If $f\left(x\right)={\sin }^2\left(\frac{{\displaystyle \pi }}{{\displaystyle 8}}+\frac{{\displaystyle x}}{{\displaystyle 2}}\right)-{\sin }^2\left(\frac{{\displaystyle \pi }}{{\displaystyle 8}}-\frac{{\displaystyle x}}{{\displaystyle 2}}\right)$, then the period of f is

• A

  $\pi$

• B

  $\frac{\pi }{2}$

• C

  $\frac{\pi }{3}$

• D

  $2\pi$