I found this article at SPIE, thought it would be a good reminder to keep the mind on the physics rather than blindly following the nice mathematical formulas.
The following excerpt gives the physical picture of two-wave interference by focusing on the detection :
"The detecting dipole molecule tries to undulate in response to both superposed EM stimulations. Dark fringes are found where the fields are 180° out of phase because the detecting dipoles cannot undulate in two opposing directions at the same moment. They are not stimulated and hence cannot absorb energy from the fields. The field energy (photons) are not absent from these locations. They simply cannot be absorbed. Bright fringes are found where the two fields stimulate the dipole undulations in phase and in the same direction, maximizing the absorption of energy. The operation or ‘summation’ of amplitudes and phases, represented by the superposition equation, is carried out by the detecting dipoles, not by the two fields themselves. Superposition fringes are locally created by the subnanometer-size detecting molecules!"