd file. If it does not exist it is created and the signal is written to it.scan_number (
int
) – Scan number in name of HDF dataset when writing to an existing, but not open, h5ebsd file.kwargs – Keyword arguments passed to
h5py:Group.require_dataset()
.
 kikuchipy.io.plugins.h5ebsd.get_desired_scan_groups(file, scan_group_names=None)[source]#
Get the desired HDF5 groups with scans within them.
 Parameters:
 Returns:
A list of the desired scan group(s) in the file.
 Return type:
scan_groups
 kikuchipy.io.plugins.h5ebsd.get_scan_groups(file)[source]#
Return a list of the scan group names from an h5ebsd file.
 Parameters:
file (h5py:File) – File where manufacturer, version and scan datasets should reside in the top group.
 Returns:
scan_groups – List of available scan groups.
 Return type:
h5py:Group
 kikuchipy.io.plugins.h5ebsd.h5ebsd2signaldict(scan_group, manufacturer, version, lazy=False)[source]#
Return a dictionary with
signal
,metadata
andoriginal_metadata
from an h5ebsd scan. Parameters:
 Returns:
scan – Dictionary with patterns,
metadata
andoriginal_metadata
. Return type:
 kikuchipy.io.plugins.h5ebsd.h5ebsdheader2dicts(scan_group, manufacturer, version, lazy=False)[source]#
Return three dictionaries in HyperSpy’s
hyperspy.misc.utils.DictionaryTreeBrowser
format, one with the h5ebsd scan header parameters as kikuchipy metadata, another with all datasets in the header as original metadata, and the last with info about scan size, image size and detector pixel size. Parameters:
 Return type:
Tuple
[DictionaryTreeBrowser
,DictionaryTreeBrowser
,DictionaryTreeBrowser
] Returns:
md – kikuchipy
metadata
elements available in file.omd – All metadata available in file.
scan_size – Scan, image, step and detector pixel size available in file.
 kikuchipy.io.plugins.h5ebsd.hdf5group2dict(group, dictionary=None, recursive=False, data_dset_names=None, **kwargs)[source]#
Return a dictionary with values from datasets in a group in an opened HDF5 file.
 Parameters:
 Returns:
dictionary – Dataset values in group (and subgroups if recursive=True).
 Return type:
 kikuchipy.io.plugins.h5ebsd.kikuchipyheader2dicts(scan_group, md)[source]#
Return scan metadata dictionaries from a kikuchipy h5ebsd file.
 Parameters:
scan_group (h5py:Group) – HDF group of scan data and header.
md (
DictionaryTreeBrowser
) – Dictionary with empty fields from kikuchipy’s metadata.
 Return type:
Tuple
[DictionaryTreeBrowser
,DictionaryTreeBrowser
,DictionaryTreeBrowser
] Returns:
md – kikuchipy
metadata
elements available in kikuchipy file.omd – All metadata available in kikuchipy file.
scan_size – Scan, image, step and detector pixel size available in kikuchipy file.
nordif#
Read/write support for EBSD patterns in NORDIF’s binary format.
 kikuchipy.io.plugins.nordif.file_reader(filename, mmap_mode=None, scan_size=None, pattern_size=None, setting_file=None, lazy=False)[source]#
Read electron backscatter patterns from a NORDIF data file.
 Parameters:
filename (
str
) – File path to NORDIF data file.scan_size (
Union
[None
,int
,Tuple
[int
,...
]]) – Scan size in number of patterns in width and height.pattern_size (
Optional
[Tuple
[int
,...
]]) – Pattern size in detector pixels in width and height.setting_file (
Optional
[str
]) – File path to NORDIF setting file (default is Setting.txt in same directory asfilename
).lazy (
bool
) – Open the data lazily without actually reading the data from disk until required. Allows opening arbitrary sized datasets. Default is False.
 Returns:
scan – Data, axes, metadata and original metadata.
 Return type:
list of dicts
 kikuchipy.io.plugins.nordif.file_writer(filename, signal)[source]#
Write an
EBSD
orLazyEBSD
object to a NORDIF binary file. Parameters:
filename (
str
) – Full path of HDF file.signal (kikuchipy.signals.EBSD or kikuchipy.signals.LazyEBSD) – Signal instance.
 kikuchipy.io.plugins.nordif.get_settings_from_file(filename)[source]#
Return metadata with parameters from NORDIF setting file.
 Parameters:
filename (
str
) – File path of NORDIF setting file. Return type:
Tuple
[DictionaryTreeBrowser
,DictionaryTreeBrowser
,DictionaryTreeBrowser
] Returns:
md – Metadata complying with HyperSpy’s metadata structure.
omd – Metadata that does not fit into HyperSpy’s metadata structure.
scan_size – Information on image size, scan size and scan steps.
nordif_calibration_patterns#
Read support for NORDIF’s calibration patterns.
oxford_binary#
Read support for uncompressed EBSD patterns in Oxford Instruments’ binary .ebsp file format.
Information about the file format was provided by Oxford Instruments.
 class kikuchipy.io.plugins.oxford_binary.OxfordBinaryFileReader(file)[source]#
Bases:
object
Oxford Instruments’ binary .ebsp file reader.
 property all_patterns_present: bool#
Whether all or only nonindexed patterns are stored in the file.
 Return type:
 property first_pattern_position: int#
File byte position of first pattern after the file header.
 Return type:
 get_memmap()[source]#
Return a memory map of the pattern header, actual patterns, and a potential pattern footer.
The memory map has the shape of (n indexed patterns,), and the patterns have the correct signal shape (n rows, n columns).
If the pattern footer is available, the memory map has these fields:
Name
Data type
Shape
is_compressed
int32
(1,)
nrows
int32
(1,)
ncols
int32
(1,)
n_bytes
int32
(1,)
pattern
uint8 or uint16
(n rows, n columns)
has_beam_x
bool
(1,)
beam_x
float64
(1,)
has_beam_y
bool
(1,)
beam_y
float64
(1,)
 Return type:
Return the navigation shape and step size.
An equal step size between rows and columns is assumed.
The navigation shape is determined by evaluating the beam row and column position of the upper left and lower right patterns. The step size is determined from the difference in column position of the upper left pattern and the pattern in the next column.
Return the pattern footer data types to be used when memory mapping.
 get_pattern_starts()[source]#
Return the file byte positions of each pattern.
 Parameters:
pattern_starts – Integer array of file byte positions.
 Return type:
 get_patterns(lazy)[source]#
Return the EBSD patterns in the file.
The patterns are read from the memory map. They are sorted into their correct navigation (map) position if necessary.
 Parameters:
lazy (
bool
) – Whether to return anumpy.ndarray
ordask.array.Array
. Returns:
EBSD patterns of shape (n navigation rows, n navigation columns, n signal rows, n signal columns).
 Return type:
data
 get_scan(lazy)[source]#
Return a dictionary with the necessary information to initialize an
EBSD
instance. Parameters:
lazy (
bool
) – Whether to return the EBSD patterns as anumpy.ndarray
ordask.array.Array
. Returns:
Dictionary of axes, data, metadata and original metadata.
 Return type:
scan
Return a single pattern footer with pattern beam positions.
 Parameters:
offset (
int
) – File byte pattern start of the pattern of interest. Returns:
The format of this depends on the file
version
. Return type:
footer
 get_single_pattern_header(offset)[source]#
Return a single pattern header.
 Parameters:
offset (
int
) – File byte pattern start of the pattern of interest. Return type:
 Returns:
is_compressed – Whether the pattern is compressed.
nrows – Number of signal (detector) rows.
ncols – Number of signal (detector) columns.
n_bytes – Number of pattern bytes.
 get_version()[source]#
Return the .ebsp file version.
The first version of the .ebsp format did not store a version number. Subsequent versions store the version number as a negative number.
 Return type:
version
 guess_number_of_patterns(min_assumed_n_pixels=1600)[source]#
Guess the number of patterns in the file based upon an assumed lower bound for the number of pattern pixels and the file size.
 Parameters:
min_assumed_n_pixels (
int
) – Assumed lower bound for the number of pattern pixels. Default is 1600 pixels. Returns:
Guess of the number of EBSD patterns in the file.
 Return type:
n_patterns
 pattern_header_dtype = [('is_compressed', <class 'numpy.int32'>, (1,)), ('nrows', <class 'numpy.int32'>, (1,)), ('ncols', <class 'numpy.int32'>, (1,)), ('n_bytes', <class 'numpy.int32'>, (1,))]#
 pattern_header_size = 16#
 property pattern_is_present: ndarray#
Boolean array indicating whether a pattern listed in the file header is present in the file or not. If not, its pattern_starts entry is zero.
 Return type:
 kikuchipy.io.plugins.oxford_binary.file_reader(filename, lazy=False)[source]#
Read EBSD patterns from an Oxford Instruments’ binary .ebsp file.
Only uncompressed patterns can be read. If only nonindexed patterns are stored in the file, the navigation shape will be 1D.
 Parameters:
 Returns:
Data, axes, metadata and original metadata.
 Return type:
scan
Notes
Information about the .ebsp file format was provided by Oxford Instruments.
pattern#
Single and chunk pattern processing used by signals.
Functions for operating on 


Compute the discrete Fast Fourier Transform (FFT) of an EBSD pattern. 

Filter an EBSD patterns in the frequency domain. 

Get the frequency vectors in a Fourier Transform spectrum. 

Compute the FFT spectrum of a Fourier transformed EBSD pattern. 

Get the dynamic background in an EBSD pattern. 

Return the image quality of an EBSD pattern. 

Compute the inverse Fast Fourier Transform (IFFT) of an FFT of an EBSD pattern. 

Normalize image intensities to a mean of zero and a given standard deviation. 

Remove the dynamic background in an EBSD pattern. 

