Figure 4:

Top: f_δ,ζ(x, y, x₀, y₀) image obtained with a fixed (x₀, y₀) = (0, 0) and various ζ. Middle: k(x, y, z = 0, x₀, y₀, z₀ = 0) computed with various $r_0=\sqrt{x_0^2+y_0^2}$. Bottom: K(x−x₀, y−y₀, 0) along y = 0 (left-most), x = 0 (second to left) and diagonal (middle) directions. Second to right: Blurring kernel K(x−x₀, y−y₀, 0). Right-most: Blurring kernel K(0, 0, z − z₀).