2. As shown in the figure, two identical sectors $OAB$ and $O^{\prime}A^{\prime}B^{\prime}$ overlap, with central angles of $90^{\circ}$ and radii of $1$. Points $P$ and $Q$ are the midpoints of $OA$ and $O^{\prime}B^{\prime}$, respectively. The area difference between regions $S_{1}$ and $S_{2}$ in the figure is ( ).
A. $\frac{3 \sqrt{3}}{4}-\frac{\pi}{3}$
B. $\frac{3 \sqrt{3}}{4}-\frac{\pi}{6}$
C. $\frac{3 \sqrt{3}}{8}-\frac{\pi}{6}$
D. $\frac{3 \sqrt{3}}{4}+\frac{\pi}{6}$
E. $\frac{3 \sqrt{3}}{8}+\frac{\pi}{6}$
$\mathrm{C}$