Rescale intensities in an EBSD pattern. 
Functions operating on single EBSD patterns as ndarray
.
Single and chunk pattern processing used by signals.
 kikuchipy.pattern.fft(pattern, apodization_window=None, shift=False, real_fft_only=False, **kwargs)[source]#
Compute the discrete Fast Fourier Transform (FFT) of an EBSD pattern.
Very light wrapper around routines in
scipy.fft
. The routines are wrapped instead of used directly to accommodate easy setting of shift and real_fft_only. Parameters:
pattern (
ndarray
) – EBSD pattern.apodization_window (
Union
[None
,ndarray
,Window
]) – An apodization window to apply before the FFT in order to suppress streaks.shift (
bool
) – Whether to shift the zerofrequency component to the centre of the spectrum (default is False).real_fft_only (
bool
) – If True, the discrete FFT is computed for real input usingscipy.fft.rfft2()
. If False (default), it is computed usingscipy.fft.fft2()
.kwargs – Keyword arguments pass to
scipy.fft.fft2()
orscipy.fft.rfft2()
.
 Returns:
out – The result of the 2D FFT.
 Return type:
 kikuchipy.pattern.fft_filter(pattern, transfer_function, apodization_window=None, shift=False)[source]#
Filter an EBSD patterns in the frequency domain.
 Parameters:
pattern (
ndarray
) – EBSD pattern.transfer_function (
Union
[ndarray
,Window
]) – Filter transfer function in the frequency domain.apodization_window (
Union
[None
,ndarray
,Window
]) – An apodization window to apply before the FFT in order to suppress streaks.shift (
bool
) – Whether to shift the zerofrequency component to the centre of the spectrum. Default is False.
 Returns:
filtered_pattern – Filtered EBSD pattern.
 Return type:
 kikuchipy.pattern.fft_frequency_vectors(shape)[source]#
Get the frequency vectors in a Fourier Transform spectrum.
 Parameters:
 Returns:
frequency_vectors – Frequency vectors.
 Return type:
 kikuchipy.pattern.fft_spectrum(fft_pattern)[source]#
Compute the FFT spectrum of a Fourier transformed EBSD pattern.
 Parameters:
fft_pattern (
ndarray
) – Fourier transformed EBSD pattern. Returns:
fft_spectrum – 2D FFT spectrum of the EBSD pattern.
 Return type:
 kikuchipy.pattern.get_dynamic_background(pattern, filter_domain='frequency', std=None, truncate=4.0)[source]#
Get the dynamic background in an EBSD pattern.
The background is obtained either in the frequency domain, by a low pass Fast Fourier Transform (FFT) Gaussian filter, or in the spatial domain by a Gaussian filter.
Data type is preserved.
 Parameters:
pattern (
ndarray
) – EBSD pattern.filter_domain (
str
) – Whether to obtain the dynamic background by applying a Gaussian convolution filter in the “frequency” (default) or “spatial” domain.std (
Union
[None
,int
,float
]) – Standard deviation of the Gaussian window. If None (default), a deviation of pattern width/8 is chosen.truncate (
Union
[int
,float
]) – Truncate the Gaussian window at this many standard deviations. Default is 4.0.
 Returns:
dynamic_bg – The dynamic background.
 Return type:
 kikuchipy.pattern.get_image_quality(pattern, normalize=True, frequency_vectors=None, inertia_max=None)[source]#
Return the image quality of an EBSD pattern.
The image quality is calculated based on the procedure defined by Krieger Lassen [Lassen1994].
 Parameters:
pattern (
ndarray
) – EBSD pattern.normalize (
bool
) – Whether to normalize the pattern to a mean of zero and standard deviation of 1 before calculating the image quality (default is True).frequency_vectors (
Optional
[ndarray
]) – Integer 2D array assigning each FFT spectrum frequency component a weight. If None (default), these are calculated fromfft_frequency_vectors()
. This only depends on the pattern shape.inertia_max (
Union
[None
,int
,float
]) – Maximum possible inertia of the FFT power spectrum of the image. If None (default), this is calculated from the frequency_vectors, which in this case must be passed. This only depends on the pattern shape.
 Returns:
image_quality – Image quality of the pattern.
 Return type:
 kikuchipy.pattern.ifft(fft_pattern, shift=False, real_fft_only=False, **kwargs)[source]#
Compute the inverse Fast Fourier Transform (IFFT) of an FFT of an EBSD pattern.
Very light wrapper around routines in
scipy.fft
. The routines are wrapped instead of used directly to accommodate easy setting of shift and real_fft_only. Parameters:
fft_pattern (
ndarray
) – FFT of EBSD pattern.shift (
bool
) – Whether to shift the zerofrequency component back to the corners of the spectrum (default is False).real_fft_only (
bool
) – If True, the discrete IFFT is computed for real input usingscipy.fft.irfft2()
. If False (default), it is computed usingscipy.fft.ifft2()
.kwargs – Keyword arguments pass to
scipy.fft.ifft()
.
 Returns:
pattern – Real part of the IFFT of the EBSD pattern.
 Return type:
 kikuchipy.pattern.normalize_intensity(pattern, num_std=1, divide_by_square_root=False)[source]#
Normalize image intensities to a mean of zero and a given standard deviation.
Data type is preserved.
 Parameters:
 Returns:
normalized_pattern – Normalized pattern.
 Return type:
Notes
Data type should always be changed to floating point, e.g.
np.float32
withnumpy.ndarray.astype()
, before normalizing the intensities.
 kikuchipy.pattern.remove_dynamic_background(pattern, operation='subtract', filter_domain='frequency', std=None, truncate=4.0, dtype_out=None)[source]#
Remove the dynamic background in an EBSD pattern.
The removal is performed by subtracting or dividing by a Gaussian blurred version of the pattern. The blurred version is obtained either in the frequency domain, by a low pass Fast Fourier Transform (FFT) Gaussian filter, or in the spatial domain by a Gaussian filter. Returned pattern intensities are rescaled to fill the input data type range.
 Parameters:
pattern (
ndarray
) – EBSD pattern.operation (
str
) – Whether to “subtract” (default) or “divide” by the dynamic background pattern.filter_domain (
str
) – Whether to obtain the dynamic background by applying a Gaussian convolution filter in the “frequency” (default) or “spatial” domain.std (
Union
[None
,int
,float
]) – Standard deviation of the Gaussian window. If None (default), it is set to width/8.truncate (
Union
[int
,float
]) – Truncate the Gaussian window at this many standard deviations. Default is 4.0.dtype_out (
Union
[None
,dtype
,type
,Tuple
[int
,int
],Tuple
[float
,float
]]) – Data type of corrected pattern. If None (default), it is set to input patterns’ data type.
 Returns:
corrected_pattern – Pattern with the dynamic background removed.
 Return type:
 kikuchipy.pattern.rescale_intensity(pattern, in_range=None, out_range=None, dtype_out=None)[source]#
Rescale intensities in an EBSD pattern.
Pattern max./min. intensity is determined from out_range or the data type range of
numpy.dtype
passed to dtype_out.This method is based on
skimage.exposure.rescale_intensity()
. Parameters:
pattern (
ndarray
) – EBSD pattern.in_range (
Optional
[Tuple
[Union
[int
,float
],...
]]) – Min./max. intensity values of the input pattern. If None (default), it is set to the pattern’s min./max intensity.out_range (
Optional
[Tuple
[Union
[int
,float
],...
]]) – Min./max. intensity values of the rescaled pattern. If None (default), it is set to dtype_out min./max according to skimage.util.dtype.dtype_range.dtype_out (
Union
[None
,dtype
,type
]) – Data type of the rescaled pattern. If None (default), it is set to the same data type as the input pattern.
 Returns:
rescaled_pattern – Rescaled pattern.
 Return type:
chunk#
Functions for operating on ndarray
or Array
chunks
of EBSD patterns.

Local contrast enhancement of a chunk of EBSD patterns with adaptive histogram equalization. 

Average a chunk of patterns with its neighbours within a window. 

Filter a chunk of EBSD patterns in the frequency domain. 

Obtain the dynamic background in a chunk of EBSD patterns. 

[Deprecated] Compute the image quality in a chunk of EBSD patterns. 

Normalize intensities in a chunk of EBSD patterns to a mean of zero with a given standard deviation. 

[Deprecated] Correct the dynamic background in a chunk of EBSD patterns. 

[Deprecated] Remove the static background in a chunk of EBSD patterns. 

Rescale pattern intensities in a chunk of EBSD patterns. 
Functions for operating on numpy.ndarray
or
dask.array.Array
chunks of EBSD patterns.
Warning
This module will be become private for internal use only in v0.7.
If you need to process multiple EBSD patterns at once, please do
this using EBSD
.
 kikuchipy.pattern.chunk.adaptive_histogram_equalization(patterns, kernel_size, clip_limit=0, nbins=128)[source]#
Local contrast enhancement of a chunk of EBSD patterns with adaptive histogram equalization.
This method makes use of
skimage.exposure.equalize_adapthist()
. Parameters:
kernel_size (
Union
[Tuple
[int
,int
],List
[int
]]) – Shape of contextual regions for adaptive histogram equalization.clip_limit (
Union
[int
,float
]) – Clipping limit, normalized between 0 and 1 (higher values give more contrast). Default is 0.nbins (
int
) – Number of gray bins for histogram. Default is 128.
 Returns:
equalized_patterns – Patterns with enhanced contrast.
 Return type:
 kikuchipy.pattern.chunk.average_neighbour_patterns(patterns, window_sums, window, dtype_out=None)[source]#
Average a chunk of patterns with its neighbours within a window.
The amount of averaging is specified by the window coefficients. All patterns are averaged with the same window. Map borders are extended with zeros. Resulting pattern intensities are rescaled to fill the input patterns’ data type range individually.
 Parameters:
 Returns:
averaged_patterns – Averaged patterns.
 Return type:
 kikuchipy.pattern.chunk.fft_filter(patterns, filter_func, transfer_function, dtype_out=None, **kwargs)[source]#
Filter a chunk of EBSD patterns in the frequency domain.
Patterns are transformed via the Fast Fourier Transform (FFT) to the frequency domain, where their spectrum is multiplied by a filter transfer_function, and the filtered spectrum is subsequently transformed to the spatial domain via the inverse FFT (IFFT).
Filtered patterns are rescaled to the data type range of dtype_out.
 Parameters:
patterns (
ndarray
) – EBSD patterns.filter_func (
Union
[fft_filter
,_fft_filter
]) – Function to apply transfer_function with.transfer_function (
Union
[ndarray
,Window
]) – Filter transfer function in the frequency domain.dtype_out (
Union
[None
,dtype
,Tuple
[int
,int
],Tuple
[float
,float
]]) – Data type of output patterns. If None (default), it is set to the input patterns’ data type.kwargs – Keyword arguments passed to the filter_func.
 Returns:
filtered_patterns – Filtered EBSD patterns.
 Return type:
 kikuchipy.pattern.chunk.get_dynamic_background(patterns, filter_func, dtype_out=None, **kwargs)[source]#
Obtain the dynamic background in a chunk of EBSD patterns.
 Parameters:
filter_func (
Union
[gaussian_filter
,fft_filter
]) – Function where a Gaussian convolution filter is applied, in the frequency or spatial domain. Eitherscipy.ndimage.gaussian_filter()
orkikuchipy.util.barnes_fftfilter.fft_filter()
.dtype_out (
Union
[None
,dtype
,Tuple
[int
,int
],Tuple
[float
,float
]]) – Data type of background patterns. If None (default), it is set to input patterns’ data type.kwargs – Keyword arguments passed to the Gaussian blurring function passed to filter_func.
 Returns:
background – Large scale variations in the input EBSD patterns.
 Return type:
 kikuchipy.pattern.chunk.get_image_quality(patterns, frequency_vectors=None, inertia_max=None, normalize=True)[source]#
[Deprecated] Compute the image quality in a chunk of EBSD patterns.
The image quality is calculated based on the procedure defined by Krieger Lassen [Lassen1994].
 Parameters:
frequency_vectors (
Optional
[ndarray
]) – Integer 2D array with values corresponding to the weight given each FFT spectrum frequency component. If None (default), these are calculated fromfft_frequency_vectors()
.inertia_max (
Union
[None
,int
,float
]) – Maximum inertia of the FFT power spectrum of the image. If None (default), this is calculated from the frequency_vectors.normalize (
bool
) – Whether to normalize patterns to a mean of zero and standard deviation of 1 before calculating the image quality. Default is True.
 Returns:
image_quality_chunk – Image quality of patterns.
 Return type:
Notes
Deprecated since version 0.6: Function get_image_quality() is deprecated and will be removed in version 0.7. Use kikuchipy.signals.EBSD.get_image_quality() instead.
 kikuchipy.pattern.chunk.normalize_intensity(patterns, num_std=1, divide_by_square_root=False, dtype_out=None)[source]#
Normalize intensities in a chunk of EBSD patterns to a mean of zero with a given standard deviation.
 Parameters:
patterns (
Union
[ndarray
,Array
]) – Patterns to normalize the intensity in.num_std (
int
) – Number of standard deviations of the output intensities. Default is 1.divide_by_square_root (
bool
) – Whether to divide output intensities by the square root of the pattern size. Default is False.dtype_out (
Optional
[dtype
]) – Data type of normalized patterns. If None (default), the input patterns’ data type is used.
 Returns:
normalized_patterns – Normalized patterns.
 Return type:
Notes
Data type should always be changed to floating point, e.g.
np.float32
withnumpy.ndarray.astype()
, before normalizing the intensities.
 kikuchipy.pattern.chunk.remove_dynamic_background(patterns, filter_func, operation_func, out_range=None, dtype_out=None, **kwargs)[source]#
[Deprecated] Correct the dynamic background in a chunk of EBSD patterns.
The correction is performed by subtracting or dividing by a Gaussian blurred version of each pattern. Returned pattern intensities are rescaled to fill the input data type range.
 Parameters:
filter_func (
Union
[gaussian_filter
,fft_filter
]) – Function where a Gaussian convolution filter is applied, in the frequency or spatial domain. Eitherscipy.ndimage.gaussian_filter()
orkikuchipy.util.barnes_fftfilter.fft_filter()
.operation_func (
Union
[<ufunc ‘subtract’>, <ufunc ‘true_divide’>]) – Function to subtract or divide by the dynamic background pattern.out_range (
Union
[None
,Tuple
[int
,int
],Tuple
[float
,float
]]) – Min./max. intensity values of the output patterns. If None (default), out_range is set to dtype_out min./max according to skimage.util.dtype.dtype_range.dtype_out (
Union
[None
,dtype
,Tuple
[int
,int
],Tuple
[float
,float
]]) – Data type of corrected patterns. If None (default), it is set to input patterns’ data type.kwargs – Keyword arguments passed to the Gaussian blurring function passed to filter_func.
 Returns:
corrected_patterns – Dynamic background corrected patterns.
 Return type:
See also
kikuchipy.signals.ebsd.EBSD.remove_dynamic_background
,kikuchipy.util.pattern.remove_dynamic_background
Notes
Deprecated since version 0.6: Function remove_dynamic_background() is deprecated and will be removed in version 0.7. Use kikuchipy.signals.EBSD.remove_dynamic_background() instead.
 kikuchipy.pattern.chunk.remove_static_background(patterns, static_bg, operation_func, scale_bg=False, in_range=None, out_range=None, dtype_out=None)[source]#
[Deprecated] Remove the static background in a chunk of EBSD patterns.
Removal is performed by subtracting or dividing by a static background pattern. Resulting pattern intensities are rescaled keeping relative intensities or not and stretched to fill the available grey levels in the patterns’ data type range.
 Parameters:
static_bg (
Union
[ndarray
,Array
]) – Static background pattern. If None is passed (default) we try to read it from the signal metadata.operation_func (
Union
[<ufunc ‘subtract’>, <ufunc ‘true_divide’>]) – Function to subtract or divide by the dynamic background pattern.scale_bg (
bool
) – Whether to scale the static background pattern to each individual pattern’s data range before removal (default is False).in_range (
Union
[None
,Tuple
[int
,int
],Tuple
[float
,float
]]) – Min./max. intensity values of input and output patterns. If None (default), it is set to the overall pattern min./max, losing relative intensities between patterns.out_range (
Union
[None
,Tuple
[int
,int
],Tuple
[float
,float
]]) – Min./max. intensity values of the output patterns. If None (default), out_range is set to dtype_out min./max according to skimage.util.dtype.dtype_range.dtype_out (
Union
[None
,dtype
,Tuple
[int
,int
],Tuple
[float
,float
]]) – Data type of corrected patterns. If None (default), it is set to input patterns’ data type.
 Returns:
corrected_patterns – Patterns with the static background removed.
 Return type:
Notes
Deprecated since version 0.6: Function remove_static_background() is deprecated and will be removed in version 0.7. Use kikuchipy.signals.EBSD.remove_static_background() instead.
 kikuchipy.pattern.chunk.rescale_intensity(patterns, in_range=None, out_range=None, dtype_out=None, percentiles=None)[source]#
Rescale pattern intensities in a chunk of EBSD patterns.
Chunk max./min. intensity is determined from out_range or the data type range of
numpy.dtype
passed to dtype_out. Parameters:
in_range (
Union
[None
,Tuple
[int
,int
],Tuple
[float
,float
]]) – Min./max. intensity of input patterns. If None (default), in_range is set to pattern min./max. Contrast stretching is performed when in_range is set to a narrower intensity range than the input patterns.out_range (
Union
[None
,Tuple
[int
,int
],Tuple
[float
,float
]]) – Min./max. intensity of output patterns. If None (default), out_range is set to dtype_out min./max according to skimage.util.dtype.dtype_range.dtype_out (
Union
[None
,dtype
,Tuple
[int
,int
],Tuple
[float
,float
]]) – Data type of rescaled patterns. If None (default), it is set to the same data type as the input patterns.percentiles (
Union
[None
,Tuple
[int
,int
],Tuple
[float
,float
]]) – Disregard intensities outside these percentiles. Calculated per pattern. Must be None if in_range is passed (default is None).
 Returns:
rescaled_patterns – Rescaled patterns.
 Return type:
projections#
Various projections and transformations relevant to EBSD.
Rotations to align the EBSD detector with the tilted sample. 

