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.

全息术是一种强大的工具，可以在不丢失信息的情况下记录波，通过量化光与物质相互作用引起的相位延迟，使光学、X 射线和电子成像应用受益。然而，全息成像在技术上要求很高，因为它通常需要干涉装置、相干源和长期稳定性。在这里，我们提出了全息成像，其中相位图像是直接从倾斜照明中的单个强度测量中获得的。我们的方法基于空间域 Kramers-Kronig 关系，将强度的空间变化转换为相位的空间变化。我们从用光学显微镜和照明控制测量的强度图像中展示了微观物体和生物标本的二维全息成像和三维折射率断层扫描。所提出的方法不需要迭代过程，也不需要严格的约束，并为各种光谱范围内的非干涉式全息成像开辟了一种新方法。