Spectral cameras with integrated thin-film Fabry-Perot filters have become increasingly important in many applications. These applications often require the detection of spectral features at specific wavelengths or to quantify small variations in the spectrum. This can be challenging since thin-film filters are sensitive to the angle of incidence of the light. In prior work, we modeled and corrected for the distribution of incident angles for an ideal finite aperture. Many real lenses, however, experience vignetting. Therefore, in this paper, we generalize our model to the more common case of a vignetted aperture, which changes the distribution of incident angles. We propose a practical method to estimate the model parameters and correct undesired shifts in measured spectra. This is experimentally validated for a lens mounted on a visible-to-near-infrared spectral camera.