Filter width affects the transmittance of patterned all-dielectric Fabry-Perot filters

Thin-film all-dielectric Fabry-Perot filters can nowadays be patterned onto pixels of commercial imaging sensors used for spectral imaging. For these patterned filters, standard transfer-matrix thin-film calculations fail to predict their angular dependency. This Letter attributes the discrepancy to the finite filter size and is also, to my knowledge, the first study to analyze this for patterned all-dielectric Fabry-Perot filters. An angular spectrum approach that enables prediction without full knowledge of the filter design is introduced. In addition, the contribution of diffraction at normal incidence is characterized by a single dimensionless parameter. Knowing that patterned filter size matters and having a method to efficiently simulate its effect can guide ongoing miniaturization efforts and filter design.