Ensquared Energy and Optical Centroid Efficiency in Optical Sensors: Part 2, Primary Aberrations

We previously proposed that the optical centroid efficiency (OCE) might be a preferred figure-of-merit to the enclosed energy of a rectangular pixel (EOD) for an instrument subject to unpredictable environmental jitter and alignment conditions. Here we follow the same symbols for the corresponding quantities, particularly the width of the pixel as being equal to 2d. Here we analyze the performance of the OCE vs. the EOD for the three Seidel primary aberrations of an optical component: spherical, coma, and astigmatism, plus defocus. We show that the OCE has an approximate U-shape when graphed against the EOD, for the aberrations ranging from 0 to 1.25λ. We conclude that for pixels larger than 2d = 3λF/#, a small pixel will feature better performance when expecting jitter, misalignment, and other environmental and unpredictable conditions. When evaluating the performance of low-aberration instruments in dynamic and unpredictable environments, the choice of the lager pixel 2d = 7λF/# might be advantageous. Its selection will result in the deterioration of image resolution.