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. An intensity-based holographic imaging via space-domain Kramers–Kronig relations is presented, allowing the phase image of an object to be obtained directly from a single intensity measurement with oblique illumination.