  For a nondegenerate homogeneous polynomial $f\in\mathbb{C}[z_0, \dots,
z_{n+1}]$ with degree $n+2$, we can obtain a $tt^*$ structure from the
Landau-Ginzburg model $(\C^{n+2}, f)$ and a (new) $tt^*$ structure on the
Calabi-Yau hypersurface defined by the zero locus of $f$ in $\C P^{n+1}$. We
can prove that the big residue map considered by Steenbrink gives an
isomorphism between the two $tt^*$ structures. We also build the correspondence
for non-Calabi-Yau cases, and it turns out that only partial structure can be
preserved. As an application, we show that the $tt^*$ geometry structure of
Landau-Ginzburg model on relavant deformation space uniquely determines the
$tt^*$ geometry structure on Calabi-Yau side. This explains the folklore
conclusion in physical literature. This result is based on our early work
\cite{FLY}.
