Malgrange has written a book called "Equation differentielles a coefficients polynomiaux". The whole book is about the compatiblity of the topological Fourier transform and the Fourier-Laplace transform of D-modules in dimension 1 (even for irregular holonomic D-modules).

In the G_m equivariant, i.e. monodromic, setting, the topological Fourier transform is the Fourier-Sato transform and the compatiblity is considered well known is arbitrary but I don't know any reference.

Malgrange has written a book called "Equation differentielles a coefficients polynomiaux". The whole book is about the compatiblity of the topological Fourier transform and the Fourier-Laplace transform of D-modules in dimension 1 (even for irregular holonomic D-modules).

In the G_m equivariant, i.e. monodromic, setting, the topological Fourier transform is the Fourier-Sato transform and the compatiblity is considered well known but I don't know any reference for it.

PS: This article of L. Daia generelasizes Malgrange's results to higher dimensional vector spaces.