Fundamental limit for gain and resolution in analog optical edge detection

In this paper, the relation between gain and resolution of an ideal analog optical differentiator in two different cases and their fundamental limits are investigated. Based on this relation, a figure of merit for comparison of the designed differentiators in recent papers is proposed. The differentiators are optimized using this figure of merit, and they are compared with each other to determine the best one. Also, a new differentiator is presented based on the dielectric slab waveguide in which the trade-off between its gain and resolution is easily controllable, and its best operating point is determined.