  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.
