Dynamics of electrons underlie various processes in matter. For example, a chemical reaction starts from rearrangements of electrons or the process of conversion of light into electricity starts from excitation of electrons by light. Capturing the behavior of electrons during transformations would help to influence and control technologically relevant processes. But this is a non-trivial task, since time scales of electronic motion lie between one trillionth and one quadrillionth of a second (10^-18 … 10^-15 sec), and relevant spatial scales, which are interatomic distances, are on a nanometer scale.

It is indeed possible to measure electron dynamics experimentally by means of ultrashort light pulses. A signal from an ultrashort light pulse provides a snapshot of an electronic state at a time of measurement. We theoretically describe how to reveal information about electron dynamics from such signals.