Compute dynamic image structure function(Dqt) using Fourier transformed intensity profile and a selection of wave number(q) range.
SAM_Dqt(len_q, index_q, len_t, I_q_matrix, q_ori_ring_loc_unique_index, sz)Matrix of dynamic image structure with dimension len_q by len_t-1.
number of wave number
a vector of selected wave number index
number of time steps
intensity profile in reciprocal space (after Fourier transformation)
index for wave vector that give unique frequency
frame size of intensity profile
tools:::Rd_package_author("AIUQ")
Dynamic image structure function(Dqt) can be obtained from ensemble average of absolute values squared of Four transformed intensity difference: $$D(q,\Delta t) = \langle |\Delta \hat{I}(q,t,\Delta t)|^2\rangle$$ See 'References'.
Gu, M., He, Y., Liu, X., & Luo, Y. (2023). Ab initio uncertainty quantification in scattering analysis of microscopy. arXiv preprint arXiv:2309.02468.
Gu, M., Luo, Y., He, Y., Helgeson, M. E., & Valentine, M. T. (2021). Uncertainty quantification and estimation in differential dynamic microscopy. Physical Review E, 104(3), 034610.
Cerbino, R., & Trappe, V. (2008). Differential dynamic microscopy: probing wave vector dependent dynamics with a microscope. Physical review letters, 100(18), 188102.