.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/reference_frames/estimate_tilt_about_detector_xaxis.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_tilt_about_detector_xaxis.py>`
        to download the full example code

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

.. _sphx_glr_examples_reference_frames_estimate_tilt_about_detector_xaxis.py:


Estimate tilt about the detector x axis
=======================================

This example shows how to (robustly) estimate the tilt about the detector :math:`X_d`
axis which brings the sample plane normal into coincidence with the detector plane
normal (but in the opposite direction) :cite:`winkelmann2020refined`.

The estimate is found using :meth:`~kikuchipy.detectors.EBSDDetector.estimate_xtilt`
which performs linear regression of :attr:`~kikuchipy.detectors.EBSDDetector.pcz` vs.
:attr:`~kikuchipy.detectors.EBSDDetector.pcy`.

To test the estimation, 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 18-69



.. image-sg:: /examples/reference_frames/images/sphx_glr_estimate_tilt_about_detector_xaxis_001.png
   :alt: estimate tilt about detector xaxis
   :srcset: /examples/reference_frames/images/sphx_glr_estimate_tilt_about_detector_xaxis_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    True/estimated tilt about detector x [deg]: 20.00/21.22
    7/10 of added outliers detected






|

.. code-block:: default


    import kikuchipy as kp
    import numpy as np


    # 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)
    det = det0.extrapolate_pc(
        pc_indices=[0, 0],
        navigation_shape=nav_shape,
        step_sizes=(50, 50),
    )

    # Add +/- 0.001 as random noise to PCy and PCz
    rng = np.random.default_rng()
    det.pcy += rng.uniform(-0.001, 0.001, det.navigation_size).reshape(nav_shape)
    det.pcz += rng.uniform(-0.001, 0.001, det.navigation_size).reshape(nav_shape)

    # Add outliers by adding more noise to PCz
    outlier_idx1d = rng.choice(det.navigation_size, 10, replace=False)
    is_outlier = np.zeros(det.navigation_size, dtype=bool)
    is_outlier[outlier_idx1d] = True
    noise_outlier = rng.uniform(-0.01, 0.01, outlier_idx1d.size)
    outlier_idx2d = np.unravel_index(outlier_idx1d, shape=det.navigation_shape)
    det.pcz[outlier_idx2d] += noise_outlier

    # Robust estimation by detecting outliers
    xtilt, outlier_detected_2d = det.estimate_xtilt(
        detect_outliers=True, degrees=True, return_outliers=True
    )

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

    outlier_idx2d_detected = np.where(outlier_detected_2d)
    outlier_idx1d_detected = np.ravel_multi_index(
        outlier_idx2d_detected, det.navigation_shape
    )
    correct_outliers = np.isin(outlier_idx1d, outlier_idx1d_detected)
    print(f"{correct_outliers.sum()}/{outlier_idx1d.size} of added outliers detected")


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

   **Total running time of the script:** (0 minutes 0.703 seconds)

**Estimated memory usage:**  10 MB


.. _sphx_glr_download_examples_reference_frames_estimate_tilt_about_detector_xaxis.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_tilt_about_detector_xaxis.py <estimate_tilt_about_detector_xaxis.py>`

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

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


.. only:: html

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

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