-                      rec392464
+                      r0721c3d
 .. This is a port of the original SasView html help file to ReSTructured text
 .. by S King, ISIS, during SasView CodeCamp-III in Feb 2015.
+.. |Ang| unicode:: U+212B
+.. |pi| unicode:: U+03C0
+.. |bigdelta| unicode:: U+0394
+.. |rho| unicode:: U+03C1
+.. |phi| unicode:: U+03C6
 Invariant Calculation Perspective
 …
 Scattering_Invariant_
+How_to_Use_
 Volume_Fraction_
 Specific_Surface_Area_
-Definitions_
 Reference_
-How_to_Use_
 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
 …
 .. _Scattering_Invariant:
 Scattering Invariant
 --------------------
+Scattering (Porod) Invariant
+----------------------------
 The scattering invariant (Q*) is a model-independent quantity that can be
 easily calculated from scattering data.
+The scattering, or Porod, invariant (Q*\) is a model-independent quantity that
+can be easily calculated from scattering data.
+For two phase systems, the scattering invariant, Q*, is defined as the
+integral of the square of the wave transfer (q) multiplied by the scattering
+cross section over the full range of q.
+Q* is given by the following equation
+For two phase systems, the scattering invariant is defined as the integral of
+the square of the wave transfer (Q) multiplied by the scattering cross section
+over the full range of Q from zero to infinity, that is
 .. image:: image001.gif
+This model independent quantity (Q*) is calculated from the scattering data
+that can be used to determine the volume fraction and the specific area of the
+sample under consideration.
+where *g = Q* for pinhole geometry (SAS) and *g = Qv* (the slit height) for
+slit geometry (USAS).
+These quantities are useful in their own right and can be used in further
+analysis. With this scattering invariant module users will also be able to
+determine the consistency of those properties between data. There is no real
+data defined from zero to infinity, there usually have limited range.
+The worth of Q*\  is that it can be used to determine the volume fraction and
+the specific area of a sample. Whilst these quantities are useful in their own
+right they can also be used in further analysis.
+Q* is not really computed from zero to infinity. Our maximum q range is
+e-5 ~ 10 (1/Angstrom). The lower and/or higher q range than data given can be
+extrapolated by fitting some data nearby.
+The difficulty with using Q*\  arises from the fact that experimental data is
+never measured over the range 0 =< *Q* =< infinity. At best, combining USAS and
+WAS data might cover the range 1e-5 =< *Q* =< 10 1/\ |Ang| . Thus it is usually
+necessary to extrapolate the experimental data to low and high *Q*. For this
+The scattering invariant is computed as follows
+High-*Q* region (>= *Qmax* in data)
+*I(q)* = *I(q)*  w/o background : If the data includes a background, user sets
+the value to subtract the background for the Q* computation.
+*  The power law function *C*/*Q*\ :sup:`4` is used where the constant
+   *C* (= 2.\ |pi|\ .(\ |bigdelta|\ |rho|\ ).\ *Sv*\ ) is to be found by fitting part of data
+   within the range *Q*\ :sub:`N-m` to *Q*\ :sub:`N` (where m < N).
+Reset *I(q)* = *I(q)* scaling factor* , delta *I(q) =*  delta *I(q)*scaling
+factor* : If non-zero scaling factor is given, it will be considered.
+Low-*Q* region (<= *Qmin* in data)
+Invariant
+*  The Guinier function *I0.exp(-Rg*\ :sup:`2`\ *Q*\ :sup:`2`\ */3)* where *I0*
+   and *Rg* are obtained by fitting as for the high-*Q* region above.
+   Alternatively a power law can be used.
 .. image:: image001.gif
+.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
+where *g =q*  for the pinhole geometry and *g =qv*  (the slit height) for the
+slit geometry which can be given in data or as a value.
+.. _How_to_Use:
+Higher q-region (\>= qmax in data)
+How to Use
+----------
+Power law (w/o background term) function = C/q4will be used
+) Select *Invariant* from the *Analysis* menu on the SasView toolbar.
