We show that the affine surface area as(∂K) of a convex body K in ${ℝ}^n$ can be computed as $as\left(\partial K\right)=li{m}_{\delta \to 0}{d}_n(vo{l}_n\left(K^{\delta }\right)-vo{l}_n\left(K\right))/\left({\delta }^{2/(n+1)}\right)$ where $d_n$ is a constant and $K^{\delta }$ is the illumination body.