Hessian normal form of a plane given by polar coordinates. 

Spherical projection of a cartesian vector according to the ISO 3111 standard [SphericalWolfram]. 
ebsd_projections#

Rotation U_K from detector frame D to direct crystal lattice frame K. 

Rotation U_Kstar from detector to reciprocal crystal lattice frame Kstar. 

Rotation U_S to align detector frame D with sample frame S. 
Rotations to align the EBSD detector with the tilted sample. Notation from [BJG+16].
 kikuchipy.projections.ebsd_projections.detector2direct_lattice(sample_tilt, detector_tilt, lattice, rotation)[source]#
Rotation U_K from detector frame D to direct crystal lattice frame K.
 kikuchipy.projections.ebsd_projections.detector2reciprocal_lattice(sample_tilt, detector_tilt, lattice, rotation)[source]#
Rotation U_Kstar from detector to reciprocal crystal lattice frame Kstar.
HesseNormalForm#
Hessian normal form of a plane given by polar coordinates. (Not currently used anywhere.)
 class kikuchipy.projections.hesse_normal_form.HesseNormalForm[source]#
Bases:
object
Hessian normal form of a plane given by polar coordinates.
 static project_cartesian(cartesian, radius=10)[source]#
Return the Hesse normal form of plane(s) given by cartesian coordinates.
SphericalProjection#
Spherical projection of a cartesian vector according to the ISO 3111 standard [SphericalWolfram].
 class kikuchipy.projections.spherical_projection.SphericalProjection[source]#
Bases:
object
Spherical projection of a cartesian vector according to the ISO 3111 standard [SphericalWolfram].
References
[SphericalWolfram] (1,2,3,4)Weisstein, Eric W. “Spherical Coordinates,” From MathWorld–A Wolfram Web Resource, url: https://mathworld.wolfram.com/SphericalCoordinates.html
 spherical_region = SphericalRegion (1,) [[0 0 1]]#
 classmethod vector2xy(v)[source]#
Convert from cartesian to spherical coordinates according to the ISO 3111 standard [SphericalWolfram].
 Parameters:
v (
Union
[Vector3d
,ndarray
]) – 3D vector(s) on the form [[x0, y0, z0], [x1, y1, z1], …]. Returns:
Spherical coordinates theta, phi and r on the form [[theta1, phi1, r1], [theta2, phi2, r2], …].
 Return type:
spherical_coordinates
Examples
>>> import numpy as np >>> from kikuchipy.projections.spherical_projection import ( ... SphericalProjection ... ) >>> v = np.random.random_sample(30).reshape((10, 3)) >>> theta, phi, r = SphericalProjection.vector2xy(v).T >>> np.allclose(np.arccos(v[:, 2] / r), theta) True >>> np.allclose(np.arctan2(v[:, 1], v[:, 0]), phi) True
signals#
Experimental and simulated diffraction patterns and virtual backscatter electron images.

Scan of Electron Backscatter Diffraction (EBSD) patterns. 

Simulated Electron Backscatter Diffraction (EBSD) master pattern. 

Virtual backscatter electron (BSE) image(s). 
Signal utilities for handling signal metadata and attributes, output from signal methods, and for controlling chunking of lazy signal data in 
EBSD#
All methods listed here are also available to LazyEBSD
instances.
See Signal2D
for methods inherited from HyperSpy.
Enhance the local contrast in an EBSD scan inplace using adaptive histogram equalization. 


Average patterns inplace with its neighbours within a window. 

Match each experimental pattern to a dictionary of simulated patterns of known orientations to index the them [CPW+15, JPDeGraef19]. 

Filter an EBSD scan inplace in the frequency domain. 
Get a map of the average dot product between patterns and their neighbours within an averaging window. 


Get the model signal generated with the selected number of principal components from a decomposition. 

Get the dynamic background per EBSD pattern in a scan. 

Compute the image quality map of patterns in an EBSD scan. 

Get an array with dot products of a pattern and its neighbours within a window. 

Get a virtual backscatter electron (VBSE) image formed from intensities within a region of interest (ROI) on the detector. 

Normalize image intensities in inplace to a mean of zero with a given standard deviation. 

Plot an interactive virtual backscatter electron (VBSE) image formed from intensities within a specified and adjustable region of interest (ROI) on the detector. 

Refine orientations by searching orientation space around the best indexed solution using fixed projection centers. 

Refine orientations and projection centers simultaneously by searching the orientation and PC parameter space. 

Refine projection centers by searching the parameter space using fixed orientations. 

Remove the dynamic background in an EBSD scan inplace. 

Remove the static background inplace. 

Rescale image intensities inplace. 

Write the signal to file in the specified format. 

Set detector pixel size in microns. 

[Deprecated] Set experimental parameters in signal metadata. 

[Deprecated] Set parameters for one phase in signal metadata. 

