K-Space Approach in Optical Coherence Tomography: Rigorous Digital Transformation of Arbitrary-Shape Beams,...

Area of Science:

• Optical Coherence Tomography (OCT)
• K-space analysis
• Digital image processing

Background:

• Optical Coherence Tomography (OCT) commonly uses plane-parallel scanning for image formation.
• Existing OCT descriptions often assume Gaussian beams and paraxial approximations.
• The single-scattering assumption is a primary limitation in current OCT methodologies.

Purpose of the Study:

• To develop a rigorous K-space description for OCT scan formation applicable to arbitrary beam shapes.
• To derive a filtering function for digitally transforming OCT data.
• To demonstrate enhanced image processing capabilities, including aberration correction and super-resolution.

Main Methods:

• Utilizing spectral representation for axial and lateral OCT signal structure.
• Developing a K-space framework independent of paraxial approximation or Gaussian beam assumptions.
• Analytically deriving a filtering function for digital transformation of 3D OCT data.

Main Results:

• A compact and rigorous K-space description for OCT scan formation is presented.
• A novel filtering function is derived, enabling both amplitude and phase transformations.
• The filtering function successfully demonstrated digital refocusing, aberration elimination, and digital "super-refocusing" for improved lateral resolution.

Conclusions:

• The proposed K-space description offers a general and powerful framework for OCT image formation and processing.
• The derived filtering function significantly enhances OCT data manipulation capabilities.
• Digital super-refocusing offers a pathway to achieve sub-diffraction-limited lateral resolution in OCT imaging.