Regularity for elliptic pairs over C[[h]]

We extend the results of Schapira and Schneiders on relative regularity and finiteness of elliptic pairs to the framework of $\text{shd}[[\mathrm{\hslash }]]$-modules and $\mathbb{R}$-constructible sheaves of $\text{C}[[\text{h}]]$-modules. We also construct a relative duality morphism for elliptic pairs in the smooth case and we prove that it is an isomorphism if the elliptic pair satisfies the finiteness criteria.