# source:sasmodels/sasmodels/models/spherepy.py@b3f6bc3

core_shell_microgelscostrafo411magnetic_modelrelease_v0.94release_v0.95ticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
Last change on this file since b3f6bc3 was b3f6bc3, checked in by pkienzle, 10 years ago

support pure python model Iq/Iqxy?

• Property mode set to 100644
File size: 3.4 KB
Line
1r"""
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
30Our model uses the form factor calculations as defined in the IGOR
31package provided by the NIST Center for Neutron Research (Kline, 2006).
32
33Validation
34----------
35
36Validation of our code was done by comparing the output of the 1D model
37to the output of the software provided by the NIST (Kline, 2006).
38Figure :num:figure #sphere-comparison shows a comparison of the output
39of our model and the output of the NIST software.
40
41.. _sphere-comparison:
42
43.. figure:: img/sphere_comparison.jpg
44
45    Comparison of the DANSE scattering intensity for a sphere with the
46    output of the NIST SANS analysis software. The parameters were set to:
47    *scale* = 1.0, *radius* = 60 |Ang|, *contrast* = 1e-6 |Ang^-2|, and
48    *background* = 0.01 |cm^-1|.
49
50
51Reference
52---------
53
54A Guinier and G. Fournet, *Small-Angle Scattering of X-Rays*,
55John Wiley and Sons, New York, (1955)
56
57*2013/09/09 and 2014/01/06 - Description reviewed by S King and P Parker.*
58"""
59
60from numpy import pi, inf, sin, cos, sqrt
61
62name = "sphere"
63title = "Spheres with uniform scattering length density"
64description = """\
65P(q)=(scale/V)*[3V(sld-solvent_sld)*(sin(qR)-qRcos(qR))
66                /(qR)^3]^2 + background
68    V: The volume of the scatter
69    sld: the SLD of the sphere
70    solvent_sld: the SLD of the solvent
71"""
72
73parameters = [
74#   [ "name", "units", default, [lower, upper], "type",
75#     "description" ],
76    [ "sld", "1e-6/Ang^2", 1, [-inf,inf], "",
77      "Layer scattering length density" ],
78    [ "solvent_sld", "1e-6/Ang^2", 6, [-inf,inf], "",
79      "Solvent scattering length density" ],
80    [ "radius", "Ang",  50, [0, inf], "volume",
82    ]
83
84
87
89    #print "q",q
92    sn, cn = sin(qr), cos(qr)
93    # FOR VECTORIZED VERSION, UNCOMMENT THE NEXT TWO LINES
94    bes = 3 * (sn-qr*cn)/qr**3 # may be 0/0 but we fix that next line
95    bes[qr==0] = 1
96    # FOR NON VECTORIZED VERSION, UNCOMMENT THE NEXT LINE
97    #bes = 3 * (sn-qr*cn)/qr**3 if qr>0 else 1
98    fq = bes * (sld - solvent_sld) * form_volume(radius)
99    return 1.0e-4*fq**2
100# FOR VECTORIZED VERSION, UNCOMMENT THE NEXT LINE
101Iq.vectorized = True
102
103def Iqxy(qx, qy, sld, solvent_sld, radius):
104    return Iq(sqrt(qx**2 + qy**2), sld, solvent_sld, radius)
105Iqxy.vectorized = True
106