Finding a conformal map between an irregular region between two disks and an annulus

If I am given a region $R$ defined as the the region between a unit disk $D_1(0)$ and $D_{ \frac{1}{4}}$$(\frac{1}{4})$, what is a strategy to conformally map this to an annulus $a \lt z \lt 1$? Specifically, where does the constraint on $a$ come from?

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This is very similar to math.stackexchange.com/questions/238205/… –  copper.hat Nov 16 '12 at 6:22
Thank you for this. –  tacos_tacos_tacos Nov 16 '12 at 9:03