Changeset e964ab1 in sasmodels for doc/guide/orientation/orientation.rst


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Timestamp:
Oct 28, 2017 9:11:13 PM (7 years ago)
Author:
Paul Kienzle <pkienzle@…>
Branches:
master, core_shell_microgels, magnetic_model, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
Children:
3d40839
Parents:
5f8b72b
Message:

reformat orientation docs to 80 columns

File:
1 edited

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  • doc/guide/orientation/orientation.rst

    reda8b30 re964ab1  
    44================== 
    55 
    6 With two dimensional small angle diffraction data SasView will calculate scattering from 
    7 oriented particles, applicable for example to shear flow or orientation in a magnetic field. 
     6With two dimensional small angle diffraction data SasView will calculate 
     7scattering from oriented particles, applicable for example to shear flow 
     8or orientation in a magnetic field. 
    89 
    9 In general we first need to define the mean, or a reference orientation of the particles with respect  
    10 to the incoming neutron or X-ray beam. This is done using three angles: $\theta$ and $\phi$ define the  
    11 orientation of the axis of the particle, angle $\Psi$ is defined as the orientation of the major 
    12 axis of the particle cross section with respect to its starting position along the beam direction. 
    13 The figures below are for an elliptical cross section cylinder, 
    14 but may be applied analogously to other shapes of particle. 
     10In general we first need to define the mean, or a reference orientation 
     11of the particles with respect to the incoming neutron or X-ray beam. This 
     12is done using three angles: $\theta$ and $\phi$ define the orientation of 
     13the axis of the particle, angle $\Psi$ is defined as the orientation of 
     14the major axis of the particle cross section with respect to its starting 
     15position along the beam direction. The figures below are for an elliptical 
     16cross section cylinder, but may be applied analogously to other shapes of 
     17particle. 
    1518 
    1619.. note:: 
    17     It is very important to note that these angles, in particular $\theta$ and $\phi$, are NOT in general 
    18     the same as the $\theta$ and $\phi$ appearing in equations for the scattering form factor which gives  
    19     the scattered intensity or indeed in the equation for scattering vector $Q$. 
    20     The $\theta$ rotation must be applied before the $\phi$ rotation, else there is an ambiguity. 
     20    It is very important to note that these angles, in particular $\theta$ 
     21    and $\phi$, are NOT in general the same as the $\theta$ and $\phi$ 
     22    appearing in equations for the scattering form factor which gives the 
     23    scattered intensity or indeed in the equation for scattering vector $Q$. 
     24    The $\theta$ rotation must be applied before the $\phi$ rotation, else 
     25    there is an ambiguity. 
    2126 
    2227.. figure:: 
    2328    orient_img/elliptical_cylinder_angle_definition.png 
    2429 
    25     Definition of angles for oriented elliptical cylinder, where axis_ratio b/a is shown >1, 
    26     Note that rotation $\theta$, initially in the $xz$ plane, is carried out first, then 
    27     rotation $\phi$ about the $z$ axis, finally rotation $\Psi$ is around the axis of the cylinder. 
    28     The neutron or X-ray beam is along the $z$ axis. 
     30    Definition of angles for oriented elliptical cylinder, where axis_ratio 
     31    b/a is shown >1, Note that rotation $\theta$, initially in the $xz$ 
     32    plane, is carried out first, then rotation $\phi$ about the $z$ axis, 
     33    finally rotation $\Psi$ is around the axis of the cylinder. The neutron 
     34    or X-ray beam is along the $z$ axis. 
    2935 
    3036.. figure:: 
    3137    orient_img/elliptical_cylinder_angle_projection.png 
    3238 
    33     Some examples of the orientation angles for an elliptical cylinder, with $\Psi$ = 0. 
     39    Some examples of the orientation angles for an elliptical cylinder, 
     40    with $\Psi$ = 0. 
    3441 
    35 Having established the mean direction of the particle we can then apply angular orientation distributions. 
    36 This is done by a numerical integration over a range of angles in a similar way to polydispersity for particle size. 
    37 In the current version of sasview the orientational dispersity is defined with respect to the axes of the particle. 