Set the step size in microns. 
 class kikuchipy.signals.EBSD(*args, **kwargs)[source]#
Bases:
CommonImage
,Signal2D
Scan of Electron Backscatter Diffraction (EBSD) patterns.
This class extends HyperSpy’s Signal2D class for EBSD patterns, with common intensity processing methods and some analysis methods.
Methods inherited from HyperSpy can be found in the HyperSpy user guide.
See the docstring of
hyperspy.signal.BaseSignal
for a list of attributes in addition to the ones listed below. adaptive_histogram_equalization(kernel_size=None, clip_limit=0, nbins=128)[source]#
Enhance the local contrast in an EBSD scan inplace using adaptive histogram equalization.
This method uses
skimage.exposure.equalize_adapthist()
. Parameters:
kernel_size (
Union
[Tuple
[int
,int
],List
[int
],None
]) – Shape of contextual regions for adaptive histogram equalization, default is 1/4 of image height and 1/4 of image width.clip_limit (
Union
[int
,float
]) – Clipping limit, normalized between 0 and 1 (higher values give more contrast). Default is 0.nbins (
int
) – Number of gray bins for histogram (“data range”), default is 128.
See also
Examples
To best understand how adaptive histogram equalization works, we plot the histogram of the same image before and after equalization:
>>> import numpy as np >>> import matplotlib.pyplot as plt >>> import kikuchipy as kp >>> s = kp.data.nickel_ebsd_small() >>> s2 = s.inav[0, 0].deepcopy() >>> s2.adaptive_histogram_equalization() >>> hist, _ = np.histogram( ... s.inav[0, 0].data, bins=255, range=(0, 255) ... ) >>> hist2, _ = np.histogram(s2.data, bins=255, range=(0, 255)) >>> fig, ax = plt.subplots(nrows=2, ncols=2) >>> _ = ax[0, 0].imshow(s.inav[0, 0].data) >>> _ = ax[1, 0].plot(hist) >>> _ = ax[0, 1].imshow(s2.data) >>> _ = ax[1, 1].plot(hist2)
Notes
It is recommended to perform adaptive histogram equalization only after static and dynamic background corrections, otherwise some unwanted darkening towards the edges might occur.
The default window size might not fit all pattern sizes, so it may be necessary to search for the optimal window size.
 as_lazy(*args, **kwargs)[source]#
Create a copy of the given Signal as a
LazySignal
. Parameters:
copy_variance (bool) – Whether or not to copy the variance from the original Signal to the new lazy version. Default is True.
copy_navigator (bool) – Whether or not to copy the navigator from the original Signal to the new lazy version. Default is True.
copy_learning_results (bool) – Whether to copy the learning_results from the original signal to the new lazy version. Default is True.
 Returns:
res – The same signal, converted to be lazy
 Return type:
 average_neighbour_patterns(window='circular', window_shape=(3, 3), **kwargs)[source]#
Average patterns inplace with its neighbours within a window.
The amount of averaging is specified by the window coefficients. All patterns are averaged with the same window. Map borders are extended with zeros. Resulting pattern intensities are rescaled to fill the input patterns’ data type range individually.
Averaging is accomplished by correlating the window with the extended array of patterns using
scipy.ndimage.correlate()
. Parameters:
window (
Union
[str
,ndarray
,Array
,Window
]) – Name of averaging window or an array. Available types are listed inscipy.signal.windows.get_window()
, in addition to a"circular"
window (default) filled with ones in which corner coefficients are set to zero. A window element is considered to be in a corner if its radial distance to the origin (window centre) is shorter or equal to the half width of the window’s longest axis. A 1D or 2Dnumpy.ndarray
,dask.array.Array
orWindow
can also be passed.window_shape (
Tuple
[int
,...
]) – Shape of averaging window. Not used if a custom window orWindow
object is passed towindow
. This can be either 1D or 2D, and can be asymmetrical. Default is (3, 3).kwargs – Keyword arguments passed to the available window type listed in
scipy.signal.windows.get_window()
. If not given, the default values of that particular window are used.
 deepcopy()[source]#
Return a “deep copy” of this Signal using the standard library’s
deepcopy()
function. Note: this means the underlying data structure will be duplicated in memory.See also
 property detector: EBSDDetector#
An
EBSDDetector
describing the EBSD detector dimensions, the projection/pattern centre, and the detectorsample geometry. Return type:
 dictionary_indexing(dictionary, metric='ncc', keep_n=20, n_per_iteration=None, signal_mask=None, rechunk=False, dtype=None)[source]#
Match each experimental pattern to a dictionary of simulated patterns of known orientations to index the them [CPW+15, JPDeGraef19].
A suitable similarity metric, the normalized crosscorrelation (
NormalizedCrossCorrelationMetric
), is used by default, but a valid userdefined similarity metric may be used instead. The metric must be a class implementing theSimilarityMetric
abstract class methods. The normalized dot product (NormalizedDotProductMetric
) is available as well.A
CrystalMap
with “scores” and “simulation_indices” as properties is returned. Parameters:
dictionary (EBSD) – EBSD signal with dictionary patterns. The signal must have a 1D navigation axis, an xmap property with crystal orientations set, and equal detector shape.
metric (
Union
[SimilarityMetric
,str
]) – Similarity metric, by default “ncc” (normalized crosscorrelation). “ndp” (normalized dot product) is also available.keep_n (
int
) – Number of best matches to keep, by default 20 or the number of dictionary patterns if fewer than 20 are available.n_per_iteration (
Optional
[int
]) – Number of dictionary patterns to compare to all experimental patterns in each indexing iteration. If not given, and the dictionary is a LazyEBSD signal, it is equal to the chunk size of the first pattern array axis, while if if is an EBSD signal, it is set equal to the number of dictionary patterns, yielding only one iteration. This parameter can be increased to use less memory during indexing, but this will increase the computation time.signal_mask (
Optional
[ndarray
]) – A boolean mask equal to the experimental patterns’ detector shape (n rows, n columns), where only pixels equal to False are matched. If not given, all pixels are used.rechunk (
bool
) – Whether metric is allowed to rechunk experimental and dictionary patterns before matching. Default is False. If a custom metric is passed, whatever metric.rechunk is set to will be used. Rechunking usually makes indexing faster, but uses more memory.dtype (
Union
[None
,dtype
,type
]) – Which data type metric shall cast the patterns to before matching. If not given,float32
will be used unless a custom metric is passed and it has set the dtype attribute, which will then be used instead.float32
andfloat64
is allowed for the available “ncc” and “ndp” metrics.
 Returns:
xmap – A crystal map with keep_n rotations per point with the sorted best matching orientations in the dictionary. The corresponding best scores and indices into the dictionary are stored in the xmap.prop dictionary as “scores” and “simulation_indices”.
 Return type:
Notes
Merging of single phase crystal maps into one multi phase map and calculations of an orientation similarity map can be done afterwards with
merge_crystal_maps()
andorientation_similarity_map()
, respectively.Changed in version 0.5: Only one dictionary can be passed, the n_per_iteration parameter replaced n_slices, and the return_merged_crystal_map and get_orientation_similarity_map parameters were removed.
New in version 0.5: The signal_mask, rechunk, and dtype parameters.
 fft_filter(transfer_function, function_domain, shift=False)[source]#
Filter an EBSD scan inplace in the frequency domain.
Patterns are transformed via the Fast Fourier Transform (FFT) to the frequency domain, where their spectrum is multiplied by the transfer_function, and the filtered spectrum is subsequently transformed to the spatial domain via the inverse FFT (IFFT). Filtered patterns are rescaled to input data type range.
Note that if function_domain is “spatial”, only real valued FFT and IFFT is used.
 Parameters:
transfer_function (
Union
[ndarray
,Window
]) – Filter to apply to patterns. This can either be a transfer function in the frequency domain of pattern shape or a kernel in the spatial domain. What is passed is determined from function_domain.function_domain (
str
) – Options are “frequency” and “spatial”, indicating, respectively, whether the filter function passed to filter_function is a transfer function in the frequency domain or a kernel in the spatial domain.shift (
bool
) – Whether to shift the zerofrequency component to the centre. Default is False. This is only used when function_domain=”frequency”.
Examples
Applying a Gaussian low pass filter with a cutoff frequency of 20 to an EBSD object
s
:>>> import kikuchipy as kp >>> s = kp.data.nickel_ebsd_small() >>> pattern_shape = s.axes_manager.signal_shape[::1] >>> w = kp.filters.Window( ... "lowpass", cutoff=20, shape=pattern_shape ... ) >>> s.fft_filter( ... transfer_function=w, ... function_domain="frequency", ... shift=True, ... )
See also
 get_average_neighbour_dot_product_map(window=None, zero_mean=True, normalize=True, dtype_out=<class 'numpy.float32'>, dp_matrices=None)[source]#
Get a map of the average dot product between patterns and their neighbours within an averaging window.
 Parameters:
window (
Optional
[Window
]) – Window with integer coefficients defining the neighbours to calculate the average with. If None (default), the four nearest neighbours are used. Must have the same number of dimensions as signal navigation dimensions.zero_mean (
bool
) – Whether to subtract the mean of each pattern individually to center the intensities about zero before calculating the dot products. Default is True.normalize (
bool
) – Whether to normalize the pattern intensities to a standard deviation of 1 before calculating the dot products. This operation is performed after centering the intensities if zero_mean is True. Default is True.dtype_out (
dtype
) – Data type of the output map. Default isnumpy.float32
.dp_matrices (
Optional
[ndarray
]) – Optional precalculated dot product matrices, by default None. If an array is passed, the average dot product map is calculated from this array. The dp_matrices array can be obtained fromget_neighbour_dot_product_matrices()
. It’s shape must correspond to the signal’s navigation shape and the window’s shape.
 Return type:
 get_decomposition_model(components=None, dtype_out=<class 'numpy.float32'>)[source]#
Get the model signal generated with the selected number of principal components from a decomposition.
Calls HyperSpy’s
hyperspy.learn.mva.MVA.get_decomposition_model()
. Learning results are preconditioned before this call, doing the following: (1) setnumpy.dtype
to desired dtype_out, (2) remove unwanted components, and (3) rechunk, ifdask.array.Array
, to suitable chunks. Parameters:
components (
Union
[None
,int
,List
[int
]]) – If None (default), rebuilds the signal from all components. If int, rebuilds signal from components in range 0given int. If list of ints, rebuilds signal from only components in given list.dtype_out (
dtype
) – Data type to cast learning results to (default isnumpy.float32
). Note that HyperSpy casts them tonumpy.float64
.
 Returns:
s_model
 Return type:
 get_dynamic_background(filter_domain='frequency', std=None, truncate=4.0, dtype_out=None, **kwargs)[source]#
Get the dynamic background per EBSD pattern in a scan.
 Parameters:
filter_domain (
str
) – Whether to apply a Gaussian convolution filter in the “frequency” (default) or “spatial” domain.std (
Union
[None
,int
,float
]) – Standard deviation of the Gaussian window. If None (default), it is set to width/8.truncate (
Union
[int
,float
]) – Truncate the Gaussian filter at this many standard deviations. Default is 4.0.dtype_out (
Optional
[dtype
]) – Data type of the background patterns. If None (default), it is set to the same data type as the input pattern.kwargs – Keyword arguments passed to the Gaussian blurring function determined from filter_domain.
 Returns:
background_signal – Signal with the large scale variations across the detector.
 Return type:
 get_image_quality(normalize=True)[source]#
Compute the image quality map of patterns in an EBSD scan.
The image quality is calculated based on the procedure defined by Krieger Lassen [Lassen1994].
 Parameters:
normalize (
bool
) – Whether to normalize patterns to a mean of zero and standard deviation of 1 before calculating the image quality. Default isTrue
. Returns:
Image quality map of same shape as navigation axes. This is a Dask array if the signal is lazy.
 Return type:
image_quality_map
References
Examples
>>> import matplotlib.pyplot as plt >>> import kikuchipy as kp >>> s = kp.data.nickel_ebsd_small() >>> iq = s.get_image_quality() >>> plt.imshow(iq)
See also
 get_neighbour_dot_product_matrices(window=None, zero_mean=True, normalize=True, dtype_out=<class 'numpy.float32'>)[source]#
Get an array with dot products of a pattern and its neighbours within a window.
 Parameters:
window (
Optional
[Window
]) – Window with integer coefficients defining the neighbours to calculate the dot products with. If None (default), the four nearest neighbours are used. Must have the same number of dimensions as signal navigation dimensions.zero_mean (
bool
) – Whether to subtract the mean of each pattern individually to center the intensities about zero before calculating the dot products. Default is True.normalize (
bool
) – Whether to normalize the pattern intensities to a standard deviation of 1 before calculating the dot products. This operation is performed after centering the intensities if zero_mean is True. Default is True.dtype_out (
dtype
) – Data type of the output map. Default isnumpy.float32
.
 Return type:
 get_virtual_bse_intensity(roi, out_signal_axes=None)[source]#
Get a virtual backscatter electron (VBSE) image formed from intensities within a region of interest (ROI) on the detector.
Adapted from
pyxem.signals.common_diffraction.CommonDiffraction.get_integrated_intensity()
. Parameters:
 Returns:
virtual_image – VBSE image formed from detector intensities within an ROI on the detector.
 Return type:
Examples
>>> import hyperspy.api as hs >>> import kikuchipy as kp >>> rect_roi = hs.roi.RectangularROI( ... left=0, right=5, top=0, bottom=5 ... ) >>> s = kp.data.nickel_ebsd_small() >>> vbse_image = s.get_virtual_bse_intensity(rect_roi)
See also
 normalize_intensity(num_std=1, divide_by_square_root=False, dtype_out=None)[source]#
Normalize image intensities in inplace to a mean of zero with a given standard deviation.
 Parameters:
num_std (
int
) – Number of standard deviations of the output intensities. Default is 1.divide_by_square_root (
bool
) – Whether to divide output intensities by the square root of the signal dimension size. Default is False.dtype_out (
Optional
[dtype
]) – Data type of normalized images. If None (default), the input images’ data type is used.
Notes
Data type should always be changed to floating point, e.g.
np.float32
withchange_dtype()
, before normalizing the intensities.Examples
>>> import numpy as np >>> import kikuchipy as kp >>> s = kp.data.nickel_ebsd_small() >>> np.mean(s.data) 146.0670987654321 >>> s.normalize_intensity(dtype_out=np.float32) >>> np.mean(s.data) 2.6373216e08
Notes
Rescaling RGB images is not possible. Use RGB channel normalization when creating the image instead.
 plot_virtual_bse_intensity(roi, out_signal_axes=None, **kwargs)[source]#
Plot an interactive virtual backscatter electron (VBSE) image formed from intensities within a specified and adjustable region of interest (ROI) on the detector.
Adapted from
pyxem.signals.common_diffraction.CommonDiffraction.plot_integrated_intensity()
. Parameters:
roi (
BaseInteractiveROI
) – Any interactive ROI detailed in HyperSpy.out_signal_axes (
Union
[None
,Iterable
[int
],Iterable
[str
]]) – Which navigation axes to use as signal axes in the virtual image. If None (default), the first two navigation axes are used.**kwargs – Keyword arguments passed to the plot method of the virtual image.
Examples
>>> import hyperspy.api as hs >>> import kikuchipy as kp >>> s = kp.data.nickel_ebsd_small() >>> rect_roi = hs.roi.RectangularROI( ... left=0, right=5, top=0, bottom=5 ... ) >>> s.plot_virtual_bse_intensity(rect_roi)
See also
 refine_orientation(xmap, detector, master_pattern, energy, mask=None, method='minimize', method_kwargs=None, trust_region=None, compute=True, rechunk=True, chunk_kwargs=None)[source]#
Refine orientations by searching orientation space around the best indexed solution using fixed projection centers.
Refinement attempts to optimize (maximize) the similarity between patterns in this signal and simulated patterns projected from a master pattern. The only supported similarity metric is the normalized crosscorrelation (NCC). The orientation, represented by three Euler angles (\(\phi_1\), \(\Phi\), \(\phi_2\)), is changed during projection, while the sampledetector geometry, represented by the three projection center (PC) parameters (PCx, PCy, PCz), are fixed.
 A subset of the optimization methods in SciPy are available:
 Local optimization:
minimize()
(includes NelderMead, Powell etc.)
 Global optimization:
 Parameters:
xmap (
CrystalMap
) – Single phase crystal map with at least one orientation per point. The orientations are assumed to be relative to the EDAX TSL sample reference frame RDTDND.detector (
EBSDDetector
) – Detector describing the detectorsample geometry with either one PC to be used for all map points or one for each point.master_pattern (EBSDMasterPattern) – Master pattern in the square Lambert projection of the same phase as the one in the crystal map.
energy (
Union
[int
,float
]) – Accelerating voltage of the electron beam in kV specifying which master pattern energy to use during projection of simulated patterns.mask (
Optional
[ndarray
]) – Boolean mask of signal shape to be applied to the simulated pattern before comparison. Pixels set to True are masked away. If not given, all pixels are matched.method (str, optional) – Name of the
scipy.optimize
optimization method, among “minimize”, “differential_evolution”, “dual_annealing”, “basinhopping”, and “shgo”. Default is “minimize”, which by default performs local optimization with the NelderMead method unless another “minimize” method is passed to method_kwargs.method_kwargs (
Optional
[dict
]) – Keyword arguments passed to thescipy.optimize
method. For example, to perform refinement with the modified Powell algorithm, pass method=”minimize” and method_kwargs=dict(method=”Powell”).trust_region (
Optional
[list
]) – List of +/ angular deviation in degrees as bound constraints on the three Euler angles. If not given and method requires bounds, they are set to [1, 1, 1]. If given, method is assumed to support bounds and they are passed to method.compute (
bool
) – Whether to refine now (True) or later (False). Default is True. Seecompute()
for more details.rechunk (
bool
) – If True (default), rechunk the dask array with patterns used in refinement (not the signal data inplace) if it is returned fromget_dask_array()
in a single chunk. This ensures small data sets are rechunked so as to utilize multiple CPUs.chunk_kwargs (
Optional
[dict
]) – Keyword arguments passed toget_chunking()
if rechunk is True and the dask array with patterns used in refinement is returned fromget_dask_array()
in a single chunk.
 Returns:
Crystal map with refined orientations and similarity metrics in a “scores” property if compute is True. If compute is False, a dask array of navigation shape + (4,) is returned, to be computed later. See
compute_refine_orientation_results()
. Each navigation point has the optimized score and the three Euler angles in radians in element 0, 1, 2, and 3, respectively. Return type:
CrystalMap
orArray
 refine_orientation_projection_center(xmap, detector, master_pattern, energy, mask=None, method='minimize', method_kwargs=None, trust_region=None, compute=True, rechunk=True, chunk_kwargs=None)[source]#
Refine orientations and projection centers simultaneously by searching the orientation and PC parameter space.
