The phase of a field is often more important than the amplitude. This is in particular true for focusing of light.
To improve the quality of imaging it is often desirable to consider the phase in the exit pupil of the imaging system. The determination of both phase and amplitude are essential in coherent lensless imaging.
Phase can be measured directly using interferometry, but that requires a highly stable measurement system. Alternatively one can retrieve the phase from several intensity measurements. This is the topic of phase retrieval.
In the topic of phase retrieval the aim is to design and implement measurement systems and algorithms to compute the phase from intensity measurements. Examples are the retrieval of the phase in the exit pupil of an imaging system from through focus intensity measurements in at least two planes. Another method of phase retrieval is ptychography, where the complex transmission or reflection function of an object is retrieved from far field intensity measurements for a sequence of partial illuminations of the object. It is also possible to use spatial light modulators to introduce a known perturbation of a field. By measuring the intensity the unknown field can be reconstructed.
Phase retrieval methods are very important in coherent imaging a very short wavelengths (e.g. EUV and x-rays) at which no good optical components exist.
They also play an important role in 3D imaging.