Phasenrückgewinnung

Phasenrückgewinnung, also known as phase recovery or phase retrieval, is a computational technique used to reconstruct the phase of a signal from its magnitude. In many imaging and signal processing applications, such as X-ray crystallography, microscopy, and holography, direct measurement of the phase is difficult or impossible. However, the phase information is crucial for reconstructing a complete and accurate representation of the object or signal. Phasenrückgewinnung algorithms aim to infer this missing phase information using a series of measurements of the signal's intensity, which is the square of its magnitude.

The core principle behind phasenrückgewinnung relies on the fact that the magnitude alone does not uniquely determine a signal. Therefore, additional constraints or prior knowledge about the signal are often incorporated into the algorithms. These constraints can include properties like the object being real-valued, non-negative, or confined to a specific region. Iterative algorithms are commonly employed, where an initial guess for the phase is refined over multiple steps. In each iteration, the algorithm enforces the known constraints and the measured intensity, gradually converging towards a phase that is consistent with the observed data.

Several phasenrückgewinnung algorithms exist, each with its own strengths and weaknesses. Popular methods include Gerchberg-Saxton, Fienup's error-reduction algorithm, and hybrid input-output. The success of phasenrückgewinnung is dependent on the quality of the measurements, the accuracy of the applied constraints, and the convergence properties of the chosen algorithm. Despite the challenges, phasenrückgewinnung has proven to be a powerful tool for extending the capabilities of various imaging and measurement techniques, enabling the visualization and analysis of structures that would otherwise remain hidden.