Insight into Phase-Sensitive Optical Coherence Tomography Displacement Measurement

A range of label-free and functional imaging techniques such as Doppler optical coherence tomography (OCT), dynamic OCT and optical coherence elastography use phase-sensitive OCT to measure sample motion. This is done by calculating the phase difference between two or more OCT image acquisitions of the same region of tissue, each at different times. It was shown recently by numerical and experimental means that, even in the absence of noise, the accuracy of phase-difference based displacement estimation is reduced in the presence of dark speckles. In this work, we demonstrate analytically, for the first time, why displacement is not in general proportional to phase difference in OCT images containing speckle. We do this by deriving a novel expansion of phase difference in compression optical coherence elastography which contains previously unknown higher order terms, in addition to the currently applied term which assumes a linear relationship between phase and displacement. We then use this expansion to reveal significant insight into the nature of phase difference in compression optical coherence elastography. In particular, we show that neglecting these higher-order terms introduces errors in displacement estimation methods, which increase with depth and/or in regions with large strain discontinuities, such as in turbid samples. We show that in speckle there are two principal phenomena which perturb the assumed linear relationship between displacement and phase difference. We also show that one of these perturbations leads to features in phase difference maps that resemble phase wrapping events, which are likely being mitigated by techniques intended to perform phase unwrapping. Finally, we introduce a novel method for displacement estimation in OCE, which overcomes the limitations of existing approaches, achieving an error two orders of magnitude lower, and higher SNR. We believe our analysis will have a significant impact upon the the way displacement is estimated from phase-sensitive OCT data, beyond compression optical coherence elastography, and will therefore be important to the extensive range applications of phase-sensitive OCT.