Changeset 19dcb933 in sasmodels for sasmodels/models/sphere.py

Timestamp:

Sep 3, 2014 1:16:10 AM (10 years ago)

Author:

Paul Kienzle <pkienzle@…>

Branches:

master, core_shell_microgels, costrafo411, magnetic_model, release_v0.94, release_v0.95, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests

Children:

1c7ffdc

Parents:

87985ca

Message:

build docs for models

File:

• sasmodels/models/sphere.py (modified) (2 diffs)

sasmodels/models/sphere.py

@@ -1 +1 @@
 r"""
+For information about polarised and magnetic scattering, click here_.
 
+.. _here: polar_mag_help.html
+
+Definition
+----------
+
+The 1D scattering intensity is calculated in the following way (Guinier, 1955)
+
+.. math::
+
+    I(Q) = \frac{\text{scale}}{V} \cdot \left[ \
+        3V(\Delta\rho) \cdot \frac{\sin(QR) - QR\cos(QR))}{(QR)^3} \
+        \right]^2 + \text{background}
+
+where *scale* is a volume fraction, $V$ is the volume of the scatterer,
+$R$ is the radius of the sphere, *background* is the background level and
+*sld* and *solvent_sld* are the scattering length densities (SLDs) of the
+scatterer and the solvent respectively.
+
+Note that if your data is in absolute scale, the *scale* should represent
+the volume fraction (which is unitless) if you have a good fit. If not,
+it should represent the volume fraction times a factor (by which your data
+might need to be rescaled).
+
+The 2D scattering intensity is the same as above, regardless of the
+orientation of $\vec q$.
+
+Our model uses the form factor calculations as defined in the IGOR
+package provided by the NIST Center for Neutron Research (Kline, 2006).
+
+Validation
+----------
+
+Validation of our code was done by comparing the output of the 1D model
+to the output of the software provided by the NIST (Kline, 2006).
+Figure :num:`figure #sphere-comparison` shows a comparison of the output
+of our model and the output of the NIST software.
+
+.. _sphere-comparison:
+
+.. figure:: img/sphere_comparison.jpg
+
+    Comparison of the DANSE scattering intensity for a sphere with the
+    output of the NIST SANS analysis software. The parameters were set to:
+    *scale* = 1.0, *radius* = 60 |Ang|, *contrast* = 1e-6 |Ang^-2|, and
+    *background* = 0.01 |cm^-1|.
+
+
+Reference
+---------
+
+A Guinier and G. Fournet, *Small-Angle Scattering of X-Rays*,
+John Wiley and Sons, New York, (1955)
+
+*2013/09/09 and 2014/01/06 - Description reviewed by S King and P Parker.*
 """
 
@@ -6 +61 @@
 
 name = "sphere"
-title = "Spheres with uniform SLD"
+title = "Spheres with uniform scattering length density"
 description = """\
-        [Sphere Form Factor]
+P(q)=(scale/V)*[3V(sld-solvent_sld)*(sin(qR)-qRcos(qR))
+                /(qR)^3]^2 + background
+    R: radius of sphere
+    V: The volume of the scatter
+    sld: the SLD of the sphere
+    solvent_sld: the SLD of the solvent
 """