Wide-angle narrow-bandpass optical detection system optimally designed to have a large signal-to-noise ratio

A method for achieving optimal design of a wide-angle narrow-bandpass optical detection system composed of a spherical interference filter and a circular photodetector is introduced. It was found that there is an optimal photodetector diameter that maximizes the signal-to-noise ratio (SNR) for a given filter configuration. We show how to optimize optical detection systems based on spherical interference filters for all the important parameters simultaneously. The SNR values of these systems are compared with the SNR values of spherical-step-filter-based detection systems. When large silicon photodetectors are used, the two systems have equal SNR values so that the more economical step-filter systems are preferable. The results given here in the near-infrared region can be used for the optimization of any configuration of a detection system based on a spherical interference filter and a silicon photodetector working at the same wavelength range, without further calculations.