Ensquared Energy and Optical Centroid Efficiency in Optical Sensors: Part 1, Theory

High-performance megapixel focal plane arrays with small pixels have been widely used in modern optical remote sensing, astronomical, and surveillance instruments. In the prediction models applied in the traditional instrument performance analysis, the image of a point source is assumed to fall on the center of a detector pixel. A geometrical image of a point source in the realistic optical system may actually fall on any position on the detector pixel because the sensor's line of sight includes pointing errors and jitter. This traditional assumption may lead to an optimistic error, estimated at between 10% and 20%. We present the critical factors that impact the performance estimate in a realistic instrument design based on the prediction for the noise-equivalent power (NEP). They are the optical centroid efficiency (OCE) and the ensquared energy, or more precisely, the energy on the rectangular detector pixel (EOD). We performed the simulation studies for imaging with an optical system with and without a generalized rectangular central obscuration.