Focal plane filter array engineering I: Rectangular lattices

Focal planes arrays (FPA) measure values proportional to an integrated irradiance with little sensitivity to wavelength or polarization in the optical wavelength range. The measurement of spectral properties is often achieved via a spatially varying color filter array. Recently, spatially varying polarization filter arrays have been used to extract polarization information. Although measurement of color and polarization utilize separate physical methods, the underlying design and engineering methodology is linked. In this communication we derive a formalism which can be used to design any type of periodic filter array on a rectangular lattice. A complete system description can be obtained from the number of unit cells, the pixel shape, and the unit cell geometry. This formalism can be used to engineer the channel structure for any type of periodic tiling of a rectangular lattice for any type of optical filter array yielding irradiance measurements.