  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 experiments. Ionization occurs by a net
3-photon absorption process, driven via the $4s\rightarrow4p$ 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.
