Spatial aliasing errors comparison and non-uniform sampling in optical imaging

Sampling is how data is collected, used, and stored in this day and age. Having the correct sampling, not too high, not too low, is imperative for high collection speed, an increase in today's neural network speed, a lower power consumption, particularly when used in real-time on-board feedback systems, and a reduction in overall storage, all while maintaining an acceptable error limit as required (e.g., by a neural network). This paper explicitly shows the aliasing error, an error due to insufficient sampling, compares this with existing aliasing error formulae, and the "2% aliasing error" rule-of-thumb is accommodated. Further, the reconstruction (interpolation) function, akin to Shannon's, for a fixed non-uniform sampling is generated and its aliasing error is calculated and, again, it is compared with its derived aliasing error formula. Finally, a comparison between the two sampling schemes is discussed, showing that uniform sampling is advantageous over bunched non-uniform sampling from an aliasing error perspective.