source: sasmodels/sasmodels/models/sphere.py @ c691551

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Last change on this file since c691551 was c691551, checked in by mathieu, 8 years ago

Fix pylint

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1r"""
2For information about polarised and magnetic scattering, click here_.
3
4.. _here: polar_mag_help.html
5
6Definition
7----------
8
9The 1D scattering intensity is calculated in the following way (Guinier, 1955)
10
11.. math::
12
13    I(q) = \frac{\text{scale}}{V} \cdot \left[
14        3V(\Delta\rho) \cdot \frac{\sin(qr) - qr\cos(qr))}{(qr)^3}
15        \right]^2 + \text{background}
16
17where *scale* is a volume fraction, $V$ is the volume of the scatterer,
18$r$ is the radius of the sphere, *background* is the background level and
19*sld* and *solvent_sld* are the scattering length densities (SLDs) of the
20scatterer and the solvent respectively.
21
22Note that if your data is in absolute scale, the *scale* should represent
23the volume fraction (which is unitless) if you have a good fit. If not,
24it should represent the volume fraction times a factor (by which your data
25might need to be rescaled).
26
27The 2D scattering intensity is the same as above, regardless of the
28orientation of $\vec q$.
29
30Validation
31----------
32
33Validation of our code was done by comparing the output of the 1D model
34to the output of the software provided by the NIST (Kline, 2006).
35Figure :num:`figure #sphere-comparison` shows a comparison of the output
36of our model and the output of the NIST software.
37
38.. _sphere-comparison:
39
40.. figure:: img/sphere_comparison.jpg
41
42    Comparison of the DANSE scattering intensity for a sphere with the
43    output of the NIST SANS analysis software. The parameters were set to:
44    *scale* = 1.0, *radius* = 60 |Ang|, *contrast* = 1e-6 |Ang^-2|, and
45    *background* = 0.01 |cm^-1|.
46
47
48References
49----------
50
51A Guinier and G. Fournet, *Small-Angle Scattering of X-Rays*,
52John Wiley and Sons, New York, (1955)
53
54*2013/09/09 and 2014/01/06 - Description reviewed by S King and P Parker.*
55"""
56
57from numpy import inf
58
59name = "sphere"
60title = "Spheres with uniform scattering length density"
61description = """\
62P(q)=(scale/V)*[3V(sld-solvent_sld)*(sin(qr)-qr cos(qr))
63                /(qr)^3]^2 + background
64    r: radius of sphere
65    V: The volume of the scatter
66    sld: the SLD of the sphere
67    solvent_sld: the SLD of the solvent
68"""
69category = "shape:sphere"
70
71#             ["name", "units", default, [lower, upper], "type","description"],
72parameters = [["sld", "1e-6/Ang^2", 1, [-inf, inf], "",
73               "Layer scattering length density"],
74              ["solvent_sld", "1e-6/Ang^2", 6, [-inf, inf], "",
75               "Solvent scattering length density"],
76              ["radius", "Ang", 50, [0, inf], "volume",
77               "Sphere radius"],
78             ]
79
80source = ["lib/sph_j1c.c"]
81
82# No volume normalization despite having a volume parameter
83# This should perhaps be volume normalized?
84form_volume = """
85    return 1.333333333333333*M_PI*radius*radius*radius;
86    """
87
88Iq = """
89    const double qr = q*radius;
90    const double bes = sph_j1c(qr);
91    const double fq = bes * (sld - solvent_sld) * form_volume(radius);
92    return 1.0e-4*fq*fq;
93    """
94
95Iqxy = """
96    // never called since no orientation or magnetic parameters.
97    //return -1.0;
98    return Iq(sqrt(qx*qx + qy*qy), sld, solvent_sld, radius);
99    """
100
101def ER(radius):
102    """
103        Return equivalent radius (ER)
104    """
105    return radius
106
107# VR defaults to 1.0
108
109demo = dict(scale=1, background=0,
110            sld=6, solvent_sld=1,
111            radius=120,
112            radius_pd=.2, radius_pd_n=45)
113oldname = "SphereModel"
114oldpars = dict(sld='sldSph', solvent_sld='sldSolv', radius='radius')
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