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

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

.. _sphx_glr_auto_examples_correlation_plot_estimate_noise.py:


==============================================
Estimating the noise of the correlation curves
==============================================

Introduction
============

There are many approaches to estimate the noise in correlation functions
(see: :cite:`Wohland2001`, :cite:`Qian1990`, :cite:`Starchev2001`). An
analytical calculation of the noise is difficult because it involves diverging
integrals for the correlations decaying functions :cite:`Wohland2001`. For TTTR
data an analytical solution of the noise in the correlation is however not
necessary, as the data contained in the photon stream can be split to yield a set
of correlation functions that is used to yield an estimate for the expected
correlation function and the associated noise by the mean and the standard
deviation :cite:`Kapusta2007`, :cite:`Enderlein1997`, :cite:`Bohmer2002`.

Here it is illustrated how the data is split into multiple subsets to estimate the
noise for quantitative analysis of correlation curves.

.. GENERATED FROM PYTHON SOURCE LINES 25-30

Implementation
--------------
First, we import libraries read the data into a new TTTR container.
We inspect the header information to find header tags that inform
on the macro time calibration.

.. GENERATED FROM PYTHON SOURCE LINES 30-37

.. code-block:: Python


    import pylab as plt
    import tttrlib
    import numpy as np

    data = tttrlib.TTTR('../../tttr-data/pq/ptu/pq_ptu_hh_t2.ptu')








.. GENERATED FROM PYTHON SOURCE LINES 38-40

Here, we manually compute the calibration. This may not be
necessary in many cases.

.. GENERATED FROM PYTHON SOURCE LINES 40-42

.. code-block:: Python

    time_calibration = data.header.tag('MeasDesc_GlobalResolution')['value']








.. GENERATED FROM PYTHON SOURCE LINES 43-44

Next, we split the TTTR data into n_chunks subsets of equal size.

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.. code-block:: Python

    n_chunks = 4
    n_ph = int(len(data) / n_chunks)








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Before correlating the data, we define the number of bins and the number
of coarsening steps for the multi-tau correlation algorithm and create
a new correlator instance.

.. GENERATED FROM PYTHON SOURCE LINES 51-73

.. code-block:: Python

    print("Used routing channels:", data.used_routing_channels)
    ch1 = [0]
    ch2 = [2]
    corr_settings = {
        "n_bins": 5,
        "n_casc": 30
    }
    correlator = tttrlib.Correlator(**corr_settings)

    # use start-stop to create new TTTR objects that are correlated
    correlations = list()
    for i in range(0, len(data), n_ph):
        tttr_slice = data[i: i + n_ph]
        tttr_ch1 = tttr_slice[tttr_slice.get_selection_by_channel(ch1)]
        tttr_ch2 = tttr_slice[tttr_slice.get_selection_by_channel(ch2)]
        correlator.set_tttr(
            tttr_1=tttr_ch1,
            tttr_2=tttr_ch2
        )
        correlations.append(correlator.correlation)
    correlations = np.array(correlations)





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

 .. code-block:: none

    Used routing channels: [0 2]




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Finally,
Plot the all correlations
plot the unsliced correlation

.. GENERATED FROM PYTHON SOURCE LINES 77-102

.. code-block:: Python

    correlator = tttrlib.Correlator(
        tttr=data,
        channels=(ch1, ch2),
        **corr_settings
    )

    means = correlations.mean(axis=0)
    stds = correlations.std(axis=0)
    x_axis = correlator.x_axis
    fig, ax = plt.subplots(nrows=1, ncols=2, sharey=True, sharex=True)
    ax[0].semilogx(x_axis, correlator.correlation, label="All photons", color="green")
    ax[0].semilogx(x_axis, means, label="Mean", color="blue")
    ax[0].fill_between(x_axis, means-stds, means+stds, alpha=.5)
    ax[0].set_title('Correlation all data')
    ax[1].set_title('Correlation of slices')
    for y in correlations:
        ax[1].semilogx(x_axis, y)
    ax[0].set_ylim([0.9, 3.5])
    ax[0].set_xlabel(r'corr. time (s) ')
    ax[1].set_xlabel(r'corr. time (s) ')
    ax[0].set_ylabel(r'corr. amplitude')
    ax[0].legend()
    plt.show()





.. image-sg:: /auto_examples/correlation/images/sphx_glr_plot_estimate_noise_001.png
   :alt: Correlation all data, Correlation of slices
   :srcset: /auto_examples/correlation/images/sphx_glr_plot_estimate_noise_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 103-105

The standard deviation computed over multiple correlation curves can be
used as an estimate for the noise.


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

   **Total running time of the script:** (0 minutes 6.095 seconds)


.. _sphx_glr_download_auto_examples_correlation_plot_estimate_noise.py:

.. only:: html

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

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

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

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

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


.. only:: html

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

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