  The intergalactic helium became fully ionized by the end of cosmic noon
($z\sim2$). Similarly to the reionization of hydrogen, helium reionization is
expected to be patchy, driven by luminous quasars that ionize the intergalactic
gas in their surrounding environment. Probing the morphology of ionized
electrons during this epoch can provide crucial information about early
structure formation, including the clustering and luminosities of quasars, the
accretion rates, variability, and lifetimes of active galactic nuclei, as well
as the growth and evolution of supermassive black holes. In this study, we
present how measurements of the cosmic microwave background (CMB) can be used
to reconstruct the optical-depth fluctuations resulting from patchy helium
reionization. As helium reionization occurred at lower redshifts, upcoming
probes of large-scale structure surveys will present a significant opportunity
to enhance the prospects of probing this epoch by their combined analysis with
the CMB. Using a joint information-matrix analysis of hydrogen and helium
reionization, we show that near-future galaxy and CMB surveys will have enough
statistical power to detect optical-depth fluctuations due to doubly-ionized
helium, providing a way of measuring the redshift and duration of helium
reionization to high significance. We also show that modeling uncertainties in
helium reionization can impact the measurement precision of parameters
characterizing hydrogen reionization.
