IntegratePeaksProfileFitting-v1.rst



Description
This algorithm performs integration of single crystal Bragg peaks by fitting
the intensity distribution as a 3D distribution made of an Ikeda-Carpenter
function (TOF coordinate) and a bivariate Normal distribution.

Similar algorithms
See :ref:`algm-IntegratePeaksMD` or :ref:`algm-IntegrateEllipsoids` for peak-minus-background
integration algorithms in reciprocal space.

Inputs
The algorithms takes two input workspaces:

A MDEventWorkspace containing the events in multi-dimensional space.
This would be the output of
:ref:`algm-ConvertToMD`.
As well as a PeaksWorkspace containing single-crystal peak locations.
This could be the output of :ref:`algm-FindPeaksMD` or :ref:`algm-PredictPeaks`
The OutputPeaksWorkspace will contain a copy of the input PeaksWorkspace,
with the integrated intensities and errors changed.
The OutputParamsWorkspace is a TableWorkspace containing the fit parameters.
Peaks which could not be fit are omitted.


Instrument-Defined Parameters
In addition to the input parameters defined above, there are several other parameters
to be aware of which are pre-defined for each instrument.  The instrument is determined
from the instrument that is loaded into PeaksWorkspace. If the instrument parameters file
does not contain paramters, the algorithm defaults to MaNDi parameters. Default
values are below:


Parameter
Description
MaNDi
TOPAZ
CORELLI


DQPixel
The side length for each
voxel used for fitting.
Units: 1/Angstrom
0.003
0.01
0.007


FracHKL
The distance between peaks
(in fraction of hkl) that
is used for fitting.
0.4
0.4
0.4


MinDtBinWidth
The smallest time bin used
for fitting the TOF profile
Units: microseconds
15
2
2


MaxDtBinWidth
The largest time bin used
for fitting the TOF profile
Units: microseconds
50
15
60


NTheta
The number of bins along
the scattering direction
used for BVG fitting.
50
50
50


NPhi
The number of bins along
the azimuthal direction
used for BVG fitting.
50
50
50


Calculations
This algorithm will fit a set of peaks in a PeaksWorkspace.  The intensity profile
is fit to an MDHisto workspace formed around the peak location.

Constructing the Measured Intensity Distribution
To construct the measured distribution to be fit, a histogram of events is made around the peak.
This histogram is in (q_x,  q_y, q_z) and composed of voxels of side
length dQPixel.  To minimize the effect of neighboring peaks on profile fitting, the variable
qMask is used to only consider a region around the peak in (h,k,l) space.  It will filter voxels
outside of (h ± fracHKL, k ± fracHKL, l ± fracHKL) from calculations used for profile
fitting. In practice, values of 0.35 < fracHKL < 0.5 seem to work best.

Fitting the Time-of-Flight Coordinate
The time-of-flight (TOF), t, of each voxel is determined as:
t = k \times \frac{(L_1 + L_2)\sin(\theta)}{|\vec{q}|}

The events are histogrammed by their t values to create a TOF profile.  This profile can then be fit
to the Ikeda Carpenter function.  To separate the peak and background, different levels of intensity are
filtered out.  The predicted background level is determined as the average background not near the peak or off the edge
and values within minppl_frac and maxppl_frac times the predicted value are tried.  The best fit to the expected
moderator emission (determined by the moderator coefficients defined in ModeratorCoefficientsFile) is
taken and these voxels are considered to be signal.

Fitting the Non-TOF Coordinate
TOF goes as 1/|\vec{q}| and so it is natural to use spherical coordinate.  In that sense, the other two coordinates
are  (q_{\theta} ,  q_{\phi_az}) - along the scattering angle and azimuthal angle, respectively.  From the
MDHisto Workspace (filtered by qMask and using only the signal voxels from the TOF fight), a 2D histogram is constructed
which is fit to a bivariate normal distribution.  The histogram has nTheta \times nPhi bins.
For weak peaks or peaks near detector edges, the 2D histogram likely does not reflect the full profile.  To address this, the
profile of the nearest strong peaks is forced when doing the BVG fit.  The profile is fit (allowed to vary 10% in
\sigma_x, \sigma_y, \rho ) and location and amplitude are not fixed.  Weak peaks are defined as peaks with fewer
than forceCutoff counts from peak-minus-background integration or within dEdge pixels of the detector edge.

Integrating the Model
The final intensity profile is given by
Y(\vec{q}) = A \times Y_{TOF}(\vec{q}) \times Y_{BVG}(\vec{q}) + B

where A and B are scaling constants.  Here the background is assumed to be constant B over the volume of
the peak, so the model of the peak itself is Y_{model}(\vec{q}) = A \times Y_{TOF}(\vec{q}) \times Y_{BVG}(\vec{q}).
The peak intensity I, is given by summing Y_{model}(\vec{q}) over voxels which are greater than FracStop of the maximum.
\sigma(I) is given  as
\sigma(I) = \sqrt{\Sigma N_{obs} + \Sigma N_{BG} + \frac{\Sigma N_{obs}(N_{obs}-N_{model})^2}{\Sigma N_{obs}}}

where the first two terms come from Poissionian statistics and the final term is the variance of the fit. Those
sums are over the same voxels used to calculate intensity.

Usage
Example - IntegratePeaksProfileFitting