Phase retrieval

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Phase retrieval concerns the solution to the phase problem. Given a complex signal F(k), of amplitude | F(k) | , and phase φ(k):

F(k) = | F(k) | e^iφ(k),

phase retrieval consists in finding the phase that for a measured amplitude satisfies a set of constraints. For example if F(k) is the Fourier transform of f(x), a typical constraint would be that f(x) is a bounded real and positive function.

The most important application of phase retrieval is X-ray crystallography, awarded of several Nobel prizes.

[edit] See also

• Phase problem
• Crystallography
• X-ray crystallography