+where the constant C(=2pi(delta(rho))Sv) is to be found by fitting part of
+data with the range of qN-mto qN(m\<N).
+) Load some data with the *Data Explorer*.
+Lower q-region (\<= qmin in data):
+) Select a dataset and use the *Send To* button on the *Data Explorer* to load
+   the dataset into the *Invariant* perspective.
+Guinier function = *I0exp(-Rg2q2/3)*  where I0and Rgare obtained by fitting,
+) Use the *Customised Input* boxes on the *Invariant* perspective to subtract
+   any background, specify the contrast (i.e. difference in SLDs - this must be
+   specified for the eventual value of Q*\  to be on an absolute scale), or to
+   rescale the data.
+similarly to the high q region above.
+) Adjust the extrapolation range as necessary. In most cases the default
+   values will suffice.
+Power law can also be used.
+) Click the *Compute* button.
+) To include a lower and/or higher Q range, check the relevant *Enable
+   Extrapolate* check boxes.
+   If power law extrapolations are chosen, the exponent can be either held
+   fixed or fitted. The number of points, Npts, to be used for the basis of the
+   extrapolation can also be specified.
+) If the value of Q*\  calculated with the extrapolated regions is invalid, a
+   red warning will appear at the top of the *Invariant* perspective panel.
+   The details of the calculation are available by clicking the *Details*
+   button in the middle of the panel.
+.. image:: image005.gif
 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
 …
 ---------------
+The volume fraction |phi| is related to Q*\  by
 .. image:: image002.gif
 where delta(rho) is the SLD contrast of which value is given by users.
+where |bigdelta|\ |rho| is the SLD contrast.
 .. image:: image003.gif
-Thus
-where 0 =\< *A*  =\<1/4 in order for these values to be physically valid.
 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
 …
 ---------------------
+The specific surface area *Sv* is related to Q*\  by
 .. image:: image004.gif
+where *A*  and *Q**  are obtained from previous sections, and the Porod
+constant *Cp*  is given by users.
+.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
+.. _Definitions:
+Definitions
+-----------
+Q: the magnitude of neutron (or X-ray) momentum transfer vector.
+I(Q): the scattering intensity as a function of the momentum transfer Q.
+Invariant total is the sum of the invariant calculated from datas q range and
+the invariant resulting from extrapolation at low q range and at high q range
+if considered.
+where *Cp* is the Porod constant.
 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
 …
 ----------
+Chapter 2 in O. Glatter and O. Kratky, "Small Angle X-Ray Scattering", Academic
+Press, New York, 1982
+O. Glatter and O. Kratky
+Chapter 2 in *Small Angle X-Ray Scattering*
+Academic Press, New York, 1982
 http://physchem.kfunigraz.ac.at/sm/
 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
+.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
+.. _How_to_Use:
+How to Use
+----------
+. Loading data to the panel: Open the data file from File in the menu bar.
+Select loaded data from a plot panel by highlighting that it until its color
+turns yellow. Then right click on that the data and selects the option Compute
+Invariant. The application automatically computes the invariant value if the
+data loaded is valid.
+. To subtract a background or/and to rescale the data, type the values in
+Customized Input box.
+. If you want to calculate the volume fraction and the specific surface
+area, type the optional inputs in the customized input box, and then press
+'Compute' button.
+. The invariant can also be calculated including the outside of the data Q
+range:  To include the lower Q and/or the higher Q range, check in the enable
+extrapolation check box in 'Extrapolation' box. If the power low is chosen,
+the power (exponent) can be either held or fitted by checking the
+corresponding radio button.  The Npts that is being used for the extrapolation
+can be specified.
+. If the invariant calculated from the extrapolated region is too large, it
+will be warn in red at the top of the panel, which means that your data is not
+proper to calculate the invariant.
+. The details of the calculation is available by clicking the 'Details'
+button in the middle of the panel.
+.. image:: image005.gif
+.. note::  This help document was last changed by Steve King, 19Feb2015

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