Rank two aCM bundles on general determinantal quartic surfaces in ${\mathbb{P}}^3$

Let $F\subseteq {\mathbb{P}}^3$ be a smooth determinantal quartic surface which is general in the N"other-Lefschetz sense. In the present paper we give a complete classification of locally free sheaves $\mathcal{E}$ of rank $2$ on $F$ such that $h^1(F,\mathcal{E}(th))=0$ for $t\in \mathbb{Z}$.