The Strominger-Yau-Zaslow programme says that there should be a theory of fiberwise Fourier transforms along special Lagrangian fibrations which would explain mirror symmetry. This programme has been verified successfully in special cases when quantum corrections do not arise. In this article we will describe a theory of Fourier transforms of flat branes on tori and how it can be applied in the family setting. And in certain special circumstances this explains quantum corrections in SYZ transformations.