Coherent Fourier Optics Model for the Synthesis of Large Format Lens Based Focal Plane Arrays

Future sub-millimetre imagers are being developed with large focal plane arrays (FPAs) of lenses to increase the field of view (FoV) and the imaging speed. A full-wave electromagnetic analysis of such arrays is numerically cumbersome and time-consuming. This paper presents a spectral technique based on Fourier Optics combined with Geometrical Optics for analysing, in reception, lens based FPAs with wide FoVs. The technique provides a numerically efficient methodology to derive the Plane Wave Spectrum (PWS) of a secondary Quasi Optical component. This PWS is used to calculate the power received by an antenna or absorber placed at the focal region of a lens. The method is applied to maximize the scanning performance of imagers with monolithically integrated lens feeds without employing an optimization algorithm. The derived PWS can be directly used to define the lens and feed properties. The synthesized FPA achieved scan losses much lower than the ones predicted by standard formulas for horn based FPAs. In particular, a FPA with scan loss below 1dB while scanning up to ±17.5° (~ ± 44 beam-widths) is presented with directivity of 52dBi complying with the needs for future sub-millimetre imagers. The technique is validated via a Physical Optics code with excellent agreement.