We investigate atomic ionization driven by an attosecond broadband XUV pulse and streaked by a phase-locked IR field. The resulting set of streaking spectrograms, comprising sequences of photoelectron spectra recorded at varying XUV or IR delays is analyzed to retrieve the XUV photoionization phase and the associated atomic time delay. By applying a rainbow-style timing analysis to the full streaking trace, we extract the phase and time delay continuously across a wide range of photoelectron energies. We illustrate the method for ionization of He $1s$, Ar $3p$, and Xe $4d$. In helium, the near-threshold delay is dominated by the Coulomb phase, with an offset introduced by Coulomb-laser coupling in the IR field. In argon and xenon, the retrieved time delays resolve the characteristic features of the Cooper minimum and the giant shape resonance, respectively. These features are canonical examples of strong, correlation- and structure-driven phase variations in photoionization and their associated time-delay signatures. Our results are benchmarked against conventional narrowband streaking and reconstruction of attosecond beating by interference of two-photon transitions, demonstrating that rainbow streaking provides a robust and unified route to broadband phase and time-delay reconstruction.

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• Atomic & molecular processes in external fields
• Multiphoton or tunneling ionization & excitation