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The diffraction patterns of 1D aperiodic Fibonacci gratings (FGs) are investigated here. We derive a set of simple formulae which allow the finding of the positions and the intensities of the strongest diffraction peaks amongst the infinite ones present inside a given reciprocal space interval , chosen according to a user-defined threshold. In this way the diffraction spectrum of FGs and of their generalizations, generalised Fibonacci gratings (GFGs), can be approximated to a good level as a set of discrete, properly indexed peaks with varying intensity, similarly to what is done for periodic structures. This approach is applied to real cases of GFGs fabricated and tested by two dedicated setups on a substrate of photorefractive Fe: LiNbO3. The experimental results are in excellent agreement with the proposed description and confirm the applicability of our approach.

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