Let $S_1=(x,y)|{\log }_2(1+x^2+y^2)\le 1+{\log }_2(x+y)$ and $S_2=(x,y)|{\log }_2(2+x^2+y^2)\le 2+{\log }_2(x+y)$. What is the ratio of the area of $S_2$ to the area of $S_1$?