PyDDM.ddm_calc.get_MSD_from_DDM_data

PyDDM.ddm_calc.get_MSD_from_DDM_data#

get_MSD_from_DDM_data(q, A, D, B, qrange_to_avg)#

Finds the mean squared displacement (MSD) from the DDM matrix as well as values for the amplitude (A) and background (B). Uses the method described in the papers below. [1] [2]

\[MSD(\Delta t) = \frac{4}{q^2} \ln \left[ \frac{A(q)}{A(q)-D(q,\Delta t)+B(q)} \right]\]
Parameters:
  • q (array) – 1D array of the magnitudes of wavevectors

  • A (array) – Array of same size as q of the amplitude

  • D (array) – 2D array containing the DDM matrix

  • B (array or float) – Background

  • qrange_to_avg (array_like) – 2-element array or list.

Returns:

  • msd_mean (array) – Mean squared displacment, averaged over the range of q values specified

  • msd_stddev (array) – Standard deviation of the mean squared displacements

References