[07142f3] | 1 | r""" |
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| 2 | For information about polarised and magnetic scattering, click here_. |
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| 3 | |
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| 4 | .. _here: polar_mag_help.html |
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| 5 | |
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| 6 | Definition |
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| 7 | ---------- |
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| 8 | |
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| 9 | The 1D scattering intensity is calculated in the following way (Guinier, 1955) |
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| 10 | |
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| 11 | .. math:: |
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| 12 | |
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| 13 | I(q) = \frac{\text{scale}}{V} \cdot \left[ |
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| 14 | 3V(\Delta\rho) \cdot \frac{\sin(qr) - qr\cos(qr))}{(qr)^3} |
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| 15 | \right]^2 + \text{background} |
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| 16 | |
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| 17 | where *scale* is a volume fraction, $V$ is the volume of the scatterer, |
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| 18 | $r$ is the radius of the sphere, *background* is the background level and |
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| 19 | *sld* and *solvent_sld* are the scattering length densities (SLDs) of the |
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| 20 | scatterer and the solvent respectively. |
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| 21 | |
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| 22 | Note that if your data is in absolute scale, the *scale* should represent |
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| 23 | the volume fraction (which is unitless) if you have a good fit. If not, |
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| 24 | it should represent the volume fraction times a factor (by which your data |
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| 25 | might need to be rescaled). |
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| 26 | |
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| 27 | The 2D scattering intensity is the same as above, regardless of the |
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| 28 | orientation of $\vec q$. |
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| 29 | |
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| 30 | Validation |
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| 31 | ---------- |
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| 32 | |
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| 33 | Validation of our code was done by comparing the output of the 1D model |
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| 34 | to the output of the software provided by the NIST (Kline, 2006). |
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| 35 | Figure :num:`figure #sphere-comparison` shows a comparison of the output |
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| 36 | of our model and the output of the NIST software. |
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| 37 | |
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| 38 | .. _sphere-comparison: |
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| 39 | |
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| 40 | .. figure:: img/sphere_comparison.jpg |
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| 41 | |
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| 42 | Comparison of the DANSE scattering intensity for a sphere with the |
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| 43 | output of the NIST SANS analysis software. The parameters were set to: |
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| 44 | *scale* = 1.0, *radius* = 60 |Ang|, *contrast* = 1e-6 |Ang^-2|, and |
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| 45 | *background* = 0.01 |cm^-1|. |
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| 46 | |
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| 47 | |
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| 48 | References |
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| 49 | ---------- |
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| 50 | |
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| 51 | A Guinier and G. Fournet, *Small-Angle Scattering of X-Rays*, |
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| 52 | John Wiley and Sons, New York, (1955) |
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| 53 | |
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| 54 | *2013/09/09 and 2014/01/06 - Description reviewed by S King and P Parker.* |
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| 55 | """ |
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| 56 | |
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| 57 | from numpy import inf |
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| 58 | |
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| 59 | name = "bessel" |
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| 60 | title = "Bessel function testing" |
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| 61 | description = """\ |
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| 62 | Levraging current infrastracture to test Bessel function performance on |
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| 63 | """ |
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| 64 | category = "special_fucntions:bessel" |
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| 65 | |
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| 66 | # ["name", "units", default, [lower, upper], "type","description"], |
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| 67 | #Bessel |
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| 68 | parameters = [ |
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[cbd37a7] | 69 | ["ignored", "", 0.0, [-inf, inf], "", "no parameterless functions"], |
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[07142f3] | 70 | ] |
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| 71 | |
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[ad9af31] | 72 | source = ["lib/sas_gamma.c"] |
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[07142f3] | 73 | |
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| 74 | # No volume normalization despite having a volume parameter |
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| 75 | # This should perhaps be volume normalized? |
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| 76 | form_volume = """ |
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| 77 | """ |
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| 78 | |
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| 79 | Iq = """ |
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[ad9af31] | 80 | return sas_gamma(q); |
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[07142f3] | 81 | """ |
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| 82 | |
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| 83 | Iqxy = """ |
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| 84 | // never called since no orientation or magnetic parameters. |
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| 85 | //return -1.0; |
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| 86 | """ |
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| 87 | |
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| 88 | # VR defaults to 1.0 |
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| 89 | |
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| 90 | demo = dict(scale=1, background=0, |
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| 91 | ) |
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| 92 | oldname = "Bessel" |
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| 93 | oldpars = dict() |
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