.. _guinier:

guinier
=======================================================



========== ================== ======= =============
Parameter  Description        Units   Default value
========== ================== ======= =============
scale      Source intensity   None                1
background Source background  |cm^-1|         0.001
rg         Radius of Gyration |Ang|              60
========== ================== ======= =============

The returned value is scaled to units of |cm^-1| |sr^-1|, absolute scale.


**Definition**

This model fits the Guinier function

.. math::

    I(q) = \text{scale} \cdot \exp{\left[ \frac{-Q^2R_g^2}{3} \right]}
            + \text{background}

to the data directly without any need for linearisation (*cf*. the usual
plot of $\ln I(q)$ vs $q^2$\ ). Note that you may have to restrict the data
range to include small q only, where the Guinier approximation actually
applies. See also the guinier_porod model.

For 2D data the scattering intensity is calculated in the same way as 1D,
where the $q$ vector is defined as

.. math:: q = \sqrt{q_x^2 + q_y^2}


.. figure:: img/guinier_autogenfig.png

    1D plot corresponding to the default parameters of the model.

**References**

A Guinier and G Fournet, *Small-Angle Scattering of X-Rays*,
John Wiley & Sons, New York (1955)