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.. "auto_examples/correlation/plot_normal_correlation.py"
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.. only:: html

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

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

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

.. _sphx_glr_auto_examples_correlation_plot_normal_correlation.py:


============================
Normal multi-tau correlation
============================

An alternative approach is to calculate the FCS curve by software
on the basis of the directly recorded asynchronous photon count data.
The straightforward approach would be to generate a continuous file of
fluorescence intensity values in consecutive time bins of fixed bin
width, and to use this file for a conventional autocorrelation calculation.
But then again, one encounters the same unreasonably large amount of data
as when directly recording fluorescence intensity values in a synchronous
data acquisition mode.


When applying the algorithm only at the increasingly spaced lag
times as given by Eq. (2), it will completely miss, e.g., the strong
autocorrelation of any periodic signal with a repetition time not
included within the vector of used lag times. To avoid that, one usually
applies an averaging procedure by coarsening the time resolution of the photon
detection times tj when coming to the calculation of the autocorrelation
function at increasingly larger lag time. This is equivalent to the multiple-tau
and multiple-sampling time correlation method employed in hardware
correlators [12].

:cite:`Wahl2003`.

.. GENERATED FROM PYTHON SOURCE LINES 30-121



.. image-sg:: /auto_examples/correlation/images/sphx_glr_plot_normal_correlation_001.png
   :alt: plot normal correlation
   :srcset: /auto_examples/correlation/images/sphx_glr_plot_normal_correlation_001.png
   :class: sphx-glr-single-img





.. code-block:: Python

    import matplotlib.pylab as plt
    import tttrlib
    import numpy as np


    fig, ax = plt.subplots(sharex='col', sharey='row')

    #  Read the data data
    data = tttrlib.TTTR('../../tttr-data/bh/bh_spc132.spc', 'SPC-130')

    # Correlator settings, if the same settings are used repeatedly it is useful to define them once
    settings = {
        "n_bins": 7,  # n_bins and n_casc defines the settings of the multi-tau
        "n_casc": 27,  # correlation algorithm
        "make_fine": False  # Do not use the microtime information
    }

    # Create correlator
    # Caution: x-axis in units of macro time counter
    # tttrlib.Correlator is unaware of the calibration in the TTTR object
    correlator = tttrlib.Correlator(**settings)

    # Select the green channels (channel number 0 and 8)
    ch1_indices = data.get_selection_by_channel([0])
    ch2_indices = data.get_selection_by_channel([8])

    # Select macro times for Ch1 and Ch2 and create array of weights
    # Note: the weights are set to 1, i.e. no weighting is used
    t = data.macro_times
    t1 = t[ch1_indices]
    w1 = np.ones_like(t1, dtype=np.float64)
    t2 = t[ch2_indices]
    w2 = np.ones_like(t2, dtype=np.float64)
    correlator.set_events(t1, w1, t2, w2)

    # scale the x-axis to have units in milliseconds (common unit in FCS)
    x = correlator.x * data.header.macro_time_resolution
    y = correlator.y

    plt.semilogx(x, y, label="Gp/Gs")

    # green-red cross correlation (red channels 1 and 9)
    # TODO: verify "if the correlator is generated using the architecture below,
    # the macro time units are known and no rescaling of the y-axis needs to be performed"
    correlator = tttrlib.Correlator(
        tttr=(
            tttrlib.TTTR(data, data.get_selection_by_channel([0, 8])),
            tttrlib.TTTR(data, data.get_selection_by_channel([1, 9]))
        ),
        **settings
    )

    # no need to scale axis - correlator aware of macro time units
    plt.semilogx(
        correlator.x,
        correlator.y,
        label="Gp,Gs/Rp,Rs"
    )

    # red channel correlation
    correlator = tttrlib.Correlator(
        channels=([9], [1]),
        tttr=data,
        **settings
    )

    plt.semilogx(
        correlator.x,
        correlator.y,
        label="pR,sR"
    )

    # Reverse cross-correlation: red-green
    correlator = tttrlib.Correlator(
        channels=([9, 1], [0, 8]),
        tttr=data,
        **settings
    )

    plt.semilogx(
        correlator.x,
        correlator.y,
        label="pRsR,pGsG"
    )

    # Show results
    plt.xlabel('corr. time / sec')
    plt.ylabel('Correlation Amplitude')
    plt.legend()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.298 seconds)


.. _sphx_glr_download_auto_examples_correlation_plot_normal_correlation.py:

.. only:: html

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

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

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

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

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


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