.. algorithm::

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Description
-----------

This algorithm corrects for detector dead time. The multiplicative correction is defined as:

.. math:: C = \frac{1}{1-\tau \cdot R}

where :math:`\tau` is the dead time coefficient in :math:`[sec]` and :math:`R` is the total count rate in :math:`[sec^{-1}]`.

The correction can be calculated for groups of pixels specified. Check the **GroupingPattern** in :ref:`GroupDetectors <algm-GroupDetectors>`.

If no grouping is specified, correction will be calculated on pixel by pixel bases.

First the counts are integrated over all the time-of-flight channels, if there are more than one and the X-axis unit id is not `Empty`.
Otherwise, the correction is calculated and applied for each frame individually.

Then for each group the counts of the pixels are summed.

This results in a total count rate for the group, which is then put in the formula to calculate the correction.

Then counts in each pixel are scaled up by the correction corresponding to the group that the pixels are in.

Note that the input workspace must be normalised by acquisition time before passing to the algorithm.

If saturation is achieved, i.e. :math:`R \geq \frac{1}{\tau}`, the correction is set to infinity.

Usage
-----

**Example - DeadTimeCorrection**

.. testcode:: DeadTimeCorrectionExample

  CreateSampleWorkspace(OutputWorkspace='in', Function="Powder Diffraction")
  DeadTimeCorrection(InputWorkspace='in', OutputWorkspace='out', Tau=0.0001, GroupingPattern='0-99,100-199')
  Divide(LHSWorkspace='out', RHSWorkspace='in', OutputWorkspace='corr')
  print("Correction is {0:.3f}".format(mtd['corr'].readY(0)[0]))

Output:

.. testoutput:: DeadTimeCorrectionExample

  Correction is 1.376

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