Photoelectron angular distributions (PADs) obtained from ionization of potassium atoms using moderately intense femtosecond IR fields ($sim$10$^{12}$Wcm$^{-2}$) of various polarization states are shown to provide a route to complete photoionization e
xperiments. Ionization occurs by a net 3-photon absorption process, driven via the $4srightarrow4p$ resonance at the 1-photon level. A theoretical treatment incorporating the intra-pulse electronic dynamics allows for a full set of ionization matrix elements to be extracted from 2D imaging data. 3D PADs generated from the extracted matrix elements are also compared to experimental, tomographically reconstructed, 3D photoelectron distributions, providing a sensitive test of their validity. Finally, application of the determined matrix elements to ionization via more complex, polarization-shaped, pulses is demonstrated, illustrating the utility of this methodology towards detailed understanding of complex ionization control schemes and suggesting the utility of such multiplexed intra-pulse processes as powerful tools for measurement.
