Photoionization of molecular species is, essentially, a multi-path interferometer with both experimentally controllable and intrinsic molecular characteristics. In this work, XUV photoionization of impulsively aligned molecular targets (N2) is used to provide a time-domain route to "complete" photoionization experiments, in which the rotational wavepacket controls the geometric part of the photoionization interferometer. The data obtained is sufficient to determine the magnitudes and phases of the ionization matrix elements for all observed channels, and to reconstruct molecular frame interferograms from lab frame measurements. In principle this methodology provides a timedomain route to complete photoionization experiments, and the molecular frame, which is generally applicable to any molecule (no prerequisites), for all energies and ionization channels.Photoionization is an interferometric process, in which the final observable results from a coherent sum over multiple quantum paths to a set of final continuum photoelectron states |k, l, m [1,2]. Interferences between these components are manifest in the observable energy spectra and photoelectron angular distributions (PADs) [2][3][4], the latter of which can be considered as a particularly high information content observable, extremely sensitive to the phases of the partial waves |l, m [4, 5]; consequently, PADs have been investigated in a large range of control and metrology scenarios [6,7] . In the context of phase-sensitive metrology, the goal is to obtain the full set of complex photoionization matrix elements, hence characterise the photoelectron wavefunction, by analysis of sets of PAD measurements -this is a "complete" photoionization experiment [8,9].In the molecular case, the number of final |l, m states is typically large, and obtaining a sufficient dataset for a complete experiment remains a challenge. In the energy domain, a number of different schemes have been demonstrated in both the laboratory (LF) and molecular frames (MF) [10][11][12][13][14][15][16]. The common theme to all these measurements is some form of control over the experimental contributions to the photoionization interferometer (e.g. rotational state, polarization geometry), to which the intrinsic molecular contributions remain invariant. The difficulties in such cases are the ability to obtain a sufficiently large dataset, and molecular specificity in the methodologies, i.e. prerequisites such as low density of states [14], resonances [15] or dissociative channels [11][12][13].In the time-domain, rotational wavepackets can be utilized to control the geometric part of the interferometer. In this case, a high degree of spatio-temporal control of the axis distribution (alignment) of the ionizing molecular ensemble in the LF can be obtained via preparation of a broad rotational wavepacket. Although this idea is conceptually obvious, the theory is complex; it has been elucidated by multiple authors (e.g. refs. [5,[17][18][19][20][21]), but -to date -there have been no experimental d...

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