> For every direction where there is destructive interference and a > loss of energy there is a direction where there is constructive > interference that piles up energy. If you integrate over all directions > energy is conserved.
For the total integrated energy to be conserved, energy will have to be created in certain directions to compensate for the loss in other directions. So in a direction in which the condition is met, the total will have to be more than the sum of the waves in that direction. How about considering the possibility that all photons coming into the sample are diffracted -- just in different directions. So that what is happening is not constructive and destructive interference but a kind sorting of the photons based on a certain property of the photons, maybe the phase.
