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

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

.. _sphx_glr_auto_examples_validation_angular_convergence.py:


Convergence of solid-angle quadrature
=====================================

Hold the random volumes, Born order, and voxel grid fixed while increasing
polar Gauss-Legendre nodes and uniform azimuth samples. Plot angles are
independent of the integration nodes: adding points to an angular plot does
not refine the integral. The finest calculation is a numerical reference,
not an exact solution, and both quadrature axes need checking independently.

.. GENERATED FROM PYTHON SOURCE LINES 11-56

.. code-block:: Python


    from bornsim.medium.random_medium import GaussianMedium

    import sys

    import matplotlib.pyplot as plt
    import numpy as np

    from bornsim import EnsembleSampling, AngularSampling, Grid, Solver, Source
    from bornsim.units import ureg

    medium = GaussianMedium(
        refractive_index_std=0.001,
        correlation_length=600 * ureg.nanometer,
        background_refractive_index=1.33,
    )

    source_configuration_1 = Source(wavelength=400 * ureg.nanometer)

    solver = Solver(
        source=source_configuration_1,
        order=1,
    )

    grid = Grid(
        shape=(6, 6, 6),
        spacing=300 * ureg.nanometer,
    )

    ensemble_sampling = EnsembleSampling(
        realizations=2,
        seed=42,
    )

    options = dict(
        grid=grid,
        ensemble_sampling=ensemble_sampling,
    )

    reference_sampling = AngularSampling(
        angles=[0] * ureg.radian,
        polar_samples=96,
        azimuth_samples=32,
    )








.. GENERATED FROM PYTHON SOURCE LINES 57-61

Refine one angular axis at a time
---------------------------------
Identical consecutive seeds give the same volumes in every calculation.
Voxel and finite-sample errors remain fixed throughout this comparison.

.. GENERATED FROM PYTHON SOURCE LINES 61-124

.. code-block:: Python

    reference = solver.ensemble(
        medium=medium,
        **options,
        sampling=reference_sampling,
    )

    reference_mu = reference.mu_s.to("1 / meter").magnitude[0]

    samples = np.array([16, 32, 64, 96])

    polar_error = []

    for count in samples:
        sampling = AngularSampling(
            angles=[0] * ureg.radian,
            polar_samples=int(count),
            azimuth_samples=32,
        )

        result = solver.ensemble(
            medium=medium,
            **options,
            sampling=sampling,
        )

        polar_error.append(abs(result.mu_s.to("1 / meter").magnitude[0] / reference_mu - 1))

    azimuths = np.array([4, 8, 16, 32])

    azimuth_error = []

    for count in azimuths:
        sampling = AngularSampling(
            angles=[0] * ureg.radian,
            polar_samples=96,
            azimuth_samples=int(count),
        )

        result = solver.ensemble(
            medium=medium,
            **options,
            sampling=sampling,
        )

        azimuth_error.append(abs(result.mu_s.to("1 / meter").magnitude[0] / reference_mu - 1))

    figure, axes = plt.subplots(1, 2, figsize=(10, 4), layout="constrained")

    for axis, counts, errors, label in (
        (axes[0], samples, polar_error, "Polar Gauss nodes; azimuth fixed at 32"),
        (axes[1], azimuths, azimuth_error, "Azimuth samples; polar fixed at 96"),
    ):
        # A floor permits plotting exact equality with the reference on a log axis.
        axis.semilogy(counts, np.maximum(errors, np.finfo(float).eps), "o-")

        axis.set(xlabel=label, ylabel="Relative error in finite-sample μs")

        axis.grid(alpha=0.25)

    figure.suptitle("Angular quadrature convergence (floor at machine precision)")

    plt.show()




.. image-sg:: /auto_examples/validation/images/sphx_glr_angular_convergence_001.png
   :alt: Angular quadrature convergence (floor at machine precision)
   :srcset: /auto_examples/validation/images/sphx_glr_angular_convergence_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 125-131

Inspect one ensemble realization in 3D
--------------------------------------
This is the first realization (seed 42) on the calculation grid,
not an ensemble average or an infinite-medium material boundary.
Drag to rotate and scroll to zoom in the embedded browser view.
Regions with higher refractive index are more opaque; opacity is not absorption.

.. GENERATED FROM PYTHON SOURCE LINES 131-144

.. code-block:: Python

    preview_volume = medium.to_volume(
        grid=grid,
        seed=42,
    )

    medium_figure = preview_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/angular_convergence-1.html" title="Refractive index n: volume" width="100%" height="560" loading="lazy" style="border:0;"></iframe>






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

   **Total running time of the script:** (0 minutes 0.959 seconds)


.. _sphx_glr_download_auto_examples_validation_angular_convergence.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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