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Multispectral image acquisition considerably improves color accuracy in comparison to RGB technology. A common multispectral camera design concept features a filter-wheel consisting of six or more optical bandpass filters. By shifting the filters sequentially into the optical path, the electromagnetic spectrum is acquired through the channels, thus making an approximate reconstruction of the spectrum feasible. However, since the optical filters exhibit different thicknesses, refraction indices and may not be aligned in a perfectly coplanar manner, geometric distortions occur in each spectral channel: The reconstructed RGB images thus show rainbow-like color fringes. To compensate for these, we analyze the optical path and derive a mathematical model of the distortions. Based on this model we present two different algorithms for compensation and show that the color fringes vanish completely after application of our algorithms. We also evaluate our compensation algorithms in terms of accuracy and execution time.