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

.. only:: html

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

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

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

.. _sphx_glr_auto_examples_validation_grid_refinement.py:


Grid refinement against an exact cube integral
==============================================

Refine a fixed physical cube rather than drawing a new random field on each
grid. Its first-order amplitude has an independent closed-form reference,
so this example isolates voxel midpoint-quadrature error. It does not test
higher-order Green-tensor discretization or random-field synthesis.

.. GENERATED FROM PYTHON SOURCE LINES 10-87

.. code-block:: Python


    import sys

    import matplotlib.pyplot as plt
    import numpy as np

    from bornsim import Grid, Solver, Source, Volume
    from bornsim.units import ureg
    from bornsim import Directions

    source = Source(wavelength=633 * ureg.nanometer)

    solver = Solver(
        source=source,
        order=1,
    )

    side = 180 * ureg.nanometer

    background = 1.33

    delta_refractive_index = 0.01

    direction = np.array([[1.0, 0.0, 0.0]])

    k0 = 2 * np.pi / source.wavelength.to("meter").magnitude

    length = side.to("meter").magnitude

    q = background * k0 * (np.array([0.0, 0.0, 1.0]) - direction[0])

    integral = length**3 * np.prod(np.sinc(q * length / (2 * np.pi)))

    # Linearized dielectric contrast; y polarization is transverse to +x.
    reference = k0**2 * (2 * background * delta_refractive_index) * integral / (4 * np.pi)

    cells = np.array([2, 4, 8, 16])

    relative_errors = []

    observation_directions = Directions(vectors=direction)

    for count in cells:
        grid = Grid(
            shape=(count,) * 3,
            spacing=side / count,
        )

        volume = Volume(
            delta_refractive_index=np.full((count,) * 3, delta_refractive_index),
            grid=grid,
            background_refractive_index=background,
        )

        result = solver.solve_cut(
            target=volume,
            directions=observation_directions,
        )

        amplitude = result.amplitudes.to("meter").magnitude[0, 0, 1, 1]

        relative_errors.append(abs(amplitude - reference) / abs(reference))

    figure, axis = plt.subplots(layout="constrained")

    axis.loglog(cells, relative_errors, "o-", label="First-order amplitude error")

    axis.loglog(cells, relative_errors[0] * (cells[0] / cells) ** 2, "--", label="Second-order reference slope")

    axis.set(xlabel="Cells per axis (fixed 180 nm cube)", ylabel="Relative amplitude error", title="Voxel refinement")

    axis.grid(alpha=0.25, which="both")

    axis.legend()

    plt.show()




.. image-sg:: /auto_examples/validation/images/sphx_glr_grid_refinement_001.png
   :alt: Voxel refinement
   :srcset: /auto_examples/validation/images/sphx_glr_grid_refinement_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 88-95

Inspect the medium in 3D
------------------------
Inspect the actual finite input sample with physical spatial axes.
Drag to rotate and scroll to zoom in the embedded browser view.
Regions with higher refractive index are more opaque; opacity is not absorption.
This is the finest grid. The refractive index is constant throughout the sample;
orthogonal slices show the uniform cube and its physical extent.

.. GENERATED FROM PYTHON SOURCE LINES 95-103

.. code-block:: Python

    medium_figure = volume.plot_3d(
        mode="volume",
        field="refractive_index",
        opacity_scale="increasing",
    )

    if "--no-browser" not in sys.argv:
        medium_figure.show(renderer="browser")



.. raw:: html

   <iframe src="../../_static/gallery/grid_refinement-1.html" title="Refractive index n: volume (uniform field)" width="100%" height="560" loading="lazy" style="border:0;"></iframe>






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

   **Total running time of the script:** (0 minutes 0.287 seconds)


.. _sphx_glr_download_auto_examples_validation_grid_refinement.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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