On Fourier Phase Retrieval from Differential Intensity Measurements with Applications to Wavefront Sensing
This work provides a theoretical framework and practical algorithms for phase retrieval in adaptive optics, benefiting applications like astronomical imaging and microscopy.
The authors address Fourier phase retrieval from differential intensity measurements, showing that the phase can be determined via partial differential or integro-differential equations, and design efficient algorithms for wavefront sensors. Numerical experiments demonstrate the approach's effectiveness.
In this paper, we consider Fourier phase retrieval from differential intensity measurements, i.e., the problem of determining the phase of a complex-valued function from a series of intensity measurements differing only by slight modulations in Fourier domain. These modulations may be induced by optical elements such as prisms or phase plates, or via spatial-light modulators. Generalizing the principles behind the transport of intensity equation, we show that given such differential intensity measurements, the phase can be determined as the solution of certain partial differential or integro-differential equations. This is then used to design efficient reconstruction algorithms for a number of Fourier-type wavefront sensors, such as the pyramid wavefront sensor, commonly used in adaptive optics. Numerical experiments illustrate the usefulness of our proposed approach.