Changeset 727c05f in sasview for src/sas/sasgui/perspectives/invariant/media

Timestamp:

Apr 6, 2017 5:42:59 PM (8 years ago)

Author:

Paul Kienzle <pkienzle@…>

Branches:

master, ESS_GUI, ESS_GUI_Docs, ESS_GUI_batch_fitting, ESS_GUI_bumps_abstraction, ESS_GUI_iss1116, ESS_GUI_iss879, ESS_GUI_iss959, ESS_GUI_opencl, ESS_GUI_ordering, ESS_GUI_sync_sascalc, magnetic_scatt, release-4.2.2, ticket-1009, ticket-1094-headless, ticket-1242-2d-resolution, ticket-1243, ticket-1249, ticket885, unittest-saveload

Children:

5ed76f8

Parents:

094b9eb (diff), 02b01877 (diff)
Note: this is a merge changeset, the changes displayed below correspond to the merge itself.
Use the (diff) links above to see all the changes relative to each parent.

Message:

Merge branch 'ticket-510' of github.com:sasview/sasview into ticket-510

Location:

src/sas/sasgui/perspectives/invariant/media

Files:

• image001.png (deleted)
• image002.png (deleted)
• image003.png (deleted)
• image004.png (deleted)
• invariant_help.rst (modified) (4 diffs)

src/sas/sasgui/perspectives/invariant/media/invariant_help.rst

@@ -10 +10 @@
 -----------
 
-The scattering, or Porod, invariant (Q*\) is a model-independent quantity that 
+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 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
+For two phase systems, the scattering invariant is defined as the integral of
+the square of the wavevector transfer ($Q$) multiplied by the scattering cross section
+over the full range of $Q$ from zero to infinity, that is
 
-.. image:: image001.png
+.. math::
 
-where *g = q* for pinhole geometry (SAS) and *g = q*\ :sub:`v` (the slit height) for  
-slit geometry (USAS).
+    Q^* = \int_0^\infty q^2I(q)\,dq
 
-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 
+in the case of pinhole geometry. For slit geometry the invariant is given by
+
+.. math::
+
+    Q^* = \Delta q_v \int_0^\infty qI(q)\,dq
+
+where $\Delta q_v$ is the slit height.
+
+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.
 
-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 difficulty with using $Q^*$  arises from the fact that experimental data is
+never measured over the range $0 \le Q \le \infty$. At best, combining USAS and
+WAS data might cover the range $10^{-5} \le Q \le 10$ 1/\ |Ang| . Thus it is usually
+necessary to extrapolate the experimental data to low and high $Q$. For this
 
-High-*Q* region (>= *Qmax* in data)
+High-\ $Q$ region (>= *Qmax* in data)
 
-*  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).
+*  The power law function $C/Q^4$ is used where the constant
+   $C = 2 \pi \Delta\rho S_v$ is to be found by fitting part of data
+   within the range $Q_{N-m}$ to $Q_N$ (where $m < N$).
 
-Low-*Q* region (<= *Qmin* in data)
+Low-\ $Q$ region (<= *Qmin* in data)
 
-*  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. 
+*  The Guinier function $I_0 exp(-R_g^2 Q^2/3)$ where $I_0$
+   and $R_g$ are obtained by fitting as for the high-\ $Q$ region above.
    Alternatively a power law can be used.
 
@@ -52 +59 @@
 2) Load some data with the *Data Explorer*.
 
-3) Select a dataset and use the *Send To* button on the *Data Explorer* to load 
+3) Select a dataset and use the *Send To* button on the *Data Explorer* to load
    the dataset into the *Invariant* panel.
 
-4) Use the *Customised Input* boxes on the *Invariant* panel 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 
+4) Use the *Customised Input* boxes on the *Invariant* panel 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.
 
-5) Adjust the extrapolation range as necessary. In most cases the default 
+5) Adjust the extrapolation range as necessary. In most cases the default
    values will suffice.
 
 6) Click the *Compute* button.
 
-7) To include a lower and/or higher Q range, check the relevant *Enable 
+7) 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 
+
+   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.
 
-8) If the value of Q*\  calculated with the extrapolated regions is invalid, a 
+8) If the value of $Q^*$  calculated with the extrapolated regions is invalid, a
    red warning will appear at the top of the *Invariant* panel.
 
-   The details of the calculation are available by clicking the *Details* 
+   The details of the calculation are available by clicking the *Details*
    button in the middle of the panel.
 
@@ -88 +95 @@
 ^^^^^^^^^^^^^^^
 
-The volume fraction |phi| is related to Q*\  by
+The volume fraction $\phi$ is related to $Q^*$  by
 
-.. image:: image002.png
+.. math::
 
-where |bigdelta|\ |rho| is the SLD contrast.
+    \phi(1 - \phi) = \frac{Q^*}{2\pi^2(\Delta\rho)^2} \equiv A
 
-.. image:: image003.png
+where $\Delta\rho$ is the SLD contrast.
+
+.. math::
+
+    \phi = \frac{1 \pm \sqrt{1 - 4A}}{2}
 
 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
@@ -101 +112 @@
 ^^^^^^^^^^^^^^^^^^^^^
 
-The specific surface area *Sv* is related to Q*\  by
+The specific surface area $S_v$ is related to $Q^*$  by
 
-.. image:: image004.png
+.. math::
 
-where *Cp* is the Porod constant.
+    S_v = \frac{2\pi\phi(1-\phi)C_p}{Q^*} = \frac{2\pi A C_p}{Q^*}
+
+where $C_p$ is the Porod constant.
 
 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