     42Having established the mean direction of the particle we can then apply 
     43angular orientation distributions. This is done by a numerical integration 
     44over a range of angles in a similar way to polydispersity for particle size. 
     45In the current version of sasview the orientational dispersity is defined 
     46with respect to the axes of the particle. 
    3847 
    39 The $\theta$ and $\phi$ parameters to orient the cylinder only appear in the model when fitting 2d data. 
    40 On introducing "Orientational Distribution" in the angles, "distribution of theta" and "distribution of phi" parameters will 
    41 appear. These are actually rotations about the axes $\delta_1$ and $\delta_2$ of the cylinder, the $b$ and $a$ axes of the 
    42 cylinder cross section. (When $\theta = \phi = 0$ these are parallel to the $Y$ and $X$ axes of the instrument.) 
    43 The third orientation distribution, in $\psi$, is about the $c$ axis of the particle. Some experimentation may be required to 
    44 understand the 2d patterns fully. A number of different shapes of distribution are available, as described for  
    45 polydispersity, see :ref:`polydispersityhelp` . 
     48The $\theta$ and $\phi$ parameters to orient the cylinder only appear in the 
     49model when fitting 2d data. On introducing "Orientational Distribution" in 
     50the angles, "distribution of theta" and "distribution of phi" parameters will 
     51appear. These are actually rotations about the axes $\delta_1$ and $\delta_2$ 
     52of the cylinder, the $b$ and $a$ axes of the cylinder cross section. (When 
     53$\theta = \phi = 0$ these are parallel to the $Y$ and $X$ axes of the 
     54instrument.) The third orientation distribution, in $\psi$, is about the $c$ 
     55axis of the particle. Some experimentation may be required to understand the 
     562d patterns fully. A number of different shapes of distribution are 
     57available, as described for polydispersity, see :ref:`polydispersityhelp` . 
    4658 
    47 Earlier versions of SasView had numerical integration issues in some circumstances when  
    48 distributions passed through 90 degrees. The distributions in particle coordinates are more robust, but should still be approached  
    49 with care for large ranges of angle. 
     59Earlier versions of SasView had numerical integration issues in some 
     60circumstances when distributions passed through 90 degrees. The distributions 
     61in particle coordinates are more robust, but should still be approached with 
     62care for large ranges of angle. 
    5063 
    51 Note that the form factors for asymmetric particles are also performing numerical integrations over one or more variables, so  
    52 care should be taken, especially with very large particles or more extreme aspect ratios. Users can experiment with the  
    53 values of Npts and Nsigs, the number of steps used in the integration and the range spanned in number of standard deviations. 
    54 The standard deviation is entered in units of degrees. For a rectangular (uniform) distribution the full width  
    55 should be $\pm\sqrt(3)$ ~ 1.73 standard deviations (this may be changed soon). 
     64Note that the form factors for asymmetric particles are also performing 
     65numerical integrations over one or more variables, so care should be taken, 
     66especially with very large particles or more extreme aspect ratios. Users can 
     67experiment with the values of Npts and Nsigs, the number of steps used in the 
     68integration and the range spanned in number of standard deviations. The 
     69standard deviation is entered in units of degrees. For a rectangular 
     70(uniform) distribution the full width should be $\pm\sqrt(3)$ ~ 1.73 standard 
     71deviations (this may be changed soon). 
    5672 
    57 Where appropriate, for best numerical results, keep $a < b < c$ and the $\theta$ distribution narrower than the $\phi$ distribution. 
     73Where appropriate, for best numerical results, keep $a < b < c$ and the 
     74$\theta$ distribution narrower than the $\phi$ distribution. 
    5875 
    59 Some more detailed technical notes are provided in the developer section of this manual :ref:`orientation_developer` . 
    60      
     76Some more detailed technical notes are provided in the developer section of 
     77this manual :ref:`orientation_developer` . 
     78 
    6179*Document History* 
    6280 
    63 | 2017-10-27 Richard Heenan  
     81| 2017-10-27 Richard Heenan 
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