Changeset abcac7a in sasview


Ignore:
Timestamp:
Jun 4, 2018 4:22:47 AM (7 months ago)
Author:
celinedurniak <celine.durniak@…>
Branches:
ESS_GUI, ESS_GUI_Invariant, ESS_GUI_Pr_fixes, ESS_GUI_batch_fitting, ESS_GUI_iss879, ESS_GUI_iss959, ESS_GUI_ordering
Children:
397037e
Parents:
4ac377c
Message:

Added new screenshots for documentation on Invariant

Location:
src/sas/qtgui/Perspectives/Invariant/media
Files:
4 added
1 edited

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  • src/sas/qtgui/Perspectives/Invariant/media/invariant_help.rst

    r417c03f rabcac7a  
    1010----------- 
    1111 
    12 The scattering, or Porod, invariant ($Q^*$) is a model-independent quantity that 
     12The scattering, or Porod, invariant (:math:`Q^*`) is a model-independent quantity that 
    1313can be easily calculated from scattering data. 
    1414 
    1515For two phase systems, the scattering invariant is defined as the integral of 
    16 the square of the wavevector transfer ($Q$) multiplied by the scattering cross section 
    17 over the full range of $Q$ from zero to infinity, that is 
     16the square of the wavevector transfer (:math:`Q`) multiplied by the scattering cross section 
     17over the full range of :math:`Q` from zero to infinity, that is 
     18 
    1819 
    1920.. math:: 
    2021 
    21     Q^* = \int_0^\infty q^2I(q)\,dq 
     22    Q^* = \int_0^ \infty q^2 I(q)\,dq 
    2223 
    23 in the case of pinhole geometry. For slit geometry the invariant is given by 
     24 
     25in the case of pinhole geometry (SAS). 
     26 
     27 
     28For slit geometry (USAS) the invariant is given by 
    2429 
    2530.. math:: 
    2631 
    27     Q^* = \Delta q_v \int_0^\infty qI(q)\,dq 
     32    Q^* =  \int_0^\infty \Delta q_v \, qI(q)\,dq 
    2833 
    29 where $\Delta q_v$ is the slit height. 
     34where :math:`\Delta q_v` is the slit height. 
    3035 
    31 The worth of $Q^*$  is that it can be used to determine the volume fraction and 
    32 the specific area of a sample. Whilst these quantities are useful in their own 
    33 right they can also be used in further analysis. 
     36The worth of :math:`Q^*` is that it can be used to determine the volume fraction 
     37and the specific area of a sample. Whilst these quantities are useful in their 
     38own right, they can also be used in further analysis. 
    3439 
    35 The difficulty with using $Q^*$  arises from the fact that experimental data is 
    36 never measured over the range $0 \le Q \le \infty$. At best, combining USAS and 
    37 WAS data might cover the range $10^{-5} \le Q \le 10$ 1/\ |Ang| . Thus it is usually 
    38 necessary to extrapolate the experimental data to low and high $Q$. For this 
     40The difficulty with using :math:`Q^*`  arises from the fact that experimental 
     41data is never measured over the range :math:`0 \le Q \le \infty`. At best, 
     42combining USAS and WAS data might cover the range 
     43:math:`10^{-5} \le Q \le 10`|Ang|:math:`^{-1}`. Thus it is usually 
     44necessary to extrapolate the experimental data to low and high :math:`Q`. 
     45For this 
    3946 
    40 High-\ $Q$ region (>= *Qmax* in data) 
     47High-\ :math:`Q` region (>= *Qmax* in data) 
    4148 
    42 *  The power law function $C/Q^4$ is used where the constant 
    43    $C = 2 \pi \Delta\rho S_v$ is to be found by fitting part of data 
    44    within the range $Q_{N-m}$ to $Q_N$ (where $m < N$). 
     49*  The power law function :math:`C/Q^4` is used where the constant 
     50   :math:`C = 2 \pi \Delta\rho\, S_v` with 
     51   :math:`\Delta\rho`, the scattering length density (SLD) contrast and 
     52   :math:`S_v`, the specific surface area. The value of :math:`C` is to be found 
     53   by fitting part of data within the range :math:`Q_{N-m}` to :math:`Q_N` 
     54   (where :math:`m < N`), . 
    4555 
    46 Low-\ $Q$ region (<= *Qmin* in data) 
     56Low-\ :math:`Q` region (<= *Qmin* in data) 
    4757 
    48 *  The Guinier function $I_0 exp(-R_g^2 Q^2/3)$ where $I_0$ 
    49    and $R_g$ are obtained by fitting as for the high-\ $Q$ region above. 
     58*  The Guinier function :math:`I(Q)=I(0) \exp (-R_g^2 Q^2/3)` where :math:`R_g` 
     59   is the radius of gyration. The values of :math:`I(0)` and :math:`R_g` are 
     60   obtained by fitting as for the high-\ :math:`Q` region above. 
    5061   Alternatively a power law can be used. 
    5162 
     
