Algorithms for wavefront propagation, digital holography and iterative phase retrieval
For the past two decades I have been developing novel methods and the related algorithms for imaging with coherent light, electrons, X-rays, terahertz and other waves. Some of the algorithms are available on the Matlab file exchange server.
Practical algorithms for simulation of the wavefront propagation, simulation and reconstruction of in-line digital holograms, for plane and spherical waves are described in ref. [1], Iterative phase retrieval algorithms that can be applied in holography and coherent diffraction imaging are described in [2, 3].
In 2021 I showed that a three-dimensional sample distribution can be reconstructed from a single-shot intensity distribution, such as diffraction pattern or a hologram, by applying multi-slice iterative phase retrieval algorithms [4].
In 2007, I found a solution to the twin image problem in holography [5] via applying an iterative phase retrieval algorithm. Twin image problem is a long-standing problem in holography, known since holography was invented by Denis Gabor in 1947.
[1] Practical algorithms for simulation and reconstruction of digital in-line holograms, Appl. Opt. 54, 2424–2434 (2015).
[2] Iterative phase retrieval for digital holography: tutorial, J. Opt. Soc. Am. A 36, D31–D40 (2019).
[3] Iterative phase retrieval in coherent diffractive imaging: practical issues, Appl. Opt. 57, 7187–7197 (2018).
[4] Three-dimensional structure from single two-dimensional diffraction intensity measurement, Phys. Rev. Lett. 127, 063601 (2021).
[5] Solution to the twin image problem in holography, Phys. Rev. Lett. 98, 233901 (2007).