- Timestamp:
- Dec 21, 2017 8:01:39 AM (7 years ago)
- 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
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- 1 edited
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doc/guide/orientation/orientation.rst
r8cfb486 r5fb0634 86 86 87 87 The $\theta$ and $\phi$ orientation parameters for the cylinder only appear 88 when fitting 2d data. On introducing "Orientation Distribution" in the88 when fitting 2d data. On introducing "Orientational Distribution" in the 89 89 angles, "distribution of theta" and "distribution of phi" parameters will 90 90 appear. These are actually rotations about the axes $\delta_1$ and $\delta_2$ … … 119 119 freely around the $b$ axis, with $\Delta\theta$ uniform in $[-180, 180]$. At 120 120 $\pm 90$, 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 tothe beam (which122 will be the case for $\theta=90$ and $\Psi=90$) ,the scattering pattern123 should be circularly symmetric, but it will go to zero at $ \pm 90$ due to the121 a distinct angular preference. If the spin axis is along 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 $q_x = 0$ due to the 124 124 $\sin(\Delta\theta)$ correction. This problem does not appear for a shape 125 125 that is tumbling freely around the $a$ axis, with $\Delta\phi$ uniform in 126 126 $[-180, 180]$, so swap the $a$ and $b$ axes so $\Delta\theta < \Delta\phi$ 127 and adjust $\Psi$ by 90. This works with the existingsasmodels shapes due to127 and adjust $\Psi$ by 90. This works with the current sasmodels shapes due to 128 128 symmetry. 129 129 … … 145 145 The `Guyou projection <https://en.wikipedia.org/wiki/Guyou_hemisphere-in-a-square_projection>`_ 146 146 has an excellent balance with reasonable distortion in both $\Delta\theta$ 147 and $\Delta\phi$, as well as preserving small patches. However, it is148 considerably more overhead, and we have not yet derived the formula forthe149 distortion correction, measuring the degree of stretch at the point150 $(\Delta\theta, \Delta\phi)$ on the map.147 and $\Delta\phi$, as well as preserving small patches. However, it requires 148 considerably more computational overhead, and we have not yet derived the 149 formula for the distortion correction, measuring the degree of stretch at 150 the point $(\Delta\theta, \Delta\phi)$ on the map. 151 151 152 152 .. note::
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