If $f(x)=\sin \left(\cos ^{-1}\left(\frac{1-2^{2 x}}{1+2^{2 x}}\right)\right)$ and its firs t derivative with respect to $x$ is $-\frac{b}{a} \log _e 2$ when $x=1$, where $a$ and $b$ are integers, then the minimum value of $\mid a^2- b^2 \mid$ is $\_\_\_\_$ .
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