Insight into phase-sensitive optical coherence tomography displacement measurement

Phase-sensitive optical coherence tomography (OCT) measures motion from phase differences between repeated acquisitions, supporting techniques such as Doppler OCT and optical coherence elastography (OCE). A recent numerical and experimental study showed that, even without noise, displacement estimation is less accurate in dark speckles. Here, we demonstrate analytically why displacement is not proportional to phase difference in speckled OCT images. We derive an expansion for compression OCE containing higher-order terms beyond the conventional linear term and show that neglecting them introduces errors that increase with depth and strain-discontinuity magnitude. We also identify two phenomena that perturb the phase linearity, one producing features resembling phase-wrapping events that may be mitigated by phase-unwrapping techniques. Finally, we introduce a displacement-estimation method that overcomes these limitations and achieves errors two orders of magnitude lower than conventional approaches. These phase-instability findings may reshape motion measurement beyond compression OCE, including dynamic OCT.