Refinement attempts to optimize (maximize) the similarity between patterns in this signal and simulated patterns projected from a master pattern. The only supported similarity metric is the normalized crosscorrelation (NCC). The orientation, represented by three Euler angles (\(\phi_1\), \(\Phi\), \(\phi_2\)), and the sampledetector geometry, represented by the three projection center (PC) parameters (PCx, PCy, PCz), are changed during projection.
 A subset of the optimization methods in SciPy are available:
 Local optimization:
minimize()
(includes NelderMead, Powell etc.)
 Global optimization:
 Parameters:
xmap (
CrystalMap
) – Single phase crystal map with at least one orientation per point. The orientations are assumed to be relative to the EDAX TSL sample reference frame RDTDND.detector (
EBSDDetector
) – Detector describing the detectorsample geometry with either one PC to be used for all map points or one for each point.master_pattern (EBSDMasterPattern) – Master pattern in the square Lambert projection of the same phase as the one in the crystal map.
energy (
Union
[int
,float
]) – Accelerating voltage of the electron beam in kV specifying which master pattern energy to use during projection of simulated patterns.mask (
Optional
[ndarray
]) – Boolean mask of signal shape to be applied to the simulated pattern before comparison. Pixels set to True are masked away. If not given, all pixels are matched.method (str, optional) – Name of the
scipy.optimize
optimization method, among “minimize”, “differential_evolution”, “dual_annealing”, “basinhopping”, and “shgo”. Default is “minimize”, which by default performs local optimization with the NelderMead method unless another “minimize” method is passed to method_kwargs.method_kwargs (
Optional
[dict
]) – Keyword arguments passed to thescipy.optimize
method. For example, to perform refinement with the modified Powell algorithm, pass method=”minimize” and method_kwargs=dict(method=”Powell”).trust_region (
Optional
[list
]) – List of +/ angular deviations in degrees as bound constraints on the three Euler angles and +/ percentage deviations as bound constraints on the PC parameters in the Bruker convention. The latter parameter range is [0, 1]. If not given and method requires bounds, they are set to [1, 1, 1, 0.05, 0.05, 0.05]. If given, method is assumed to support bounds and they are passed to method.compute (
bool
) – Whether to refine now (True) or later (False). Default is True. Seecompute()
for more details.rechunk (
bool
) – If True (default), rechunk the dask array with patterns used in refinement (not the signal data inplace) if it is returned fromget_dask_array()
in a single chunk. This ensures small data sets are rechunked so as to utilize multiple CPUs.chunk_kwargs (
Optional
[dict
]) – Keyword arguments passed toget_chunking()
if rechunk is True and the dask array with patterns used in refinement is returned fromget_dask_array()
in a single chunk.
 Returns:
Crystal map with refined orientations and a new EBSD detector instance with the refined PCs, if compute is True. If compute is False, a dask array of navigation shape + (7,) is returned, to be computed later. See
compute_refine_orientation_projection_center_results()
. Each navigation point has the optimized score, the three Euler angles in radians, and the three PC parameters in the Bruker convention in element 0, 1, 2, 3, 4, 5, and 6, respectively. Return type:
CrystalMap
andEBSDDetector
, orArray
Notes
The method attempts to refine the orientations and projection center at the same time for each map point. The optimization landscape is sloppy [PLS20], where the orientation and PC can make up for each other. Thus, it is possible that the set of parameters that yield the highest similarity is incorrect. It is left to the user to ensure that the output is reasonable.
 refine_projection_center(xmap, detector, master_pattern, energy, mask=None, method='minimize', method_kwargs=None, trust_region=None, compute=True, rechunk=True, chunk_kwargs=None)[source]#
Refine projection centers by searching the parameter space using fixed orientations.
Refinement attempts to optimize (maximize) the similarity between patterns in this signal and simulated patterns projected from a master pattern. The only supported similarity metric is the normalized crosscorrelation (NCC). The sampledetector geometry, represented by the three projection center (PC) parameters (PCx, PCy, PCz), is changed during projection, while the orientations are fixed.
 A subset of the optimization methods in SciPy are available:
 Local optimization:
minimize()
(includes NelderMead, Powell etc.)
 Global optimization:
 Parameters:
xmap (
CrystalMap
) – Single phase crystal map with at least one orientation per point. The orientations are assumed to be relative to the EDAX TSL sample reference frame RDTDND.detector (
EBSDDetector
) – Detector describing the detectorsample geometry with either one PC to be used for all map points or one for each point.master_pattern (EBSDMasterPattern) – Master pattern in the square Lambert projection of the same phase as the one in the crystal map.
energy (
Union
[int
,float
]) – Accelerating voltage of the electron beam in kV specifying which master pattern energy to use during projection of simulated patterns.mask (
Optional
[ndarray
]) – Boolean mask of signal shape to be applied to the simulated pattern before comparison. Pixels set to True are masked away. If not given, all pixels are matched.method (str, optional) – Name of the
scipy.optimize
optimization method, among “minimize”, “differential_evolution”, “dual_annealing”, “basinhopping”, and “shgo”. Default is “minimize”, which by default performs local optimization with the NelderMead method unless another “minimize” method is passed to method_kwargs.method_kwargs (
Optional
[dict
]) – Keyword arguments passed to thescipy.optimize
method. For example, to perform refinement with the modified Powell algorithm, pass method=”minimize” and method_kwargs=dict(method=”Powell”).trust_region (
Optional
[list
]) – List of +/ percentage deviations as bound constraints on the PC parameters in the Bruker convention. The parameter range is [0, 1]. If not given and method requires bounds, they are set to [0.05, 0.05, 0.05]. If given, method is assumed to support bounds and they are passed to method.compute (
bool
) – Whether to refine now (True) or later (False). Default is True. Seecompute()
for more details.rechunk (
bool
) – If True (default), rechunk the dask array with patterns used in refinement (not the signal data inplace) if it is returned fromget_dask_array()
in a single chunk. This ensures small data sets are rechunked so as to utilize multiple CPUs.chunk_kwargs (
Optional
[dict
]) – Keyword arguments passed toget_chunking()
if rechunk is True and the dask array with patterns used in refinement is returned fromget_dask_array()
in a single chunk.
 Returns:
New similarity metrics and a new EBSD detector instance with the refined PCs if compute is True. If compute is False, a dask array of navigation shape + (4,) is returned, to be computed later. See
compute_refine_projection_center_results()
. Each navigation point has the optimized score and the three PC parameters in the Bruker convention in element 0, 1, 2, and 3, respectively. Return type:
numpy.ndarray
andEBSDDetector
, orArray
 remove_dynamic_background(operation='subtract', filter_domain='frequency', std=None, truncate=4.0, **kwargs)[source]#
Remove the dynamic background in an EBSD scan inplace.
The removal is performed by subtracting or dividing by a Gaussian blurred version of each pattern. Resulting pattern intensities are rescaled to fill the input patterns’ data type range individually.
 Parameters:
operation (
str
) – Whether to"subtract"
(default) or"divide"
by the dynamic background pattern.filter_domain (
str
) – Whether to obtain the dynamic background by applying a Gaussian convolution filter in the"frequency"
(default) or"spatial"
domain.std (
Union
[None
,int
,float
]) – Standard deviation of the Gaussian window. If None (default), it is set to width/8.truncate (
Union
[int
,float
]) – Truncate the Gaussian window at this many standard deviations. Default is4.0
.kwargs – Keyword arguments passed to the Gaussian blurring function determined from
filter_domain
.
See also
kikuchipy.signals.EBSD.remove_static_background
,kikuchipy.signals.EBSD.get_dynamic_background
,kikuchipy.pattern.remove_dynamic_background
,kikuchipy.pattern.get_dynamic_background
Examples
Traditional background correction includes static and dynamic corrections:
>>> import kikuchipy as kp >>> s = kp.data.nickel_ebsd_small() >>> s.remove_static_background() >>> s.remove_dynamic_background(operation="divide", std=5)
 remove_static_background(operation='subtract', relative=False, static_bg=None, scale_bg=False)[source]#
Remove the static background inplace.
The removal is performed by subtracting or dividing by a static background pattern. Resulting pattern intensities are rescaled keeping relative intensities or not and stretched to fill the available grey levels in the patterns’ data type range.
 Parameters:
operation (
str
) – Whether to"subtract"
(default) or"divide"
by the static background pattern.relative (
bool
) –Keep relative intensities between patterns. Default is
False
.Deprecated since version 0.6: This parameter will be removed in version 0.7 due to the implementation not working well for large datasets. It was originally supported so that a virtual backscatter electron (VBSE) image with meaningful contrast could be navigated after static background removal. For an EBSD signal
s
, this image can be easily obtained withs_mean = s.mean(s.axes_manager.signal_indices_in_array)
.static_bg (
Union
[None
,ndarray
,Array
]) – Static background pattern. If not given, the background is obtained from theEBSD.static_background
property.scale_bg (
bool
) – Whether to scale the static background pattern to each individual pattern’s data range before removal. Default isFalse
.
See also
Examples
It is assumed that a static background pattern of the same shape and data type (e.g. 8bit unsigned integer,
uint8
) as the patterns is available in signal metadata:>>> import kikuchipy as kp >>> s = kp.data.nickel_ebsd_small() >>> s.static_background array([[84, 87, 90, ..., 27, 29, 30], [87, 90, 93, ..., 27, 28, 30], [92, 94, 97, ..., 39, 28, 29], ..., [80, 82, 84, ..., 36, 30, 26], [79, 80, 82, ..., 28, 26, 26], [76, 78, 80, ..., 26, 26, 25]], dtype=uint8)
The static background can be removed by subtracting or dividing this background from each pattern:
>>> s.remove_static_background(operation="divide")
If the
static_background
property isNone
, this must be passed in thestatic_bg
parameter as anumpy
ordask
array.
 rescale_intensity(relative=False, in_range=None, out_range=None, dtype_out=None, percentiles=None)[source]#
Rescale image intensities inplace.
Output min./max. intensity is determined from out_range or the data type range of the
numpy.dtype
passed to dtype_out if out_range is None.This method is based on
skimage.exposure.rescale_intensity()
. Parameters:
relative (
bool
) – Whether to keep relative intensities between images (default is False). If True, in_range must be None, because in_range is in this case set to the global min./max. intensity.in_range (
Union
[None
,Tuple
[int
,int
],Tuple
[float
,float
]]) – Min./max. intensity of input images. If None (default), in_range is set to pattern min./max intensity. Contrast stretching is performed when in_range is set to a narrower intensity range than the input patterns. Must be None if relative is True or percentiles are passed.out_range (
Union
[None
,Tuple
[int
,int
],Tuple
[float
,float
]]) – Min./max. intensity of output images. If None (default), out_range is set to dtype_out min./max according to skimage.util.dtype.dtype_range.dtype_out (
Union
[None
,dtype
,Tuple
[int
,int
],Tuple
[float
,float
]]) – Data type of rescaled images, default is input images’ data type.percentiles (
Union
[None
,Tuple
[int
,int
],Tuple
[float
,float
]]) – Disregard intensities outside these percentiles. Calculated per image. Must be None if in_range or relative is passed. Default is None.
Examples
>>> import numpy as np >>> import kikuchipy as kp >>> s = kp.data.nickel_ebsd_small()
Image intensities are stretched to fill the available grey levels in the input images’ data type range or any
numpy.dtype
range passed to dtype_out, either keeping relative intensities between images or not:>>> print( ... s.data.dtype, s.data.min(), s.data.max(), ... s.inav[0, 0].data.min(), s.inav[0, 0].data.max() ... ) uint8 23 246 26 245 >>> s2 = s.deepcopy() >>> s.rescale_intensity(dtype_out=np.uint16) >>> print( ... s.data.dtype, s.data.min(), s.data.max(), ... s.inav[0, 0].data.min(), s.inav[0, 0].data.max() ... ) uint16 0 65535 0 65535 >>> s2.rescale_intensity(relative=True) >>> print( ... s2.data.dtype, s2.data.min(), s2.data.max(), ... s2.inav[0, 0].data.min(), s2.inav[0, 0].data.max() ... ) uint8 0 255 3 253
Contrast stretching can be performed by passing percentiles:
>>> s.rescale_intensity(percentiles=(1, 99))
Here, the darkest and brightest pixels within the 1% percentile are set to the ends of the data type range, e.g. 0 and 255 respectively for images of
uint8
data type.Notes
Rescaling RGB images is not possible. Use RGB channel normalization when creating the image instead.
 save(filename=None, overwrite=None, extension=None, **kwargs)[source]#
Write the signal to file in the specified format.
The function gets the format from the extension: h5, hdf5 or h5ebsd for kikuchipy’s specification of the the h5ebsd format, dat for the NORDIF binary format or hspy for HyperSpy’s HDF5 specification. If no extension is provided the signal is written to a file in kikuchipy’s h5ebsd format. Each format accepts a different set of parameters.
For details see the specific format documentation under “See Also” below.
This method is a modified version of HyperSpy’s function
hyperspy.signal.BaseSignal.save()
. Parameters:
filename (
Optional
[str
]) – If None (default) and tmp_parameters.filename and tmp_parameters.folder in signal metadata are defined, the filename and path will be taken from there. A valid extension can be provided e.g. “data.h5”, see extension.overwrite (
Optional
[bool
]) – If None and the file exists, it will query the user. If True (False) it (does not) overwrite the file if it exists.extension (
Optional
[str
]) – Extension of the file that defines the file format. Options are “h5”/”hdf5”/”h5ebsd”/”dat”/”hspy”. “h5”/”hdf5”/”h5ebsd” are equivalent. If None, the extension is determined from the following list in this order: i) the filename, ii) tmp_parameters.extension or iii) “h5” (kikuchipy’s h5ebsd format).**kwargs – Keyword arguments passed to writer.
 set_detector_calibration(delta)[source]#
Set detector pixel size in microns. The offset is set to the the detector centre.
See also
Examples
>>> import kikuchipy as kp >>> s = kp.data.nickel_ebsd_small() >>> s.axes_manager['dx'].scale # Default value 1.0 >>> s.set_detector_calibration(delta=70.) >>> s.axes_manager['dx'].scale 70.0
 set_experimental_parameters(detector=None, azimuth_angle=None, elevation_angle=None, sample_tilt=None, working_distance=None, binning=None, exposure_time=None, grid_type=None, gain=None, frame_number=None, frame_rate=None, scan_time=None, beam_energy=None, xpc=None, ypc=None, zpc=None, static_background=None, manufacturer=None, version=None, microscope=None, magnification=None)[source]#
[Deprecated] Set experimental parameters in signal metadata.
 Parameters:
azimuth_angle (float, optional) – Azimuth angle of the detector in degrees. If the azimuth is zero, the detector is perpendicular to the tilt axis.
beam_energy (float, optional) – Energy of the electron beam in kV.
binning (int, optional) – Camera binning.
detector (str, optional) – Detector manufacturer and model.
elevation_angle (float, optional) – Elevation angle of the detector in degrees. If the elevation is zero, the detector is perpendicular to the incident beam.
exposure_time (float, optional) – Camera exposure time in µs.
frame_number (float, optional) – Number of patterns integrated during acquisition.
frame_rate (float, optional) – Frames per s.
gain (float, optional) – Camera gain, typically in dB.
grid_type (str, optional) – Scan grid type, only square grid is supported.
manufacturer (str, optional) – Manufacturer of software used to collect patterns.
microscope (str, optional) – Microscope used to collect patterns.
magnification (int, optional) – Microscope magnification at which patterns were collected.
sample_tilt (float, optional) – Sample tilt angle from horizontal in degrees.
scan_time (float, optional) – Scan time in s.
static_background (numpy.ndarray, optional) – Static background pattern.
version (str, optional) – Version of software used to collect patterns.
working_distance (float, optional) – Working distance in mm.
xpc (float, optional) – Pattern centre horizontal coordinate with respect to detector centre, as viewed from the detector to the sample.
ypc (float, optional) – Pattern centre vertical coordinate with respect to detector centre, as viewed from the detector to the sample.
zpc (float, optional) – Specimen to scintillator distance.
See also
Examples
>>> import kikuchipy as kp >>> s = kp.data.nickel_ebsd_small() >>> node = kp.signals.util.metadata_nodes("ebsd") >>> s.metadata.get_item(node + '.xpc') 5.64 >>> s.set_experimental_parameters(xpc=0.50726) >>> s.metadata.get_item(node + '.xpc') 0.50726
Notes
Deprecated since version 0.5: Function set_experimental_parameters() is deprecated and will be removed in version 0.6.
 set_phase_parameters(number=1, atom_coordinates=None, formula=None, info=None, lattice_constants=None, laue_group=None, material_name=None, point_group=None, setting=None, source=None, space_group=None, symmetry=None)[source]#
[Deprecated] Set parameters for one phase in signal metadata.
A phase node with default values is created if none is present in the metadata when this method is called.
 Parameters:
number (int, optional) – Phase number.
atom_coordinates (dict, optional) – Dictionary of dictionaries with one or more of the atoms in the unit cell, on the form {‘1’: {‘atom’: ‘Ni’, ‘coordinates’: [0, 0, 0], ‘site_occupation’: 1, ‘debye_waller_factor’: 0}, ‘2’: {‘atom’: ‘O’,… etc. debye_waller_factor in units of nm^2, and site_occupation in range [0, 1].
formula (str, optional) – Phase formula, e.g. ‘Fe2’ or ‘Ni’.
info (str, optional) – Whatever phase info the user finds relevant.
lattice_constants (numpy.ndarray or list of floats, optional) – Six lattice constants a, b, c, alpha, beta, gamma.
laue_group (str, optional) – Phase Laue group.
material_name (str, optional) – Name of material.
point_group (str, optional) – Phase point group.
setting (int, optional) – Space group’s origin setting.
source (str, optional) – Literature reference for phase data.
space_group (int, optional) – Number between 1 and 230.
symmetry (int, optional) – Phase symmetry.
See also
Examples
>>> import kikuchipy as kp >>> s = kp.data.nickel_ebsd_small() >>> s.metadata.Sample.Phases.Number_1.atom_coordinates.Number_1 ├── atom = Ni ├── coordinates = array([0, 0, 0]) ├── debye_waller_factor = 0.0035 └── site_occupation = 1 >>> s.set_phase_parameters( ... number=1, ... atom_coordinates={'1': { ... 'atom': 'Fe', ... 'coordinates': [0, 0, 0], ... 'site_occupation': 1, ... 'debye_waller_factor': 0.005 ... }} ... ) >>> s.metadata.Sample.Phases.Number_1.atom_coordinates.Number_1 ├── atom = Fe ├── coordinates = array([0, 0, 0]) ├── debye_waller_factor = 0.005 └── site_occupation = 1
Notes
Deprecated since version 0.5: Function set_phase_parameters() is deprecated and will be removed in version 0.6.
 set_scan_calibration(step_x=1.0, step_y=1.0)[source]#
Set the step size in microns.
 Parameters:
See also
Examples
>>> import kikuchipy as kp >>> s = kp.data.nickel_ebsd_small() >>> s.axes_manager['x'].scale 1.5 >>> s.set_scan_calibration(step_x=2) # Microns >>> s.axes_manager['x'].scale 2.0
 property xmap: CrystalMap#
A
CrystalMap
containing the phases, unit cell rotations and auxiliary properties of the EBSD data set. Return type:
These methods are exclusive to LazyEBSD instances.

