I take the definition of the Fourier transform of $f \in L^2 (\mathbb{R}^3)$ to be
$$ \widehat{f} (k) = \int\limits_{\mathbb{R}^3} e^{-2 \pi i k \cdot x} f(x) dx $$
Question: Can we say anything useful about $\widehat{|f|}$ in terms of $\widehat{f}$?