Unified k-space theory of optical coherence tomography
Kevin C. Zhou, Ruobing Qian, Al-Hafeez Dhalla, Sina Farsiu, Joseph A. Izatt
Abstract
We present a general theory of optical coherence tomography (OCT), which synthesizes the fundamental concepts and implementations of OCT under a common 3D <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>k</mml:mi></mml:math> -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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>k</mml:mi></mml:math> -space representation of the sample. While only the axial dimension of OCT is typically analyzed in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>k</mml:mi></mml:math> -space, we show that embracing a fully 3D <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>k</mml:mi></mml:math> -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.