.. _two-lorentzian: two_lorentzian ======================================================= This model calculates an empirical functional form for SAS data characterized by two Lorentzian-type functions. ================ ============================================= ======= ============= Parameter Description Units Default value ================ ============================================= ======= ============= scale Scale factor or Volume fraction None 1 background Source background |cm^-1| 0.001 lorentz_scale_1 First power law scale factor None 10 lorentz_length_1 First Lorentzian screening length |Ang| 100 lorentz_exp_1 First exponent of power law None 3 lorentz_scale_2 Second scale factor for broad Lorentzian peak None 1 lorentz_length_2 Second Lorentzian screening length |Ang| 10 lorentz_exp_2 Second exponent of power law None 2 ================ ============================================= ======= ============= The returned value is scaled to units of |cm^-1| |sr^-1|, absolute scale. **Definition** The scattering intensity $I(q)$ is calculated as .. math:: I(q) = \frac{A}{1 +(Q\xi_1)^n} + \frac{C}{1 +(Q\xi_2)^m} + \text{B} where $A$ = Lorentzian scale factor #1, $C$ = Lorentzian scale #2, $\xi_1$ and $\xi_2$ are the corresponding correlation lengths, and $n$ and $m$ are the respective power law exponents (set $n = m = 2$ for Ornstein-Zernicke behaviour). 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/two_lorentzian_autogenfig.png 1D plot corresponding to the default parameters of the model. **Source** :download:`two_lorentzian.py ` **References** None. **Authorship and Verification** * **Author:** NIST IGOR/DANSE **Date:** pre 2010 * **Last Modified by:** Piotr rozyczko **Date:** January 29, 2016 * **Last Reviewed by:** Paul Butler **Date:** March 21, 2016