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A theory and method for a matrix-based reconstruction of molecular frame (MF) photoelectron angular distributions (MFPADs) from laboratory frame (LF) measurements (LFPADs) is developed and basic applications are explored. As with prior studies of MF reconstruction, the experimental side of this protocol is based upon time-resolved LF measurements in which a rotational wavepacket is prepared and probed as a function of time via photoionization, followed by a numerical reconstruction routine. In contrast to other methodologies, the protocol presented here does not require determination of the photoionization matrix elements, and consequently takes the relatively simple numerical form of a matrix equation. Significantly, this simplicity allows the successful reconstruction of MFPADs for nonlinear polyatomic molecules with D nh point group symmetry. We numerically demonstrate this scheme for two realistic molecular photoionization cases: N 2 and C 2 H 4 . This new technique is expected to be generally applicable to a broad range of MF reconstruction problems involving photoionization of polyatomic molecules.

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