User:BWhetten/Phase retrieval

Hybrid input-output algorithm
Main article: Hybrid input output (HIO) algorithm for phase retrieval

The hybrid input-output algorithm is a modification of the error-reduction algorithm - the first three stages are identical. However,  no longer acts as an estimate of, but the input function corresponding to the output function , which is an estimate of  (Fienup 1982:2762). In the fourth step, when the function  violates the object constraints, the value of  is forced towards zero, but optimally not to zero. The chief advantage of the hybrid input-output algorithm is that the function  contains feedback information concerning previous iterations, reducing the probability of stagnation. It has been shown that the hybrid input-output algorithm converges to a solution significantly faster than the error reduction algorithm. Its convergence rate can be further improved through step size optimization algorithms.

The following section will be added after the Methods section in the current article.

Applications
Phase retrieval is a key component of coherent diffraction imaging (CDI). In CDI, the intensity of the diffraction pattern scattered from a target is measured. The phase of the diffraction pattern is then obtained using phase retrieval algorithms and an image of the target is constructed. In this way, phase retrieval allows the conversion of a diffraction pattern into an image, thus eliminating the need for an optical lens.

Using phase retrieval algorithms, it is possible to characterize complex optical systems and their aberrations. Other applications of phase retrieval include X-ray crystallography and transmission electron microscopy.