That filters dependent on interference effects show shifts with angle of incidence of the illumination has long been known and was even usefully employed more than a century ago by Pérot and Fabry. Later, in the 1950s and 1960s, there was a number of analytical studies of aspects of the effect. Then came the digital age where almost everything gets shoveled into a computer that virtually immediately spits out an answer. You might have thought you had seen the last of any analytical study of the topic. However, computing studies mostly yield empirical understanding while analytical understanding needs analytical methods. That is why this beautiful analysis in the Goossens, Geelen, Pichette, Lambrechts, and Van Hoof paper is so important. The system it examines is a wide-angle image on a detector array including narrowband filter elements for spectral sensing. Each element receives a cone of illumination with its cross section defined by a circular pupil parallel to the array, thus not quite our usual cone, and the response of the spectral sensing element moves from its reference value. The analysis is not for the faint hearted, but we can rely on it because of some careful experimental verification that is fully reported. Apart from the understanding, why is this significant? There are many, and growing, applications of spectral imaging, from remote sensing to medicine, and this effect, especially over wide angles, causes spectral shifts, reducing the effectiveness of the method. Since an analytical analysis now exists, an analytical approach to spectral correction can also exist, and this is convincingly demonstrated in the final section of the paper. And, lastly, there is the hint of further work to include vignetting.
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