Velocity map imaging and its time derivative

The information contained in the energy-dependent photoelectron angular distributions Pk 0k, tpr) [Eq. (3.93)] may be conveniently visualized as velocity map images. Examples will be given in Sec. 5.4. Comparison of such images across different delay times tpr reveal the time evolution of the system. 

When the system undergoes fast (or somewhat sudden) evolution, such d Tiamics reflected in the velocity map image can be more sensitively extracted in terms of its time derivatives. Time derivatives of the image can be computed from Pk 0k, tpi) using finite differences using a small time shift r, 

Chemical Theory Beyond the Born-Oppenheimer Paradigm 

Note that the time-derivative is to be taken with respect to the change of the time-delay between the pump and probe lasers, tpr, and not with respect to t. An example will be shown in Secs. 5.4.2.4 and 5.4.3.3, illustrating that time-derivative photoelectron velocity map imaging can be quite helpful in uncovering and/or identifying useful characteristics of wavepacket motion, which may otherwise be overlooked in the original images. 

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