Changeset e964ab1 in sasmodels for doc/guide/orientation/orientation.rst
- Timestamp:
- Oct 28, 2017 9:11:13 PM (7 years ago)
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- master, core_shell_microgels, magnetic_model, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
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doc/guide/orientation/orientation.rst (modified) (1 diff)
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doc/guide/orientation/orientation.rst
reda8b30 re964ab1 4 4 ================== 5 5 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. 6 With two dimensional small angle diffraction data SasView will calculate 7 scattering from oriented particles, applicable for example to shear flow 8 or orientation in a magnetic field. 8 9 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. 10 In general we first need to define the mean, or a reference orientation 11 of the particles with respect to the incoming neutron or X-ray beam. This 12 is done using three angles: $\theta$ and $\phi$ define the orientation of 13 the axis of the particle, angle $\Psi$ is defined as the orientation of 14 the major axis of the particle cross section with respect to its starting 15 position along the beam direction. The figures below are for an elliptical 16 cross section cylinder, but may be applied analogously to other shapes of 17 particle. 15 18 16 19 .. 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. 21 26 22 27 .. figure:: 23 28 orient_img/elliptical_cylinder_angle_definition.png 24 29 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. 29 35 30 36 .. figure:: 31 37 orient_img/elliptical_cylinder_angle_projection.png 32 38 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. 34 41 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. 42 Having established the mean direction of the particle we can then apply 43 angular orientation distributions. This is done by a numerical integration 44 over a range of angles in a similar way to polydispersity for particle size. 45 In the current version of sasview the orientational dispersity is defined 46 with respect to the axes of the particle. 38 47 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` . 48 The $\theta$ and $\phi$ parameters to orient the cylinder only appear in the 49 model when fitting 2d data. On introducing "Orientational Distribution" in 50 the angles, "distribution of theta" and "distribution of phi" parameters will 51 appear. These are actually rotations about the axes $\delta_1$ and $\delta_2$ 52 of 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 54 instrument.) The third orientation distribution, in $\psi$, is about the $c$ 55 axis of the particle. Some experimentation may be required to understand the 56 2d patterns fully. A number of different shapes of distribution are 57 available, as described for polydispersity, see :ref:`polydispersityhelp` . 46 58 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. 59 Earlier versions of SasView had numerical integration issues in some 60 circumstances when distributions passed through 90 degrees. The distributions 61 in particle coordinates are more robust, but should still be approached with 62 care for large ranges of angle. 50 63 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). 64 Note that the form factors for asymmetric particles are also performing 65 numerical integrations over one or more variables, so care should be taken, 66 especially with very large particles or more extreme aspect ratios. Users can 67 experiment with the values of Npts and Nsigs, the number of steps used in the 68 integration and the range spanned in number of standard deviations. The 69 standard deviation is entered in units of degrees. For a rectangular 70 (uniform) distribution the full width should be $\pm\sqrt(3)$ ~ 1.73 standard 71 deviations (this may be changed soon). 56 72 57 Where appropriate, for best numerical results, keep $a < b < c$ and the $\theta$ distribution narrower than the $\phi$ distribution. 73 Where appropriate, for best numerical results, keep $a < b < c$ and the 74 $\theta$ distribution narrower than the $\phi$ distribution. 58 75 59 Some more detailed technical notes are provided in the developer section of this manual :ref:`orientation_developer` . 60 76 Some more detailed technical notes are provided in the developer section of 77 this manual :ref:`orientation_developer` . 78 61 79 *Document History* 62 80 63 | 2017-10-27 Richard Heenan 81 | 2017-10-27 Richard Heenan
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