We present a theoretical model which allows to keep track of all photons in an interferometer. The model is implemented in a numerical scheme, and we simulate photon interference measurements on one, two, four, and eight slits. Measurements are simulated for the high intensity regime, where we show that our simulations describe all experimental results so far. With a slightly modified concept we can also model interference experiments in the low intensity regime, these experiments have recently been performed with single molecules. Finally, we predict the result of polarization measurements, which allow to check the model experimentally.
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