core_shell_microgelscostrafo411magnetic_modelticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
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[3330bb4] | 1 | .. currentmodule:: sasmodels |
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| 2 | .. Wim Bouwman, DUT, written at codecamp-V, Oct2016 |
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| 3 | |
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| 4 | .. _SESANS: |
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| 5 | |
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| 6 | SANS to SESANS conversion |
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| 7 | ========================= |
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| 8 | |
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| 9 | The conversion from SANS into SESANS in absolute units is a simple Hankel transformation when all the small-angle scattered neutrons are detected. |
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| 10 | First we calculate the Hankel transform including the absolute intensities by |
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| 11 | |
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| 12 | .. math:: G(\delta) = 2 \pi \int_0^{\infty} J_0(Q \delta) \frac{d \Sigma}{d \Omega} (Q) Q dQ \!, |
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| 13 | |
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| 14 | in which :math:`J_0` is the zeroth order Bessel function, :math:`\delta` the spin-echo length, :math:`Q` the wave vector transfer |
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| 15 | and :math:`\frac{d \Sigma}{d \Omega} (Q)` the scattering cross section in absolute units. |
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| 16 | This is a 1-dimensional integral, which can be rather fast. |
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| 17 | In the numerical calculation we integrate from :math:`Q_{min} = 0.1 \times 2 \pi / R_{max}` in which :math:`R_{max}` will be model dependent. |
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| 18 | We determined the factor 0.1 by varying its value until the value of the integral was stable. |
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| 19 | This happened at a value of 0.3. The have a safety margin of a factor of three we have choosen the value 0.1. |
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| 20 | For the solid sphere we took 3 times the radius for :math:`R_{max}`. |
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| 21 | The real integration is performed to :math:`Q_{max}` which is an instrumental parameter that is read in from the measurement file. |
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| 22 | From the equation above we can calculate the polarisation that we measure in a SESANS experiment: |
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| 23 | |
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| 24 | .. math:: P(\delta) = e^{t \left( \frac{ \lambda}{2 \pi} \right)^2 \left(G(\delta) - G(0) \right)} \!, |
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| 25 | |
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[4a2e1e5] | 26 | in which :math:`t` is the thickness of the sample and :math:`\lambda` is the wavelength of the neutrons. |
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