On the existence of certain one-to-one analytic function

On the existence of certain one-to-one analytic function

I am wondering if there exists any one-to-one analytic function mapping
annulus to punctuated disk? i.e. if we let $D_1=\{1/2<|z|<1\},
D_2=\{0<|z|<1\}$, is there a one-to-one analytic function $f$ maps $D_1$
to $D_2$?