  Realistic attosecond wave packets have complex profiles that, in dispersive
conditions, rapidly broaden or split into multiple components. Such behaviors
are encoded in sharp features of the wave packet spectral phase. Here, we
exploit the quantum beating between one- and two-photon transitions in an
attosecond photoionization experiment to measure the photoelectron spectral
phase continuously across a broad energy range. Supported by numerical
simulations, we demonstrate that this experimental technique is able to
reconstruct sharp fine-scale features of the spectral phase, continuously as a
function of energy and across the full spectral range of the pulse train, thus
beyond the capabilities of existing attosecond spectroscopies. In a
proof-of-principle experiment, we retrieve the periodic modulations of the
spectral phase of an attosecond pulse train due to the individual chirp of each
harmonic.
