# Multidimensional Analysis of Time-Resolved Charged Particle Imaging Experiments
## 4 Case Example: Analysis of a Femtosecond Pump-Probe VMI Experiment  
In this section, we illustrate the strategy described in Sections 2 and 3 to the analysis of an experimental image sequence obtained in a femtosecond pump-probe VMI experiment. We take as an example the photodissociation of CH\({}_{3}\)I in the \(B\)-band, using a 201.2 nm femtosecond pump laser pulse where the appearance of the I*(\({}^{2}P_{1/2}\)) fragment is probed by \((2+1)\) resonance enhanced multiphoton ionization (REMPI) with an ultrashort 305 nm laser pulse [38]. The dissociative mechanism of CH\({}_{3}\)I in the \(B\)-band is relatively simple and consists of an electronic predissociation process [39; 40; 41; 42]. The absorption of one pump photon at 201.2 nm excites the CH\({}_{3}\)I molecule from the electronic ground state into a bound Rydberg state in the ground vibrational state (\(0^{0}_{0}\) transition). This Rydberg state is crossed by a repulsive potential energy surface (PES) belonging to the \(A\)-band, which correlates with CH\({}_{3}\) and I*(\({}^{2}P_{1/2}\)) fragments [43]. The initial population in the Rydberg state can be transferred into the repulsive PES with an efficiency that depends on the coupling between the two surfaces. Once the transfer is done, the dissociation of the molecule occurs in tens of femtoseconds producing CH\({}_{3}\) and I*(\({}^{2}P_{1/2}\)). When the iodine atom is created, it can be resonantly ionized by the probe pulse using a \((2+1)\) REMPI scheme. The ionized fragments are accelerated by an external static electric field and focalized onto a microchannel plate coupled with a phosphor screen. The VMI-image (i.e., the Abel projection of the Newton sphere) is then recorded by a 12-bit Peltier cooled CCD camera. A set of images is recorded as a function of the pump-probe delay time. Each image is numerically inverted using an Abel inversion procedure [28] to retrieve the 3D velocity distribution of fragments as shown in Figure 4a,c. See Ref. [38] for further details. As usual in VMI experiments, each image contains information about the fragment velocity and angular distributions. Typically, a number of well defined rings representing the velocity-angle distribution of given photodissociation channels can be observed in the images. In the present case, the time and anisotropy evolution of one ring is clearly observed in the sequence of images. The amplitude of the signal of the ring depends on the number of iodine ions that are detected. The width of this contribution directly depends on the rovibrational temperature of the initial molecule and that of the CH\({}_{3}\) co-fragment, convoluted by the imaging apparatus resolution. The exact shape of the curve of the velocity distribution can be quite complicated; nevertheless, it can be reasonably approximated by Boltzmann, Gaussian or Lorentzian functions. In this experiment, the main ring can be modeled as the sum of two Gaussian functions, which represents the CH\({}_{3}\) co-fragment in the ground vibrational state (\(\
u=0\)) and with one quantum of vibrational excitation in the symmetric stretch mode (\(\
u_{1}=1\)). The temporal behavior expected for the relaxation of population can be modeled by an exponential function, as shown in Equation (5). The anisotropy of a single linearly polarized photon phenomenon can be described by the second Legendre polynomial, considering \(\beta_{2}\) as the only non-zero coefficient in Equation (2). The value of \(\beta_{2}\) primarily depends on the angular nature of the transition, i.e., whether the transition dipole moment is parallel or perpendicular to the dissociation axis. For the parallel case, \(\beta_{2}>0\) with a maximum value of \(\beta_{2}=2\); for the perpendicular case, \(\beta_{2}<0\) with an extreme value of \(\beta_{2}=-1\). Both theoretical calculations and experiments for CH\({}_{3}\)I have shown that the transition from the electronic ground state to the \(B\)-band is of perpendicular nature.