Changeset 5fb0634 in sasmodels


Ignore:
Timestamp:
Dec 21, 2017 8:01:39 AM (6 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:
a6d3f46, 226473d
Parents:
8cfb486
Message:

update orientation docs

File:
1 edited

Legend:

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  • doc/guide/orientation/orientation.rst

    r8cfb486 r5fb0634  
    8686 
    8787The $\theta$ and $\phi$ orientation parameters for the cylinder only appear 
    88 when fitting 2d data. On introducing "Orientation Distribution" in the 
     88when fitting 2d data. On introducing "Orientational Distribution" in the 
    8989angles, "distribution of theta" and "distribution of phi" parameters will 
    9090appear. These are actually rotations about the axes $\delta_1$ and $\delta_2$ 
     
    119119freely around the $b$ axis, with $\Delta\theta$ uniform in $[-180, 180]$. At 
    120120$\pm 90$, all points in $\Delta\phi$ map to the pole, so the jitter will have 
    121 a distinct angular preference. If the spin axis is normal to the beam (which 
    122 will be the case for $\theta=90$ and $\Psi=90$), the scattering pattern 
    123 should be circularly symmetric, but it will go to zero at $\pm 90$ due to the 
     121a distinct angular preference. If the spin axis is along the beam (which 
     122will be the case for $\theta=90$ and $\Psi=90$) the scattering pattern 
     123should be circularly symmetric, but it will go to zero at $q_x = 0$ due to the 
    124124$\sin(\Delta\theta)$ correction. This problem does not appear for a shape 
    125125that is tumbling freely around the $a$ axis, with $\Delta\phi$ uniform in 
    126126$[-180, 180]$, so swap the $a$ and $b$ axes so $\Delta\theta < \Delta\phi$ 
    127 and adjust $\Psi$ by 90. This works with the existing sasmodels shapes due to 
     127and adjust $\Psi$ by 90. This works with the current sasmodels shapes due to 
    128128symmetry. 
    129129 
     
    145145The `Guyou projection <https://en.wikipedia.org/wiki/Guyou_hemisphere-in-a-square_projection>`_ 
    146146has an excellent balance with reasonable distortion in both $\Delta\theta$ 
    147 and $\Delta\phi$, as well as preserving small patches. However, it is 
    148 considerably more overhead, and we have not yet derived the formula for the 
    149 distortion correction, measuring the degree of stretch at the point 
    150 $(\Delta\theta, \Delta\phi)$ on the map. 
     147and $\Delta\phi$, as well as preserving small patches. However, it requires 
     148considerably more computational overhead, and we have not yet derived the 
     149formula for the distortion correction, measuring the degree of stretch at 
     150the point $(\Delta\theta, \Delta\phi)$ on the map. 
    151151 
    152152.. note:: 
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