Use of Kramers-Kronig relation in phase retrieval calculation in X-ray spectro-ptychography

Makoto Hirose, Kei Shimomura, Nicolas Burdet, Yukio Takahashi

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


Coherent diffraction imaging (CDI) is a method for reconstructing the complex-valued image of an object from diffraction intensities by using iterative phasing methods. X-ray ptychography is a scanning type of CDI using X-rays, allowing us to visualize the complex transmission function of an extended specimen. We here propose the use of the Kramers-Kronig relation (KKR) as an additional constraint in phase retrieval algorithms for multiple-energy X-ray ptychography using the absorption edge of a specific element. A numerical simulation showed that the speed of convergence was increased by using the improved algorithm with the KKR. We successfully demonstrated its usefulness in a proof-of-principle experiment at SPring-8. The present algorithm is particularly useful for imaging X-ray absorption fine structures of a specific element buried within thick samples by hard X-ray spectro-ptychography.

Original languageEnglish
Pages (from-to)8593-8603
Number of pages11
JournalOptics Express
Issue number8
Publication statusPublished - 2017 Apr 17
Externally publishedYes

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics


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