Intensity-based holographic imaging via space-domain Kramers–Kronig relations


Holography is a powerful tool to record waves without loss of information that has benefited optical, X-ray and electronic imaging applications by quantifying phase delays induced by light–matter interactions. However, holographic imaging is technically demanding in that it generally requires an interferometric setup, a coherent source and long-term stability. Here, we present holographic imaging in which a phase image is obtained directly from a single intensity measurement in oblique illumination. Our approach is based on space-domain Kramers–Kronig relations that transform the spatial variation in intensity to the spatial variation in phase. We demonstrate two-dimensional holographic imaging and three-dimensional refractive index tomography of microscopic objects and biological specimens from intensity images measured with an optical microscope and illumination control. The proposed method does not require iterative processes nor strict constraints and opens up a new approach to non-interferometric holographic imaging in various spectral regimes.

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Fig. 1: Schematic of the proposed method.
Fig. 2: Experimental demonstrations with two-dimensional samples.
Fig. 3: Optical diffraction tomography with a 5 μm polystyrene bead.
Fig. 4: RI tomogram of a trinucleated A549 cell.
Fig. 5: Time-lapse tomographic imaging of an A549 cell.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.


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This work is supported by KAIST Up programme, the BK21+ programme, Tomocube, Inc. and the National Research Foundation of Korea (2017M3C1A3013923, 2015R1A3A2066550, 2018K000396).

Author information




Y.B. and Y.P. conceived the project. Y.B. developed the mathematical framework and conducted the experiment. Y.B. and Y.P. wrote the manuscript. Y.P. provided supervision.

Corresponding author

Correspondence to YongKeun Park.

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Competing interests

Y.P. has financial interests in Tomocube, Inc., a company that commercializes optical diffraction tomography and quantitative phase imaging instruments and is one of the sponsors of the work.

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Peer review information Nature Photonics thanks the anonymous reviewers for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–6 and discussion.

Supplementary Video 1

Time-lapse maximum intensity projection images of the RI tomogram of an A549 cell.

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Baek, Y., Park, Y. Intensity-based holographic imaging via space-domain Kramers–Kronig relations. Nat. Photonics (2021).

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