High resolution electron microscopy of Bis‐(‐2‐Hydroxyethyl) terephthalate crystalline polymers

Linear and non-linear symmetry properties of Gaussian wave packets

“…4. It can be viewed as a ''black box'' characterized by the so-called transfer function that transforms input functions into output functions [68,69].…”

“…For linear systems, the signal splits up into a linear combination of pulses, so the output signal will be the linear combination of the effect of the system over each individual pulse. The effect over each pulse can be obtained by convolutions or through products of their Fourier transforms via the transfer function [68,69].…”

“…The so-called ''multislice'' method was introduced in transmission electron microscopy (TEM) to determine the transfer function characteristic of a given sample [68,69]. It consists in decomposing the sample into a finite sum of ''slices'' of small width Dz.…”

“…The multislice method supposes that each slice is characterized by different transfer functions that depend on the material composition and of its structure through its refractive index. The advantage of the above method is that each transformation can be represented by a matrix and the problem of finding the output signal of any system is reduced to simple matrix multiplication [68,69] instead of the complicated convolutions used traditionally [70]. Then, to determine the output signal crossing an arbitrary system, it would be enough to know the action of each slice over a Gaussian and to sum over all the components.…”