Write the model signal generated from the selected number of principal components directly to an .hspy file. 
 class kikuchipy.signals.LazyEBSD(*args, **kwargs)[source]#
Bases:
LazySignal2D
,EBSD
Lazy implementation of the
EBSD
class.This class extends HyperSpy’s LazySignal2D class for EBSD patterns.
Methods inherited from HyperSpy can be found in the HyperSpy user guide.
See docstring of
EBSD
for attributes and methods. compute(*args, **kwargs)[source]#
Attempt to store the full signal in memory.
 Parameters:
close_file (bool, default False) – If True, attemp to close the file associated with the dask array data if any. Note that closing the file will make all other associated lazy signals inoperative.
show_progressbar (None or bool) – If
True
, display a progress bar. IfNone
, the default from the preferences settings is used.
 Return type:
None
 get_decomposition_model_write(components=None, dtype_learn=<class 'numpy.float32'>, mbytes_chunk=100, dir_out=None, fname_out=None)[source]#
Write the model signal generated from the selected number of principal components directly to an .hspy file.
The model signal intensities are rescaled to the original signals’ data type range, keeping relative intensities.
 Parameters:
components (
Union
[None
,int
,List
[int
]]) – If None (default), rebuilds the signal from all components. If int, rebuilds signal from components in range 0given int. If list of ints, rebuilds signal from only components in given list.dtype_learn (
dtype
) – Data type to set learning results to (default isnumpy.float32
) before multiplication.mbytes_chunk (
int
) – Size of learning results chunks in MB, default is 100 MB as suggested in the Dask documentation.dir_out (
Optional
[str
]) – Directory to place output signal in.
Notes
Multiplying the learning results’ factors and loadings in memory to create the model signal cannot sometimes be done due to too large matrices. Here, instead, learning results are written to file, read into dask arrays and multiplied using
dask.array.matmul()
, out of core.
EBSDMasterPattern#
All methods listed here are also available to
LazyEBSDMasterPattern
instances.
See Signal2D
for methods inherited from HyperSpy.

