We present a general theory of optical coherence tomography (OCT), which synthesizes the fundamental concepts and implementations of OCT under a common 3D $k$-space framework. At the heart of this analysis is the Fourier diffraction theorem, which relates the coherent interaction between a sample and plane wave to the Ewald sphere in the 3D $k$-space representation of the sample. While only the axial dimension of OCT is typically analyzed in $k$-space, we show that embracing a fully 3D $k$-space formalism allows explanation of nearly every fundamental physical phenomenon or property of OCT, including contrast mechanism, resolution, dispersion, aberration, limited depth of focus, and speckle. The theory also unifies diffraction tomography, confocal microscopy, point-scanning OCT, line-field OCT, full-field OCT, Bessel beam OCT, transillumination OCT, interferometric synthetic aperture microscopy (ISAM), and optical coherence refraction tomography (OCRT), among others. Our unified theory not only enables clear understanding of existing techniques but also suggests new research directions to continue advancing the field of OCT.

中文翻译：

---

光学相干断层扫描的统一k空间理论

我们提出了光学相干断层扫描 (OCT) 的一般理论，它综合了通用 3D $k$空间框架下 OCT 的基本概念和实现。该分析的核心是傅立叶衍射定理，它将样品和平面波之间的相干相互作用与样品的 3D $k$空间表示中的Ewald 球面联系起来。虽然通常只在$k$空间中分析 OCT 的轴向维度，但我们表明，拥抱全 3D $k$空间形式主义几乎可以解释 OCT 的几乎所有基本物理现象或属性，包括对比度机制、分辨率、色散、像差、有限的焦深和散斑。该理论还统一了衍射断层扫描、共聚焦显微镜、点扫描 OCT、线场 OCT、全场 OCT、贝塞尔光束 OCT、透照 OCT、干涉合成孔径显微镜 (ISAM) 和光学相干折射断层扫描 (OCRT)，其中其他。我们的统一理论不仅可以清楚地了解现有技术，而且还提出了新的研究方向，以继续推进 OCT 领域。