Modeling and compensation of geometric distortions of multispectral cameras with optical bandpass filter wheels

TLDR: A mathematical model is derived for the effects of chromatic aberration that robustly estimates the parameters of an appropriate affine coordinate transformation of multispectral cameras for high-fidelity colour reproduction.

Abstract: High-fidelity colour reproduction requires multispectral cameras for image acquisition, which, unlike RGB cameras, divide the visible electromagnetic spectrum into more than 3 channels. This can be achieved by successively placing narrow-band optical filters with different passbands between object lens and sensor of a standard b/w camera. The filters are arranged on a filter wheel, the rotation of which moves the filters sequentially into the optical path. In practice, these filters exhibit different thicknesses and refraction indices, and are also not perfectly coplanar, resulting in geometric distortions between the recorded spectral components. We derive a mathematical model for these distortions. We additionally measure the effects of chromatic aberration, and incorporate these into our model. Based on this model, we then develop a registration algorithm which robustly estimates the parameters of an appropriate affine coordinate transformation. Experimental results using a seven-channel multispectral camera confirm both the validity of our model as well as the accuracy of the registration algorithm.