Fourier optics analysis of phase-mask-based path-length-multiplexed optical coherence tomography

Optical coherence tomography (OCT) is an imaging technique that constructs a depth-resolved image by measuring the optical path-length difference between broadband light backscattered from a sample and a reference surface. For many OCT sample arm optical configurations, sample illumination and backscattered light detection share a common path. When a phase mask is placed in the sample path, features in the detected signal are observed, which suggests that an analysis of a generic common path OCT imaging system is warranted. In this study, we present a Fourier optics analysis using a Fresnel diffraction approximation of an OCT system with a path-length-multiplexing element (PME) inserted in the sample arm optics. The analysis may be generalized for most phase-mask-based OCT systems. A radial-angle-diverse PME is analyzed in detail, and the point spread function, coherent transfer function, sensitivity of backscattering angular diversity detection, and signal formation in terms of sample spatial frequency are simulated and discussed. The analysis reveals important imaging features and application limitations of OCT imaging systems with a phase mask in the sample path optics.