Fluorescent semiconductor nanoplatelets (epitaxial quantum wells) can be synthesized with excellent monodispersity and self-assembled in highly-ordered structures. Modifications of their electronic and luminescence properties when stacked, due to strong mechanical, electronic or optical interactions between them, have been the topic of intense recent discussions. In this paper, we use Fourier imaging to measure the different dipole components of various nanoplatelet assemblies. By comparing different measurement conditions and corroborating them with polarimetric analysis, we confirm an excellent precision on the dipole components. For single nanoplatelets, only in-plane dipoles (parallel to the platelet plane) are evidenced. For clusters of 2-10 platelets and chains of 30-300 platelets, on the other hand, a clear out-of-plane dipole component is demonstrated. Its contribution becomes more significant as the number of platelets is increased. We review possible explanations and suggest that the added out-of-plane dipole can be induced by strain-induced nanoplatelet deformations.