Fix theory descriptions for IDA

Refs #10711

Code/Mantid/MantidQt/CustomInterfaces/inc/MantidQtCustomInterfaces/IndirectDiffractionReduction.ui

@@ -7,7 +7,7 @@
     <x>0</x>
     <y>0</y>
     <width>495</width>
-    <height>433</height>
+    <height>500</height>
    </rect>
   </property>
   <property name="windowTitle">
@@ -130,7 +130,7 @@
       </property>
       <widget class="QWidget" name="pageCalibration">
        <property name="sizePolicy">
-        <sizepolicy hsizetype="Maximum" vsizetype="Maximum">
+        <sizepolicy hsizetype="Preferred" vsizetype="Preferred">
          <horstretch>0</horstretch>
          <verstretch>0</verstretch>
         </sizepolicy>
@@ -150,12 +150,6 @@
            </property>
            <item>
             <widget class="MantidQt::MantidWidgets::MWRunFiles" name="dem_calFile" native="true">
-             <property name="sizePolicy">
-              <sizepolicy hsizetype="Preferred" vsizetype="Maximum">
-               <horstretch>0</horstretch>
-               <verstretch>0</verstretch>
-              </sizepolicy>
-             </property>
              <property name="label" stdset="0">
               <string>Cal File</string>
              </property>
@@ -177,12 +171,6 @@
              <property name="enabled">
               <bool>true</bool>
              </property>
-             <property name="sizePolicy">
-              <sizepolicy hsizetype="Preferred" vsizetype="Maximum">
-               <horstretch>0</horstretch>
-               <verstretch>0</verstretch>
-              </sizepolicy>
-             </property>
              <property name="label" stdset="0">
               <string>Vanadium Runs</string>
              </property>
@@ -198,7 +186,7 @@
       </widget>
       <widget class="QWidget" name="pageDSpaceRebin">
        <property name="sizePolicy">
-        <sizepolicy hsizetype="Maximum" vsizetype="Maximum">
+        <sizepolicy hsizetype="Preferred" vsizetype="Preferred">
          <horstretch>0</horstretch>
          <verstretch>0</verstretch>
         </sizepolicy>

Code/Mantid/docs/source/interfaces/Indirect_Bayes.rst

@@ -79,7 +79,7 @@ Quasi
 .. interface:: Bayes
   :widget: Quasi
 
-The model that is being fitted is that of a δ-function (elastic component)
+The model that is being fitted is that of a :math:`\delta`-function (elastic component)
 of amplitude :math:`A(0)` and Lorentzians of amplitude :math:`A(j)` and HWHM
 :math:`W(j)` where :math:`j=1,2,3`. The whole function is then convolved with
 the resolution function. The -function and Lorentzians are intrinsically
@@ -97,7 +97,7 @@ ResNorm.
 For a Stretched Exponential, the choice of several Lorentzians is replaced with
 a single function with the shape : :math:`\psi\beta(x) \Leftrightarrow
 exp[-2\pi(\sigma k)\beta]`. This, in the energy to time FT transformation, is
-:math:`\psi\beta(E) \Leftrightarrow exp[-(t/\tau)\beta]`. So :math:`/sigma` is
+:math:`\psi\beta(E) \Leftrightarrow exp[-(t/\tau)\beta]`. So :math:`\sigma` is
 identified with :math:`(2\pi)\beta\hbar/\tau` .  The model that is fitted is
 that of an elastic component and the stretched exponential and the program gives
 the best estimate for the :math:`\beta` parameter and the width for each group