Return a dictionary of EBSD patterns projected onto a detector from a master pattern in the square Lambert projection [CDeGraef13], for a set of crystal rotations relative to the EDAX TSL sample reference frame (RD, TD, ND) and a fixed detectorsample geometry. 

Normalize image intensities in inplace to a mean of zero with a given standard deviation. 

Plot the master pattern sphere. 

Rescale image intensities inplace. 
 class kikuchipy.signals.EBSDMasterPattern(*args, **kwargs)[source]#
Bases:
CommonImage
,Signal2D
Simulated Electron Backscatter Diffraction (EBSD) master pattern.
This class extends HyperSpy’s Signal2D class for EBSD master patterns. Methods inherited from HyperSpy can be found in the HyperSpy user guide. See the docstring of
hyperspy.signal.BaseSignal
for a list of additional attributes. hemisphere#
Which hemisphere the data contains:
"upper"
(previously"north"
),"lower"
(previously"south"
) or"both"
. Type:
 phase#
Phase describing the crystal structure used in the master pattern simulation.
 Type:
 as_lambert()[source]#
Return a new master pattern in the Lambert projection.
Only implemented for nonlazy signals.
 Returns:
Master pattern in the Lambert projection with the same data shape but in 32bit floating point data dtype.
 Return type:
Examples
>>> import kikuchipy as kp >>> mp_sp = kp.data.nickel_ebsd_master_pattern_small() >>> mp_sp.projection 'stereographic' >>> mp_lp = mp_sp.as_lambert() >>> mp_lp.projection 'lambert'
 deepcopy()[source]#
Return a “deep copy” of this Signal using the standard library’s
deepcopy()
function. Note: this means the underlying data structure will be duplicated in memory.See also
 get_patterns(rotations, detector, energy, dtype_out=<class 'numpy.float32'>, compute=False, **kwargs)[source]#
Return a dictionary of EBSD patterns projected onto a detector from a master pattern in the square Lambert projection [CDeGraef13], for a set of crystal rotations relative to the EDAX TSL sample reference frame (RD, TD, ND) and a fixed detectorsample geometry.
 Parameters:
rotations (
Rotation
) – Crystal rotations to get patterns from. The shape of this instance, a maximum of two dimensions, determines the navigation shape of the output signal.detector (
EBSDDetector
) – EBSD detector describing the detector dimensions and the detectorsample geometry with a single, fixed projection/pattern center.energy (
Union
[int
,float
]) – Acceleration voltage, in kV, used to simulate the desired master pattern to create a dictionary from. If only a single energy is present in the signal, this will be returned no matter its energy.dtype_out (
Union
[type
,dtype
]) – Data type of the returned patterns, by default np.float32.compute (
bool
) – Whether to return a lazy result, by default False. For more information seecompute()
.kwargs – Keyword arguments passed to
get_chunking()
to control the number of chunks the dictionary creation and the output data array is split into. Only chunk_shape, chunk_bytes and dtype_out (to dtype) are passed on.
 Returns:
Signal with navigation and signal shape equal to the rotation instance and detector shape, respectively.
 Return type:
Notes
If the master pattern phase has a noncentrosymmetric point group, both the upper and lower hemispheres must be provided. For more details regarding the reference frame visit the reference frame user guide.
 normalize_intensity(num_std=1, divide_by_square_root=False, dtype_out=None)[source]#
Normalize image intensities in inplace to a mean of zero with a given standard deviation.
 Parameters:
num_std (
int
) – Number of standard deviations of the output intensities. Default is 1.divide_by_square_root (
bool
) – Whether to divide output intensities by the square root of the signal dimension size. Default is False.dtype_out (
Optional
[dtype
]) – Data type of normalized images. If None (default), the input images’ data type is used.
Notes
Data type should always be changed to floating point, e.g.
np.float32
withchange_dtype()
, before normalizing the intensities.Examples
>>> import numpy as np >>> import kikuchipy as kp >>> s = kp.data.nickel_ebsd_small() >>> np.mean(s.data) 146.0670987654321 >>> s.normalize_intensity(dtype_out=np.float32) >>> np.mean(s.data) 2.6373216e08
Notes
Rescaling RGB images is not possible. Use RGB channel normalization when creating the image instead.
 plot_spherical(energy=None, return_figure=False, style='surface', plotter_kwargs=None, show_kwargs=None)[source]#
Plot the master pattern sphere.
This requires the master pattern to be in the stereographic projection and both hemispheres to be present.
 Parameters:
energy (
Union
[None
,int
,float
]) – Acceleration voltage in kV used to simulate the master pattern to plot. If not passed, the highest energy is used.return_figure (
bool
) – Whether to return thepyvista.Plotter
instance for further modification and then plotting. Default isFalse
. IfTrue
, the figure is not plotted.style (
str
) – Visualization style of the mesh, either"surface"
(default),"wireframe"
or"points"
. In general,"surface"
is recommended when zoomed out, while"points"
is recommended when zoomed in. Seepyvista.Plotter.add_mesh()
for details.plotter_kwargs (
Optional
[dict
]) – Dictionary of keyword arguments passed topyvista.Plotter
.show_kwargs (
Optional
[dict
]) – Dictionary of keyword arguments passed topyvista.Plotter.show()
ifreturn_figure
isFalse
.
 Returns:
pl – Only returned if
return_figure
isTrue
. Return type:
Notes
Requires
pyvista
.Examples
>>> import kikuchipy as kp >>> mp = kp.data.nickel_ebsd_master_pattern_small(projection="stereographic") >>> mp.plot_spherical()
 rescale_intensity(relative=False, in_range=None, out_range=None, dtype_out=None, percentiles=None)[source]#
Rescale image intensities inplace.
Output min./max. intensity is determined from out_range or the data type range of the
numpy.dtype
passed to dtype_out if out_range is None.This method is based on
skimage.exposure.rescale_intensity()
. Parameters:
relative (
bool
) – Whether to keep relative intensities between images (default is False). If True, in_range must be None, because in_range is in this case set to the global min./max. intensity.in_range (
Union
[None
,Tuple
[int
,int
],Tuple
[float
,float
]]) – Min./max. intensity of input images. If None (default), in_range is set to pattern min./max intensity. Contrast stretching is performed when in_range is set to a narrower intensity range than the input patterns. Must be None if relative is True or percentiles are passed.out_range (
Union
[None
,Tuple
[int
,int
],Tuple
[float
,float
]]) – Min./max. intensity of output images. If None (default), out_range is set to dtype_out min./max according to skimage.util.dtype.dtype_range.dtype_out (
Union
[None
,dtype
,Tuple
[int
,int
],Tuple
[float
,float
]]) – Data type of rescaled images, default is input images’ data type.percentiles (
Union
[None
,Tuple
[int
,int
],Tuple
[float
,float
]]) – Disregard intensities outside these percentiles. Calculated per image. Must be None if in_range or relative is passed. Default is None.
Examples
>>> import numpy as np >>> import kikuchipy as kp >>> s = kp.data.nickel_ebsd_small()
Image intensities are stretched to fill the available grey levels in the input images’ data type range or any
numpy.dtype
range passed to dtype_out, either keeping relative intensities between images or not:>>> print( ... s.data.dtype, s.data.min(), s.data.max(), ... s.inav[0, 0].data.min(), s.inav[0, 0].data.max() ... ) uint8 23 246 26 245 >>> s2 = s.deepcopy() >>> s.rescale_intensity(dtype_out=np.uint16) >>> print( ... s.data.dtype, s.data.min(), s.data.max(), ... s.inav[0, 0].data.min(), s.inav[0, 0].data.max() ... ) uint16 0 65535 0 65535 >>> s2.rescale_intensity(relative=True) >>> print( ... s2.data.dtype, s2.data.min(), s2.data.max(), ... s2.inav[0, 0].data.min(), s2.inav[0, 0].data.max() ... ) uint8 0 255 3 253
Contrast stretching can be performed by passing percentiles:
>>> s.rescale_intensity(percentiles=(1, 99))
Here, the darkest and brightest pixels within the 1% percentile are set to the ends of the data type range, e.g. 0 and 255 respectively for images of
uint8
data type.Notes
Rescaling RGB images is not possible. Use RGB channel normalization when creating the image instead.
There are no methods exclusive to LazyEBSDMasterPattern instances.
 class kikuchipy.signals.LazyEBSDMasterPattern(*args, **kwargs)[source]#
Bases:
EBSDMasterPattern
,LazySignal2D
Lazy implementation of the
EBSDMasterPattern
class.This class extends HyperSpy’s LazySignal2D class for EBSD master patterns. Methods inherited from HyperSpy can be found in the HyperSpy user guide. See docstring of
EBSDMasterPattern
for attributes and methods.
VirtualBSEImage#
See Signal2D
for methods inherited from HyperSpy.

Normalize image intensities in inplace to a mean of zero with a given standard deviation. 

Rescale image intensities inplace. 
 class kikuchipy.signals.VirtualBSEImage(*args, **kwargs)[source]#
Virtual backscatter electron (BSE) image(s).
This class extends HyperSpy’s Signal2D class for virtual BSE images.
Methods inherited from HyperSpy can be found in the HyperSpy user guide.
See the docstring of
hyperspy.signal.BaseSignal
for a list of attributes. normalize_intensity(num_std=1, divide_by_square_root=False, dtype_out=None)[source]#
Normalize image intensities in inplace to a mean of zero with a given standard deviation.
 Parameters:
num_std (
int
) – Number of standard deviations of the output intensities. Default is 1.divide_by_square_root (
bool
) – Whether to divide output intensities by the square root of the signal dimension size. Default is False.dtype_out (
Optional
[dtype
]) – Data type of normalized images. If None (default), the input images’ data type is used.
Notes
Data type should always be changed to floating point, e.g.
np.float32
withchange_dtype()
, before normalizing the intensities.Examples
>>> import numpy as np >>> import kikuchipy as kp >>> s = kp.data.nickel_ebsd_small() >>> np.mean(s.data) 146.0670987654321 >>> s.normalize_intensity(dtype_out=np.float32) >>> np.mean(s.data) 2.6373216e08
Notes
Rescaling RGB images is not possible. Use RGB channel normalization when creating the image instead.
 rescale_intensity(relative=False, in_range=None, out_range=None, dtype_out=None, percentiles=None)[source]#
Rescale image intensities inplace.
Output min./max. intensity is determined from out_range or the data type range of the
numpy.dtype
passed to dtype_out if out_range is None.This method is based on
skimage.exposure.rescale_intensity()
. Parameters:
relative (
bool
) – Whether to keep relative intensities between images (default is False). If True, in_range must be None, because in_range is in this case set to the global min./max. intensity.in_range (
Union
[None
,Tuple
[int
,int
],Tuple
[float
,float
]]) – Min./max. intensity of input images. If None (default), in_range is set to pattern min./max intensity. Contrast stretching is performed when in_range is set to a narrower intensity range than the input patterns. Must be None if relative is True or percentiles are passed.out_range (
Union
[None
,Tuple
[int
,int
],Tuple
[float
,float
]]) – Min./max. intensity of output images. If None (default), out_range is set to dtype_out min./max according to skimage.util.dtype.dtype_range.dtype_out (
Union
[None
,dtype
,Tuple
[int
,int
],Tuple
[float
,float
]]) – Data type of rescaled images, default is input images’ data type.percentiles (
Union
[None
,Tuple
[int
,int
],Tuple
[float
,float
]]) – Disregard intensities outside these percentiles. Calculated per image. Must be None if in_range or relative is passed. Default is None.
Examples
>>> import numpy as np >>> import kikuchipy as kp >>> s = kp.data.nickel_ebsd_small()
Image intensities are stretched to fill the available grey levels in the input images’ data type range or any
numpy.dtype
range passed to dtype_out, either keeping relative intensities between images or not:>>> print( ... s.data.dtype, s.data.min(), s.data.max(), ... s.inav[0, 0].data.min(), s.inav[0, 0].data.max() ... ) uint8 23 246 26 245 >>> s2 = s.deepcopy() >>> s.rescale_intensity(dtype_out=np.uint16) >>> print( ... s.data.dtype, s.data.min(), s.data.max(), ... s.inav[0, 0].data.min(), s.inav[0, 0].data.max() ... ) uint16 0 65535 0 65535 >>> s2.rescale_intensity(relative=True) >>> print( ... s2.data.dtype, s2.data.min(), s2.data.max(), ... s2.inav[0, 0].data.min(), s2.inav[0, 0].data.max() ... ) uint8 0 255 3 253
Contrast stretching can be performed by passing percentiles:
>>> s.rescale_intensity(percentiles=(1, 99))
Here, the darkest and brightest pixels within the 1% percentile are set to the ends of the data type range, e.g. 0 and 255 respectively for images of
uint8
data type.Notes
Rescaling RGB images is not possible. Use RGB channel normalization when creating the image instead.
util#
Return a dictionary in HyperSpy's DictionaryTreeBrowser format with the default kikuchipy EBSD metadata. 


Get a chunk tuple based on the shape of the signal data. 

Return dask array of patterns with appropriate chunking. 

