In 1969, Emil Wolf proposed diffraction tomography using coherent holographic imaging to extract 3D information from transparent, inhomogeneous objects. In the same era, the Wolf equations were first used to describe the propagation correlations associated with partially coherent fields. Combining these two concepts, we present Wolf phase tomography (WPT), which is a method for performing diffraction tomography using partially coherent fields. WPT reconstruction works directly in the space–time domain, without the need for Fourier transformation, and decouples the refractive index (RI) distribution from the thickness of the sample. We demonstrate the WPT principle using the data acquired by a quantitative-phase-imaging method that upgrades an existing phase-contrast microscope by introducing controlled phase shifts between the incident and scattered fields. The illumination field in WPT is partially spatially coherent (emerging from a ring-shaped pupil function) and of low temporal coherence (white light), and as such, it is well suited for the Wolf equations. From three intensity measurements corresponding to different phase-contrast frames, the 3D RI distribution is obtained immediately by computing the Laplacian and second time derivative of the measured complex correlation function. We validate WPT with measurements of standard samples (microbeads), spermatozoa, and live neural cultures. The high throughput and simplicity of this method enables the study of 3D, dynamic events in living cells across the entire multiwell plate, with an RI sensitivity on the order of 10⁻⁵.

1969 年，Emil Wolf 提出了衍射断层扫描，使用相干全息成像从透明、不均匀的物体中提取 3D 信息。在同一时代，沃尔夫方程首次被用来描述与部分相干场相关的传播相关性。结合这两个概念，我们提出了沃尔夫相位断层扫描（WPT），这是一种使用部分相干场进行衍射断层扫描的方法。WPT 重建直接在时空域中进行，无需傅立叶变换，并将折射率 (RI) 分布与样品厚度解耦。我们使用定量相位成像方法获得的数据演示了 WPT 原理，该方法通过在入射场和散射场之间引入受控相移来升级现有的相差显微镜。WPT 中的照明场具有部分空间相干性（来自环形光瞳函数）和低时间相干性（白光），因此非常适合 Wolf 方程。根据对应于不同相衬帧的三个强度测量，通过计算测量的复相关函数的拉普拉斯和二阶时间导数，立即获得 3D RI 分布。我们通过测量标准样品（微珠）、精子和活体神经培养物来验证 WPT。该方法的高通量和简单性使得能够研究整个多孔板中活细胞的 3D 动态事件，RI 灵敏度约为 10 ^-5。