Spectral cameras with integrated thin-film Fabry-Perot filters enable many different applications. Some applications require the detection of spectral features that are only visible at specific wavelengths, and some need to quantify small spectral differences that are undetectable with RGB color cameras. One factor that influences the central wavelength of thin-film filters is the angle of incidence. Therefore, when light is focused from an imaging lens onto the filter array, undesirable shifts in the measured spectra are observed. These shifts limit the use of the sensor in applications that require fast lenses or lenses with large chief ray angles. To increase flexibility and enable new applications, we derive an analytical model that explains and can correct the observed shifts in measured spectra. The model includes the size of the aperture and physical position of each filter on the sensor. We experimentally validate the model with two spectral cameras: one in the visible and near-infrared region and one in the short wave infrared region.