My chemist roommate asked me the following question. Let $f : \mathbb{R} \rightarrow \mathbb{R}$ be a real-valued function and $F$ its Fourier transform. Suppose we know the modulus function $|F| : \mathbb{R} \rightarrow \mathbb{R}$. What can we deduce about $f$, can we determine it completely?

Feel free to assume any regularity conditions on $f$.