Theoretical analysis on the characterization of imaging systems using Euclid distance

The Euclid distance derived from the spatial domain distribution function for the performance characterization of imaging systems is presented and theoretically analyzed. The two-dimensional distribution functions of the objects and images, usually quadratically integrable, are investigated. The Euclid distance between the practical image and the ideal image is utilized to comprehensively characterize the imaging system performance. Moreover, the amplitude ratio and the fidelity are defined from the distribution functions of the practical and the ideal image and are related to the Euclid distance, revealing its physical meaning and merits. The geometrical representation of the Euclid distance is also derived and presented. The Euclid distance is monotonous to the performance of imaging systems, thus it can be used readily in the design and optimization of the imaging systems along with its intuitionistic and scalar features.