Top: number of black hole shadows with angular sizes larger than an angular resolution threshold θ_r and total flux densities larger than a sensitivity threshold σ_ν, as a function of the threshold values and assuming an observing frequency of 230 GHz; that is, N(θ_r, σ_ν) from Equation (7). The solid contours start with the thick contour indicating a count of N = 1 and then increase by factors of 10 toward the lower left, while the dashed contours each decrease by a factor of 10 toward the upper right. Bottom: same as the top panel, but with the additional restriction that the sources must be optically thin.