Return SEM and/or EBSD metadata nodes. 
Signal utilities for handling signal metadata and attributes, output
from signal methods, and for controlling chunking of lazy signal data in
Array
.
 kikuchipy.signals.util.ebsd_metadata()[source]#
Return a dictionary in HyperSpy’s DictionaryTreeBrowser format with the default kikuchipy EBSD metadata.
See
set_experimental_parameters()
for an explanation of the parameters. Returns:
md
 Return type:
Notes
Deprecated since version 0.5.
 kikuchipy.signals.util.get_chunking(signal=None, data_shape=None, nav_dim=None, sig_dim=None, chunk_shape=None, chunk_bytes=30000000.0, dtype=None)[source]#
Get a chunk tuple based on the shape of the signal data.
The signal dimensions will not be chunked, and the navigation dimensions will be chunked based on either chunk_shape, or be optimized based on the chunk_bytes.
This function is inspired by a similar function in pyxem.
 Parameters:
signal (kikuchipy.signals.EBSD, kikuchipy.signals.LazyEBSD or None) – If None (default), the following must be passed: data shape to be chunked data_shape, the number of navigation dimensions nav_dim, the number of signal dimensions sig_dim and the data array data type dtype.
data_shape (
Optional
[tuple
]) – Data shape, must be passed if signal is None.nav_dim (
Optional
[int
]) – Number of navigation dimensions, must be passed if signal is None.sig_dim (
Optional
[int
]) – Number of signal dimensions, must be passed if signal is None.chunk_shape (
Optional
[int
]) – Shape of navigation chunks. If None (default), this size is set automatically based on chunk_bytes. This is a square if signal has two navigation dimensions.chunk_bytes (
Union
[int
,float
,str
,None
]) – Number of bytes in each chunk. Default is 30e6, i.e. 30 MB. Only used if freedom is given to choose, i.e. if chunk_shape is None. Various parameter types are allowed, e.g. 30000000, “30 MB”, “30MiB”, or the default 30e6, all resulting in approximately 30 MB chunks.dtype (
Union
[None
,dtype
,type
]) – Data type of the array to chunk. Will take precedent over the signal data type if signal is passed. Must be passed if signal is None.
 Return type:
chunks
 kikuchipy.signals.util.get_dask_array(signal, dtype=None, **kwargs)[source]#
Return dask array of patterns with appropriate chunking.
 Parameters:
signal (
EBSD
orLazyEBSD
) – Signal with data to return dask array from.dtype (
Optional
[type
]) – Data type of returned dask array. This is also passed on toget_chunking()
.kwargs – Keyword arguments passed to
get_chunking()
to control the number of chunks the output data array is split into. Onlychunk_shape
,chunk_bytes
anddtype
are passed on.
 Returns:
Dask array with signal data with appropriate chunking and data type.
 Return type:
dask_array
simulations#
Simulations returned by a generator and handling of Kikuchi bands and zone axes.

Setup and calculation of geometrical or kinematical Kikuchi pattern simulations. 
Collection of coordinates of Kikuchi lines and zone axes on an EBSD detector for simple plotting or creation of HyperSpy markers to plot onto 

Kikuchi bands and zone axes used in geometrical EBSD simulations. 


Geometrical EBSD simulation with Kikuchi bands and zone axes. 
KikuchiPatternSimulator#

Calculate a kinematical master pattern in the stereographic projection. 

Project Kikuchi lines and zone axes onto a detector, one per crystal orientation. 

Plot reflectors as lines or bands in the stereographic or spherical projection. 
 class kikuchipy.simulations.KikuchiPatternSimulator(reflectors)[source]#
Setup and calculation of geometrical or kinematical Kikuchi pattern simulations.
 Parameters:
reflectors (ReciprocalLatticeVector) – Reflectors to use in the simulation, flattened to one navigation dimension.
 calculate_master_pattern(half_size=500, hemisphere='upper', scaling='linear')[source]#
Calculate a kinematical master pattern in the stereographic projection.
Requires that the
reflectors
have structure factors (theta
) calculated. Parameters:
half_size (
Optional
[int
]) – Number of pixels along the xdirection of the square master pattern. Default is500
. The full size will be2 * half_size + 1
, given a master pattern of shape (1001, 1001) for the default value.hemisphere (
Optional
[str
]) – Which hemisphere(s) to calculate. Options are"upper"
(default),"lower"
or"both"
.scaling (
Optional
[str
]) – Intensity scaling of the band kinematical intensities, either"linear"
(default), \(F\),"square"
, \(F^2\), or"None"
, giving all bands an intensity of1
.
 Returns:
master_pattern – Kinematical master pattern in the stereographic projection.
 Return type:
Notes
The algorithm for selecting which unit vector is within a Kikuchi band is derived from a similar routine in EMsoft.
 on_detector(detector, rotations)[source]#
Project Kikuchi lines and zone axes onto a detector, one per crystal orientation.
 Parameters:
detector (
EBSDDetector
) – EBSD detector describing the detector’s view of the sample. Ifnavigation_shape
is anything else than(1,)
, it must be equal to the shape of the inputrotations
.rotations (
Rotation
) – Crystal orientations assumed to be expressed with respect to the default EDAX TSL sample reference frame RDTDND in the Bunge convention. Rotation shape can be 1D or 2D.
 Returns:
simulations
 Return type:
Notes
This function is not optimized for large datasets, so use with care.
 plot(projection='stereographic', mode='lines', hemisphere='upper', scaling='linear', figure=None, return_figure=False, backend='matplotlib', show_plotter=True)[source]#
Plot reflectors as lines or bands in the stereographic or spherical projection.
 Parameters:
projection (
Optional
[str
]) – Either"stereographic"
(default) or"spherical"
.mode (
Optional
[str
]) – Either"lines"
(default) or"bands"
. The latter option requires thatreflectors
have Bragg angles (theta
) calculated.hemisphere (
Optional
[str
]) – Which hemisphere to plot whenprojection="stereographic"
. Options are"upper"
(default),"lower"
or"both"
. Ignored iffigure
is given.scaling (
Optional
[str
]) – Intensity scaling of the band kinematical intensities, either"linear"
(default), \(F\),"square"
, \(F^2\), or"None"
, giving all bands the same intensity.figure (matplotlib.figure.Figure or pyvista.Plotter, optional) – An existing
Figure
orPlotter
to add the reflectors to. If not given, a new figure is created.return_figure (
bool
) – Whether to return the figure. Default isFalse
. This is aFigure
ifbackend=="matplotlib"
or aPlotter
ifbackend=="pyvista"
.backend (
str
) – Which plotting library to use whenprojection="spherical"
, either"matplotlib"
(default) or"pyvista"
. The latter option requires that PyVista is installed.show_plotter (
bool
) – Whether to show thePlotter
whenprojection="spherical"
andbackend="pyvista"
. Default isTrue
.
 Returns:
figure – If
return_figure=True
, aFigure
or aPlotter
is returned. Return type:
 property reflectors: ReciprocalLatticeVector#
Reflectors to use in the simulation.
 Return type:
GeometricalKikuchiPatternSimulation#

Get a single simulation as a list of Matplotlib objects. 

Return a list of simulation markers. 

Get Kikuchi line coordinates of a single simulation. 

Plot a single simulation on the detector. 

Get zone axis coordinates of a single simulation. 
 class kikuchipy.simulations.GeometricalKikuchiPatternSimulation(detector, rotations, reflectors, lines, zone_axes)[source]#
Collection of coordinates of Kikuchi lines and zone axes on an EBSD detector for simple plotting or creation of HyperSpy markers to plot onto
kikuchipy.signals.EBSD
signals.Instances of this class are returned from
kikuchipy.simulations.KikuchiPattern.Simulator.on_detector()
, and not ment to be created directly. Parameters:
detector (
EBSDDetector
) – EBSD detector.rotations (
Rotation
) – Crystal orientations for which coordinates of Kikuchi lines and zone axes have been generated.reflectors (
ReciprocalLatticeVector
) – Reciprocal lattice vectors used in the simulation.lines (
KikuchiPatternLine
) – Collection of coordinates of Kikuchi lines on the detector.zone_axes (
KikuchiPatternZoneAxis
) – Collection of coordinates of zone axes on the detector.
 as_collections(index=None, coordinates='detector', lines=True, zone_axes=False, zone_axes_labels=False, lines_kwargs=None, zone_axes_kwargs=None, zone_axes_labels_kwargs=None)[source]#
Get a single simulation as a list of Matplotlib objects.
 Parameters:
index (
Union
[int
,tuple
,None
]) – Index of the simulation to get collections from. If not given, this is the first simulation.coordinates (
str
) – The coordinates of the plot axes, either"detector"
(default) or"gnomonic"
.lines (
bool
) – Whether to get the collection of Kikuchi lines. Default isTrue
. These are returned asmatplotlib.collections.LineCollection
.zone_axes (
bool
) – Whether to get the collection of zone axes. Default isFalse
. These are returned asmatplotlib.collections.PathCollection
.zone_axes_labels (
bool
) – Whether to get the collection of zone axes labels. Default isFalse
. These are returned as a class:list ofmatplotlib.text.Text
.lines_kwargs (
Optional
[dict
]) – Keyword arguments passed tomatplotlib.collections.LineCollection
to format Kikuchi lines iflines=True
.zone_axes_kwargs (
Optional
[dict
]) – Keyword arguments passed tomatplotlib.collections.PathCollection
to format zone axes ifzone_axes=True
.zone_axes_labels_kwargs (
Optional
[dict
]) – Keyword arguments passed tomatplotlib.text.Text
to format zone axes labels ifzone_axes_labels=True
.
 Returns:
collections – List of Matplotlib collections.
 Return type:
See also
 as_markers(lines=True, zone_axes=False, zone_axes_labels=False, pc=False, lines_kwargs=None, zone_axes_kwargs=None, zone_axes_labels_kwargs=None, pc_kwargs=None)[source]#
Return a list of simulation markers.
 Parameters:
lines (
bool
) – Whether to return Kikuchi line markers. Default isTrue
.zone_axes (
bool
) – Whether to return zone axes markers. Default isFalse
.zone_axes_labels (
bool
) – Whether to return zone axes label markers. Default isFalse
.pc (
bool
) – Whether to return projection center (PC) markers. Default isFalse
.lines_kwargs (
Optional
[dict
]) – Keyword arguments passed toaxvline()
to format the lines.zone_axes_kwargs (
Optional
[dict
]) – Keyword arguments passed toscatter()
to format the markers.zone_axes_labels_kwargs (
Optional
[dict
]) – Keyword arguments passed toText()
to format the labels.pc_kwargs (
Optional
[dict
]) – Keyword arguments passed toscatter()
to format the markers.
 Returns:
markers – List with all markers.
 Return type:
See also
 property detector: EBSDDetector#
EBSD detector onto which simulations were generated.
 Return type:
 lines_coordinates(index=None, coordinates='detector', exclude_nan=True)[source]#
Get Kikuchi line coordinates of a single simulation.
 Parameters:
index (
Union
[int
,tuple
,None
]) – Index of the simulation to get line coordinates for. If not given, this is the first simulation.coordinates (
str
) – The type of coordinates, either"detector"
(default) or"gnomonic"
.exclude_nan (
bool
) – Whether to exclude coordinates of Kikuchi lines not present in the pattern. Default isTrue
. By passingFalse
, all simulations (by varyingindex
) returns an array of the same shape.
 Returns:
coords – Kikuchi line coordinates.
 Return type:
See also
 plot(index=None, coordinates='detector', pattern=None, lines=True, zone_axes=True, zone_axes_labels=True, pc=True, pattern_kwargs=None, lines_kwargs=None, zone_axes_kwargs=None, zone_axes_labels_kwargs=None, pc_kwargs=None, return_figure=False)[source]#
Plot a single simulation on the detector.
 Parameters:
index (
Union
[int
,tuple
,None
]) – Index of the simulation to plot. If not given, this is the first simulation. Ifnavigation_shape
is 2D, andindex
is passed, it must be a 2tuple.coordinates (
str
) – The coordinates of the plot axes, either"detector"
(default) or"gnomonic"
.pattern (
Optional
[ndarray
]) – A pattern to plot the simulation onto. If not given, the simulation is plotted on a gray background.lines (
bool
) – Whether to show Kikuchi lines. Default isTrue
.zone_axes (
bool
) – Whether to show zone axes. Default isTrue
.zone_axes_labels (
bool
) – Whether to show zone axes labels. Default isTrue
.pc (
bool
) – Whether to show the projection/pattern centre (PC). Default isTrue
.pattern_kwargs (
Optional
[dict
]) – Keyword arguments passed tomatplotlib.axes.Axes.imshow()
ifpattern
is given.lines_kwargs (
Optional
[dict
]) – Keyword arguments passed tomatplotlib.collections.LineCollection
to format Kikuchi lines iflines=True
.zone_axes_kwargs (
Optional
[dict
]) – Keyword arguments passed tomatplotlib.collections.PathCollection
to format zone axes ifzone_axes=True
.zone_axes_labels_kwargs (
Optional
[dict
]) – Keyword arguments passed tomatplotlib.text.Text
to format zone axes labels ifzone_axes_labels=True
.pc_kwargs (
Optional
[dict
]) – Keyword arguments passed tomatplotlib.axes.Axes.scatter()
to format the PC ifpc=True
.return_figure (
bool
) – Whether to return the figure. Default isFalse
.
 Returns:
fig – Returned if
return_figure=True
. Return type:
See also
 property reflectors: ReciprocalLatticeVector#
Reciprocal lattice vectors used in the simulations.
 Return type:
 property rotations: Rotation#
Crystal orientations for which simulations were generated.
 Return type:
 zone_axes_coordinates(index=None, coordinates='detector', exclude_nan=