.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/processing/azimuthal_integration.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_examples_processing_azimuthal_integration.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_examples_processing_azimuthal_integration.py:


Azimuthal Integration (in Pyxem!)
=================================

pyxem now includes built in azimuthal integration functionality. This is useful for
extracting radial profiles from diffraction patterns in 1 or 2 dimensions.  The new method
will split the pixels into radial bins and then sum the intensity in each bin resulting in
a `Diffraction1D` or `Polar2D` signal.  In each case the total intensity of the diffraction
pattern is preserved.

.. GENERATED FROM PYTHON SOURCE LINES 11-26

.. code-block:: Python


    import pyxem as pxm
    import hyperspy.api as hs
    import numpy as np

    s = pxm.data.tilt_boundary_data()
    s.calibration(
        center=None
    )  # set the center to None to use center of the diffraction patterns
    s.calibration.units = "/AA^{-1}"
    s.calibration.scale = 0.03  # To angstroms
    s1d = s.get_azimuthal_integral1d(npt=100, inplace=False)

    s1d.sum().plot()




.. image-sg:: /examples/processing/images/sphx_glr_azimuthal_integration_001.png
   :alt:  Signal
   :srcset: /examples/processing/images/sphx_glr_azimuthal_integration_001.png
   :class: sphx-glr-single-img


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.. GENERATED FROM PYTHON SOURCE LINES 27-33

Aside: Actual Implementation
Here we have plotted the polygon bins which we use to integrate.  For each
bin, the pixel indicies contained are saved to an array along side the fraction
of each pixel within the bin.  Then for each diffraction pattern the fraction of
each pixel within the bin is mutiplied, then summed to "integrate" the intensity
for each radial bin.

.. GENERATED FROM PYTHON SOURCE LINES 33-44

.. code-block:: Python


    from pyxem.utils._azimuthal_integrations import _get_control_points

    cp = _get_control_points(
        10, npt_azim=72, radial_range=(0.2, 4), azimuthal_range=(-np.pi, np.pi), affine=None
    )[:, :, ::-1]
    poly = hs.plot.markers.Polygons(verts=cp, edgecolor="w", facecolor="none")
    s.plot()
    s.add_marker(poly)





.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /examples/processing/images/sphx_glr_azimuthal_integration_002.png
         :alt: azimuthal integration
         :srcset: /examples/processing/images/sphx_glr_azimuthal_integration_002.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/processing/images/sphx_glr_azimuthal_integration_003.png
         :alt:  Signal
         :srcset: /examples/processing/images/sphx_glr_azimuthal_integration_003.png
         :class: sphx-glr-multi-img





.. GENERATED FROM PYTHON SOURCE LINES 45-46

Similarly, the `get_azimuthal_integral2d` method will return a `Polar2D` signal.

.. GENERATED FROM PYTHON SOURCE LINES 46-50

.. code-block:: Python


    s_polar = s.get_azimuthal_integral2d(npt=100, npt_azim=360, inplace=False)
    s_polar.sum().plot()




.. image-sg:: /examples/processing/images/sphx_glr_azimuthal_integration_004.png
   :alt:  Signal
   :srcset: /examples/processing/images/sphx_glr_azimuthal_integration_004.png
   :class: sphx-glr-single-img


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.. GENERATED FROM PYTHON SOURCE LINES 51-65

There are also other things you can account for with azimuthal integration, such as the
effects of the Ewald sphere.  This can be done by calibrating with a known detector distance,
and beam energy. In most cases the Flat Ewald sphere assumption is good enough but occasionally,
you might want some additional Accuracy.

Here we just show the effect of just calibrating with the first peak vs. calibrating
with the known beam energy and detector distance. For things like accurate template matching good
calibration can be important when matching to high diffraction vectors. The calibration example gives
more information on how to get the correct values for your microscope/setup.

If you are doing x-ray diffraction please raise an issue on the pyxem github to let us know! The same
assumptions should apply for each case, but it would be good to test!

We only show the 1D case here, but the same applies for the 2D case as well!

