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.. "auto_examples/fluorescence_decay/plot_fit24.py"
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.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_auto_examples_fluorescence_decay_plot_fit24.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_fluorescence_decay_plot_fit24.py:


====================
Bi-exponential model
====================

fit24
-----

Fit24 optimizes is a bi-exponential model function with two fluorescence lifetimes
:math:` au_1`, :math:`  au_2`, and amplitude of the second lifetime :math:`a_2`,
the fraction scattered light :math:`\gamma`, and a constant offset to experimental
data. Fit24 does not describe anisotropy. The decays passed to the fit in the
:term:`Jordi` format. The two decays in the Jordi array are both treated by the
same model function and convoluted with the corresponding
:term:`instrument response function<IRF>`. The model function is

.. :math:

    M_i =(1-a_2) \exp(i\Delta t/        au_1) + a_2 \exp(i\Delta t/     au_2)

where :math:`\Delta t` is the time per micro time channel, :math:`i` is the micro time
channel number, :math:`a_2` is the fraction of the second species. The model function
is corrected for the fraction of background and a constant offset.

.. :math:

    g_i =(1 - \gamma) rac{M_i}{\sum_i M_i} + \gamma rac{B_i}{\sum_i B_i} + c

Where,  :math:`c` is a constant offset, :math:`B` the background pattern, :math:`M`
the model function and :math:`\gamma` the fraction of scattered light.


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

   **Total running time of the script:** (0 minutes 0.000 seconds)


.. _sphx_glr_download_auto_examples_fluorescence_decay_plot_fit24.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_fit24.ipynb <plot_fit24.ipynb>`

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

      :download:`Download Python source code: plot_fit24.py <plot_fit24.py>`


.. only:: html

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

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