Code/Mantid/docs/source/interfaces/Indirect_DataAnalysis.rst

@@ -365,7 +365,78 @@ Fit Linear
 Theory
 ~~~~~~
 
-TODO
+The measured data :math:`I(Q, \omega)` is proportional to the convolution of the
+scattering law :math:`S(Q, \omega)` with the resolution function :math:`R(Q,
+\omega)` of the spectrometer via :math:`I(Q, \omega) = S(Q, \omega) ⊗  R(Q,
+\omega)`. The traditional method of analysis has been to fit the measured
+:math:`I(Q, \omega)` with an appropriate set of functions related to the form of
+:math:`S(Q, \omega)` predicted by theory.
+
+* In quasielastic scattering the simplest form is when both the :math:`S(Q,
+  \omega)` and the :math:`R(Q, \omega)` have the form of a Lorentzian - a
+  situation which is almost correct for reactor based backscattering
+  spectrometers such as IN10 & IN16 at ILL. The convolution of two Lorentzians
+  is itself a Lorentzian so that the spectrum of the measured and resolution
+  data can both just be fitted with Lorentzians. The broadening of the sample
+  spectrum is then just the  difference of the two widths.
+* The next easiest case is when both :math:`S(Q, \omega)` and :math:`R(Q,
+  \omega)` have a simple functional form and the convolution is also a function
+  containing the parameters of the :math:`S(Q, \omega)` and R(Q, ω) functions.
+  The convoluted function may then be fitted to the data to provide the
+  parameters. An example would be the case where the :math:`S(Q, \omega)` is a
+  Lorentzian and the :math:`R(Q, \omega)` is a Gaussian.
+* For diffraction, the shape of the peak in time is a convolution of a Gaussian
+  with a decaying exponential and this function can be used to fit the Bragg
+  peaks.
+* The final case is where :math:`R(Q, \omega)` does not have a simple function
+  form so that the measured data has to be convoluted numerically with the
+  :math:`S(Q, \omega)` function to provide an estimate of the sample scattering.
+  The result is least-squares fitted to the measured data to provide values for
+  the parameters in the :math:`S(Q, \omega)` function.
+
+This latter form of peak fitting is provided by SWIFT. It employs a
+least-squares algorithm which requires the derivatives of the fitting function
+with respect to its parameters in order to be faster and more efficient than
+those algorithms which calculate the derivatives numerically. To do this the
+assumption is made that the derivative of a convolution is equal to the
+convolution of the derivative-as the derivative and the convolution are
+performed over different variables (function parameters and energy transfer
+respectively) this should be correct. A flat background is subtracted from the
+resolution data before the convolution is performed.
+
+Four types of sample function are available for :math:`S(Q, \omega)`:
+
+Quasielastic
+  This is the most common case and applies to both translational (diffusion) and
+  rotational modes, both of which have the form of a Lorentzian. The fitted
+  function is a set of Lorentzians centred at the origin in energy transfer.
+
+Elastic
+  Comprising a central elastic peak together with a set of quasi-elastic
+  Lorentzians also centred at the origin. The elastic peak is taken to be the
+  un-broadened resolution function.
+
+Shift
+  A central Lorentzian with pairs of energy shifted Lorentzians. This was
+  originally used for crystal field splitting data but more recently has been
+  applied to quantum tunnelling peaks. The fitting function assumes that the
+  peaks are symmetric about the origin in energy transfer both in position and
+  width. The widths of the central and side peaks may be different.
+
+Polymer
+  A single quasi-elastic peak with 3 different forms of shape. The theory behind
+  this is described elsewhere [1,2]. Briefly, polymer theory predicts 3 forms
+  of the :math:`I(Q,t)` in the form of :math:`exp(-at2/b)` where :math:`b` can
+  be 2, 3 or 4. The Full Width Half-Maximum (FWHM) then has a Q-dependence
+  (power law) of the form :math:`Qb`. The :math:`I(Q,t)` has been numerically
+  Fourier transformed into :math:`I(Q, \omega)` and the :math:`I(Q, \omega)`
+  have been fitted with functions of the form of a modified Lorentzian. These
+  latter functions are used in the energy fitting procedures.
+
+References:
+
+1. J S Higgins, R E Ghosh, W S Howells & G Allen, JCS Faraday II 73 40 (1977)
+2. J S Higgins, G Allen, R E Ghosh, W S Howells & B Farnoux, Chem Phys Lett 49 197 (1977)
 
 Calculate Corrections
 ---------------------
@@ -421,16 +492,16 @@ Flat
   :widget: absp_pageFlat
 
 Thickness
-  TODO
+  Thickness of sample (cm).
 
 Can Front Thickness
-  TODO
+  Thickness of front container (cm).
 
 Can Back Thickness
-  TODO
+  Thickness of back container (cm).
 
 Sample Angle
-  TODO
+  Sample angle (degrees).
 
 Cylinder
 ########
@@ -439,21 +510,49 @@ Cylinder
   :widget: absp_pageCylinder
 
 Radius 1
-  TODO
+  Sample radius 1 (cm).
 
 Radius 2
-  TODO
+  Sample radius 2 (cm).
 
 Can Radius
-  TODO
+  Radius of inside of the container (cm).
 
 Step Size
-  TODO
+  Step size used in calculation.
 
 Theory
 ~~~~~~
 
-TODO
+The main correction to be applied to neutron scattering data is that for
+absorption both in the sample and its container, when present. For flat plate
+geometry, the corrections can be analytical and have been discussed for example
+by Carlile [1]. The situation for cylindrical geometry is more complex and
+requires numerical integration. These techniques are well known and used in
+liquid and amorphous diffraction, and are described in the ATLAS manual [2]. The
+routines used here have been developed from the corrections programs in the
+ATLAS suite and take into account the wavelength variation of both the
+absorption and the scattering cross-sections for the inelastic flight paths.
+
+The absorption corrections use the formulism of Paalman and Pings [3] and
+involve the attenuation factors :math:`A_{i,j}` where :math:`i` refers to
+scattering and :math:`j` attenuation. For example, :math:`A_{s,sc}` is the
+attenuation factor for scattering in the sample and attenuation in the sample
+plus container. If the scattering cross sections for sample and container are
+:math:`\Sigma_{s}` and :math:`\Sigma_{c}` respectively, then the measured
+scattering from the empty container is :math:`I_{c} = \Sigma_{c}A_{c,c}` and
+that from the sample plus container is :math:`I_{sc} = \Sigma_{s}A_{s,sc} +
+\Sigma_{c}A_{c,sc}`, thus :math:`\Sigma_{s} = (I_{sc} - I_{c}A_{c,sc}/A_{c,c}) /
+A_{s,sc}`.  In the package, the program Acorn calculates the attenuation
+coefficients :math:`A_{i,j}` and the routine Analyse uses them to calculate Σs
+which we identify with :math:`S(Q, \omega)`.
+
+References:
+
+1. C J Carlile, Rutherford Laboratory report, RL-74-103 (1974)
+2. A K Soper, W S Howells & A C Hannon, RAL Report RAL-89-046 (1989)
+3. H H Paalman & C J Pings, J Appl Phys 33 2635 (1962)
+
 
 Apply Corrections
 -----------------