  From string theory, the notion of deformed Hermitian Yang-Mills connections
has been introduced by Mari\~no, Minasian, Moore and Strominger. After that,
Leung, Yau and Zaslow proved that it naturally appears as mirror objects of
special Lagrangian submanifolds via Fourier-Mukai transform between dual torus
fibrations. In their paper, some conditions are imposed for simplicity. In this
paper, data to glue their construction on tropical manifolds are proposed and a
generalization of the correspondence is proved without the assumption that the
Lagrangian submanifold is a section of the torus fibration.
