Multispectral filter wheel cameras: modeling aberrations for filters in front of lens

Aberrations occur in multispectral cameras featuring filter wheels because of color filters with different optical properties being present in the ray path. In order to ensure an exact compensation of these aberrations, a mathematical model of the distortions has to be developed and its parameters have to be calculated using the measured data. Such a model already exists for optical filters placed between the sensor and the lens, but not for bandpass filters placed in front of the lens. For this configuration, the rays are first distorted by the filters and then by the lens. In this paper, we derive a model for aberrations caused by filters placed in front of the lens in multispectral cameras. We compare this model with distortions obtained with simulations as well as with distortions measured during real multispectral acquisitions. In both cases, the difference between modeled and measured aberrations remains low, which corroborates the physical model. Multispectral acquisitions with filters placed between the sensor and the lens or in front of the lens are compared: the latter exhibit smaller distortions and the aberrations in both images can be compensated using the same algorithm.