Most traditional spectral sensors have spectrally adjacent bands with little overlap. This overlap is usually ignored in image processing because band-to-band correlation due to oversampling of the scene is almost always dominant. A new proposed class of adaptive spectral sensor based on bias-tunable quantum-dot infrared photodetectors (QDIPs) are different in that they have significant band-to-band overlaps. The influence of these overlaps to image processing results cannot be ignored for such sensors. To facilitate the analysis of such sensors, a generalized geometry-based model is provided here for spectral sensors with arbitrary spectral responses. It starts from the mathematical description of the interaction between sensor and the radiation from scene reaching it. In this model, the spectral responses of a sensor are used to define a sensor space. The spectral sensing process is shown to represent a projection of scene spectrum onto sensor space. The projected spectrum, which can be calculated through the output photocurrents and sensor's spectral responses, is the least-square error reconstruction of the scene spectrum. With this data interpretation, we can remove the influence of band overlap to the data. The band overlap also introduce correlation between noise of different bands, This correlation is also analyzed.