    6273   the dataset into the *Invariant* panel. 
    6374 
    64 4) Use the *Customised Input* boxes on the *Invariant* panel to subtract 
    65    any background, specify the contrast (i.e. difference in SLDs - this must be 
    66    specified for the eventual value of $Q^*$  to be on an absolute scale), or to 
    67    rescale the data. 
     75.. image:: image_invariant_load_data.png 
    6876 
    69 5) Adjust the extrapolation range as necessary. In most cases the default 
    70    values will suffice. 
     774) Use the *Customised Input* box on the *Options* tab to subtract any 
     78   background, specify the contrast (i.e. difference in SLDs - this must be 
     79   specified for the eventual value of :math:`Q^*` to be on an absolute scale), 
     80   or to rescale the data. 
    7181 
    72 6) Click the *Compute* button. 
     825) Adjust the extrapolation range in the *Options* tab as necessary. In most 
     83   cases the default values will suffice. 
    7384 
    74 7) To include a lower and/or higher $Q$ range, check the relevant *Enable 
     85 
     866) Click the *Calculate* button. 
     87 
     887) To include a lower and/or higher :math:`Q` range, check the relevant *Enable 
    7589   Extrapolate* check boxes. 
     90 
     91   .. figure:: image_invariant_option_tab.png 
     92 
     93       .. 
     94 
     95       *Option tab of the Invariant panel.* 
     96 
    7697 
    7798   If power law extrapolations are chosen, the exponent can be either held 
    7899   fixed or fitted. The number of points, Npts, to be used for the basis of the 
    79    extrapolation can also be specified. 
     100   extrapolation can also be specified in the related *Power* box(es). 
    80101 
    81 8) If the value of $Q^*$  calculated with the extrapolated regions is invalid, a 
    82    red warning will appear at the top of the *Invariant* panel. 
     102   .. figure:: image_invariant_outplot_plot.png 
     103       :width: 300pt 
    83104 
    84    The details of the calculation are available by clicking the *Details* 
    85    button in the middle of the panel. 
     105       .. 
    86106 
    87 .. image:: image005.png 
     107       *Output plot generated after calculations.* 
     108 
     1098) If the value of :math:`Q^*` calculated with the extrapolated regions is 
     110   invalid, the related box will be highlighted in red. 
     111 
     112   The details of the calculation are available by clicking the *Status* 
     113   button at the bottom of the panel. 
     114 
     115 
     116   .. image:: image_invariant_details.png 
     117      :width: 300pt 
     118 
    88119 
    89120.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 
     
    95126^^^^^^^^^^^^^^^ 
    96127 
    97 The volume fraction $\phi$ is related to $Q^*$  by 
     128The volume fraction :math:`\phi` is related to :math:`Q^*`  by 
    98129 
    99130.. math:: 
     
    101132    \phi(1 - \phi) = \frac{Q^*}{2\pi^2(\Delta\rho)^2} \equiv A 
    102133 
    103 where $\Delta\rho$ is the SLD contrast. 
     134where :math:`\Delta\rho` is the SLD contrast. 
    104135 
    105136.. math:: 
     
    112143^^^^^^^^^^^^^^^^^^^^^ 
    113144 
    114 The specific surface area $S_v$ is related to $Q^*$  by 
     145The specific surface area :math:`S_v` is related to :math:`Q^*`  by 
    115146 
    116147.. math:: 
     
    118149    S_v = \frac{2\pi\phi(1-\phi)C_p}{Q^*} = \frac{2\pi A C_p}{Q^*} 
    119150 
    120 where $C_p$ is the Porod constant. 
     151where :math:`C_p` is the Porod constant. 
    121152 
    122153.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 
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