.. algorithm::

.. summary::

.. relatedalgorithms::

.. properties::

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

Instrument resolution
---------------------

Resolution of a detector in d-spacing is defined as
:math:`\frac{\Delta d}{d}`, which is constant for an individual
detector.
If the input workspace has summed detectors, the resolution of the individual pixels with be added in quadrature.

Starting from the Bragg equation for T.O.F. diffractometer,

.. math:: d = \frac{t}{252.777\cdot L\cdot2\sin\theta}

as

.. math:: \Delta d = \sqrt{\left(\Delta T \frac{\partial d}{\partial T}\right)^2 + \left(\Delta L \frac{\partial d}{\partial L}\right)^2 + \left(\Delta \theta \frac{\partial d}{\partial \theta}\right)^2}

and thus

.. math:: \frac{\Delta d}{d} = \sqrt{\left(\frac{\Delta T}{T}\right)^2 + \left(\frac{\Delta L}{L}\right)^2 + \left(\Delta\theta\cdot\cot(\theta)\right)^2}

where,

-  :math:`\Delta T` is the time resolution, or pulse width, generally from moderator dimensions.
   If supplied through ``DeltaTOF`` parameter, the center wavelength is used to calculate the center time-of-flight.
   Alternatively, one can specify ``DeltaTOFOverTOF``.
-  :math:`\Delta\theta` is the uncertainty in angle due to the source size and coverage of the detector.
   The former is supplied through the ``SourceDeltaTheta`` parameter.
   The latter can be approximated from the square root of the solid angle of the detector to sample or is taken from the ``DivergenceWorkspace``
-  :math:`\Delta L` is the uncertainty in the flight path due to the source position and detector position.
   The former can be supplied through the ``SourceDeltaL`` parameter.
   The latter is calculated from the detector pixel dimensions.
-  :math:`L` is the total flight path of the neutron from source-to-sample (L1) and sample to detector (L2)
-  :math:`\theta` is half the Bragg angle :math:`2 \theta`, or half of the angle from the downstream beam

The optional ``DivergenceWorkspace`` specifies the values of
:math:`\Delta\theta` to use rather than those derived from the solid
angle of the detectors. :ref:`EstimateDivergence
<algm-EstimateDivergence>` can be used for estimating the divergence.

``PartialResolutionWorkspaces`` is a collection of partial resolution
functions where ``_tof`` is the time-of-flight term, ``_length`` is
the path length term, and ``_angle`` is the angular term. Note that
the total resolution is these terms added in quadriture.

Note that :math:`\frac{\Delta d}{d} = \frac{\Delta Q}{Q}`. When fitting peaks in time-of-flight the resolution is :math:`\frac{\Delta T}{T} = \frac{\Delta d}{d}`.

Factor Sheet
------------

NOMAD
#####

Detector size

-  vertical: 1 meter / 128 pixel
-  Horizontal: half inch or 1 inch

POWGEN
######

Detector size: 0.005 x 0.0543

Range of :math:`\Delta\theta\cot\theta`: :math:`(0.00170783, 0.0167497)`


Usage
-----

**Example - estimate PG3 partial detectors' resolution:**

.. testcode:: ExHistSimple

  # Load a Nexus file
  Load(Filename="PG3_2538_2k.nxs", OutputWorkspace="PG3_2538")
  # Run the algorithm to estimate detector's resolution
  EstimateResolutionDiffraction(InputWorkspace="PG3_2538", DeltaTOF=40.0, OutputWorkspace="PG3_Resolution",
                                PartialResolutionWorkspaces="PG3_Resolution_partials")
  resws = mtd["PG3_Resolution"]

  print("Size of workspace 'PG3_Resolution' =  {}".format(resws.getNumberHistograms()))
  print("Estimated resolution of detector of spectrum 0 =  {:.6f}".format(resws.readY(0)[0]))
  print("Estimated resolution of detector of spectrum 100 =  {:.6f}".format(resws.readY(100)[0]))
  print("Estimated resolution of detector of spectrum 999 =  {:.6f}".format(resws.readY(999)[0]))

.. testcleanup:: ExHistSimple

   DeleteWorkspace(resws)

Output:

.. testoutput:: ExHistSimple

  Size of workspace 'PG3_Resolution' =  1000
  Estimated resolution of detector of spectrum 0 =  0.003239
  Estimated resolution of detector of spectrum 100 =  0.003236
  Estimated resolution of detector of spectrum 999 =  0.003548

.. seealso :: Algorithms :ref:`algm-EstimateDivergence`.

.. categories::

.. sourcelink::