  The aim of this paper is to rigorously establish the
Calabi-Yau/Landau-Ginzburg (CY/LG) correspondence for the $tt^*$ geometry
structure--a generalized version of variation of Hodge structures. Although it
is well-known that there exists a map between Hodge structures on the LG and
CY's sides that preserves the Hodge filtration and bilinear form, it remains
unclear whether the real structures are also preserved. In our paper, we
conduct a detailed analysis of two period integrals on the LG's side. Based on
this analysis, we modify the real structure proposed by Cecotti on LG's side,
and show that the aforementioned map is also preserved under the modified real
structure. As a result, we establish full CY/LG correspondence for $tt^*$
structures.