.. GENERATED FROM PYTHON SOURCE LINES 65-89

.. code-block:: Python


    s.calibration.detector(
        pixel_size=0.000092,
        detector_distance=0.125,
        beam_energy=200,
        center=None,
        units="k_A^-1",
    )  # set the center= None to use the center of the diffraction patterns
    s1d_200 = s.get_azimuthal_integral1d(npt=100, inplace=False)
    s.calibration.detector(
        pixel_size=0.000092,
        detector_distance=0.075,
        beam_energy=80,
        center=None,
        units="k_A^-1",
    )  # These are just made up pixel sizes and detector distances for illustration

    s1d_80 = s.get_azimuthal_integral1d(npt=100, inplace=False)

    hs.plot.plot_spectra(
        [s1d.sum(), s1d_200.sum(), s1d_80.sum()],
        legend=["Flat Ewald Sphere Assumption", "200keV Corrected", "80keV Corrected"],
    )




.. image-sg:: /examples/processing/images/sphx_glr_azimuthal_integration_005.png
   :alt: azimuthal integration
   :srcset: /examples/processing/images/sphx_glr_azimuthal_integration_005.png
   :class: sphx-glr-single-img


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    <Axes: xlabel='Radius (k_A^-1)', ylabel='Intensity'>



.. GENERATED FROM PYTHON SOURCE LINES 90-95

At times you may want to use a mask to exclude certain pixels from the azimuthal integration or apply an affine
transformation to the diffraction patterns before azimuthal integration.  This can be done using the `mask` and
`affine` parameters of the `Calibration` object.

Here we just show a random affine transformation for illustration.

.. GENERATED FROM PYTHON SOURCE LINES 95-104

.. code-block:: Python



    mask = s.get_direct_beam_mask(radius=20)  # Mask the direct beam
    affine = np.array(
        [[0.9, 0.1, 0], [0.1, 0.9, 0], [0, 0, 1]]
    )  # Just a random affine transformation for illustration
    s.calibration(mask=mask, affine=affine)
    s.get_azimuthal_integral2d(npt=100, npt_azim=360, inplace=False).sum().plot()




.. image-sg:: /examples/processing/images/sphx_glr_azimuthal_integration_006.png
   :alt:  Signal
   :srcset: /examples/processing/images/sphx_glr_azimuthal_integration_006.png
   :class: sphx-glr-single-img


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.. GENERATED FROM PYTHON SOURCE LINES 105-107

The `azimuth_range`-argument lets you choose what angular range to calculate the azimuthal integral for.
The range can be increasing, decreasing, and does not need to be a multiple of pi.

.. GENERATED FROM PYTHON SOURCE LINES 107-123

.. code-block:: Python


    pol1 = s.get_azimuthal_integral2d(npt=100, azimuth_range=(-np.pi, np.pi))

    pol2 = s.get_azimuthal_integral2d(npt=100, azimuth_range=(0, 1))

    pol3 = s.get_azimuthal_integral2d(npt=100, npt_azim=720, azimuth_range=(0, 4 * np.pi))

    pol4 = s.get_azimuthal_integral2d(npt=100, azimuth_range=(np.pi, 0))

    hs.plot.plot_images(
        [pol1.sum(), pol2.sum(), pol3.sum(), pol4.sum()],
        label=["(-pi, pi) default", "(0, 1)", "(0, 4pi)", "(pi, 0)"],
        cmap="viridis",
        tight_layout=True,
        colorbar=None,
    )



.. image-sg:: /examples/processing/images/sphx_glr_azimuthal_integration_007.png
   :alt: (-pi, pi) default, (0, 1), (0, 4pi), (pi, 0)
   :srcset: /examples/processing/images/sphx_glr_azimuthal_integration_007.png
   :class: sphx-glr-single-img


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    [<Axes: title={'center': '(-pi, pi) default'}, xlabel='Radians axis (Rad)', ylabel='Radius axis (k_A^-1)'>, <Axes: title={'center': '(0, 1)'}, xlabel='Radians axis (Rad)', ylabel='Radius axis (k_A^-1)'>, <Axes: title={'center': '(0, 4pi)'}, xlabel='Radians axis (Rad)', ylabel='Radius axis (k_A^-1)'>, <Axes: title={'center': '(pi, 0)'}, xlabel='Radians axis (Rad)', ylabel='Radius axis (k_A^-1)'>]




.. rst-class:: sphx-glr-timing

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.. _sphx_glr_download_examples_processing_azimuthal_integration.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: azimuthal_integration.ipynb <azimuthal_integration.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: azimuthal_integration.py <azimuthal_integration.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: azimuthal_integration.zip <azimuthal_integration.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_