.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/spectro/beer_lambert/plot_01_beer_lambert.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_api_gallery_spectro_beer_lambert_plot_01_beer_lambert.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_spectro_beer_lambert_plot_01_beer_lambert.py:


Beer-Lambert absorbance, and its deviation from linearity at high concentration
==================================================================================

Absorbance is exactly linear in concentration by the ideal Beer-Lambert
law. A small amount of instrumental stray light (light that reaches the
detector without having passed through the fully absorbing sample path)
causes the apparent absorbance to fall increasingly below the true value
as concentration -- and hence true absorbance -- increases, the classic
"rolling over" deviation seen in real UV-Vis instruments.

.. GENERATED FROM PYTHON SOURCE LINES 14-30

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.spectro.systems.beer_lambert import absorbance, apparent_absorbance_with_stray_light
    from chemistrykit.spectro.visualizers.spectro_plots import plot_beer_lambert_deviation

    epsilon = 8000.0  # L mol^-1 cm^-1
    path_length = 1.0  # cm
    concentrations = np.linspace(1e-6, 5e-4, 200)

    true_absorbance = absorbance(epsilon, concentrations, path_length)
    apparent = np.array([apparent_absorbance_with_stray_light(epsilon, c, path_length, stray_light_fraction=0.002) for c in concentrations])

    print(f"At the lowest concentration, true A = {true_absorbance[0]:.4f}, apparent A = {apparent[0]:.4f}")
    print(f"At the highest concentration, true A = {true_absorbance[-1]:.4f}, apparent A = {apparent[-1]:.4f}")





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

 .. code-block:: none

    At the lowest concentration, true A = 0.0080, apparent A = 0.0071
    At the highest concentration, true A = 4.0000, apparent A = 2.6778




.. GENERATED FROM PYTHON SOURCE LINES 31-35

The deviation (true minus apparent) grows sharply once the true
absorbance gets large enough that the fixed stray-light fraction is no
longer negligible next to the (exponentially shrinking) transmitted
intensity:

.. GENERATED FROM PYTHON SOURCE LINES 35-40

.. code-block:: Python


    deviation = true_absorbance - apparent
    print(f"Deviation at A~0.1: {deviation[np.argmin(np.abs(true_absorbance - 0.1))]:.5f}")
    print(f"Deviation at A~3.5: {deviation[np.argmin(np.abs(true_absorbance - 3.5))]:.5f}")





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

 .. code-block:: none

    Deviation at A~0.1: 0.00111
    Deviation at A~3.5: 0.86348




.. GENERATED FROM PYTHON SOURCE LINES 41-43

.. code-block:: Python

    ax = plot_beer_lambert_deviation(molar_absorptivity=epsilon, path_length=path_length, concentrations=concentrations, stray_light_fraction=0.002)
    plt.show()



.. image-sg:: /api/gallery/spectro/beer_lambert/images/sphx_glr_plot_01_beer_lambert_001.png
   :alt: Beer-Lambert law: deviation from linearity
   :srcset: /api/gallery/spectro/beer_lambert/images/sphx_glr_plot_01_beer_lambert_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.036 seconds)


.. _sphx_glr_download_api_gallery_spectro_beer_lambert_plot_01_beer_lambert.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_01_beer_lambert.ipynb <plot_01_beer_lambert.ipynb>`

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

      :download:`Download Python source code: plot_01_beer_lambert.py <plot_01_beer_lambert.py>`

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

      :download:`Download zipped: plot_01_beer_lambert.zip <plot_01_beer_lambert.zip>`


.. only:: html

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

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