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

.. only:: html

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

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

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

.. _sphx_glr_examples_reference_frames_estimate_tilts_about_detector_xaxis_zaxis.py:


Estimate tilts about the detector x and z axis
==============================================

This example shows how to (robustly) estimate the tilts about the detector :math:`X_d`
and :math:`Z_d` axes, which bring the sample plane normal into coincidence with the
detector plane normal (but in the opposite direction) :cite:`winkelmann2020refined`.

Estimates are found using
:meth:`~kikuchipy.detectors.EBSDDetector.estimate_xtilt_ztilt`, which fits a hyperplane
to :attr:`~kikuchipy.detectors.EBSDDetector.pc` using singular value decomposition.

To test the estimations, we add some noise to realistic projection center (PC) values
(PCx, PCy, PCz). The realistic PCs are extrapolated from a PC in the upper left corner
of a map, assuming a nominal sample tilt of 70 degrees, a detector tilt of 0 degrees, a
detector pixel size of 70 microns and a sample step size of 50 microns.

.. GENERATED FROM PYTHON SOURCE LINES 18-73



.. image-sg:: /examples/reference_frames/images/sphx_glr_estimate_tilts_about_detector_xaxis_zaxis_001.png
   :alt: estimate tilts about detector xaxis zaxis
   :srcset: /examples/reference_frames/images/sphx_glr_estimate_tilts_about_detector_xaxis_zaxis_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    True/estimated tilt about detector x [deg]: 20.00/19.21
    True/estimated tilt about detector z [deg]: 0/-1.98






|

.. code-block:: default


    import kikuchipy as kp
    import matplotlib.pyplot as plt
    import numpy as np


    plt.rcParams["font.size"] = 18

    # Create an initial detector with one PC assumed to be for the upper
    # left corner of a map
    det0 = kp.detectors.EBSDDetector(
        shape=(480, 480),
        pc=(0.5, 0.3, 0.5),
        sample_tilt=70,
        tilt=0,
        px_size=70,
    )

    # Extrapolate a map of PCs
    nav_shape = (15, 20)
    nav_size = np.prod(nav_shape)
    det = det0.extrapolate_pc(
        pc_indices=[0, 0],
        navigation_shape=nav_shape,
        step_sizes=(50, 50),
    )

    # Add +/- 0.0025 as random noise
    dev_noise = 0.001
    rng = np.random.default_rng()
    det.pcx += rng.uniform(-dev_noise, dev_noise, nav_size).reshape(nav_shape)
    det.pcy += rng.uniform(-dev_noise, dev_noise, nav_size).reshape(nav_shape)
    det.pcz += rng.uniform(-dev_noise, dev_noise, nav_size).reshape(nav_shape)

    # Add outliers by adding more noise
    dev_outlier = 0.01
    n_outliers = 20
    outlier_idx1d = rng.choice(nav_size, n_outliers, replace=False)
    is_outlier = np.zeros(nav_size, dtype=bool)
    is_outlier[outlier_idx1d] = True
    outlier_idx2d = np.unravel_index(outlier_idx1d, shape=det.navigation_shape)
    det.pcx[outlier_idx2d] += rng.uniform(-dev_outlier, dev_outlier, n_outliers)
    det.pcy[outlier_idx2d] += rng.uniform(-dev_outlier, dev_outlier, n_outliers)
    det.pcz[outlier_idx2d] += rng.uniform(-dev_outlier, dev_outlier, n_outliers)

    # Plot PC values
    det.plot_pc("scatter")

    # Robust estimation by detecting outliers
    xtilt, ztilt = det.estimate_xtilt_ztilt(degrees=True)

    # Print true tilt and estimated tilt
    true_xtilt = 90 - det.sample_tilt + det.tilt
    print(f"True/estimated tilt about detector x [deg]: {true_xtilt:.2f}/{xtilt:.2f}")
    print(f"True/estimated tilt about detector z [deg]: {0}/{ztilt:.2f}")


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

   **Total running time of the script:** (0 minutes 0.589 seconds)

**Estimated memory usage:**  9 MB


.. _sphx_glr_download_examples_reference_frames_estimate_tilts_about_detector_xaxis_zaxis.py:

.. only:: html

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




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

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

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

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


.. only:: html

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

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