Endoscopic optical coherence tomography to measure vibration vector of gerbil tympanic membrane

Conventional optical coherence tomography (OCT) vibrometry measures displacement only along the beam axis, limiting its ability to capture the full vibration vectors in 3D space in structures like the tympanic membrane (TM) and ossicles. We present a method that reconstructs full vibrational magnitude and direction from angularly resolved OCT measurements using a least-squares analytical solution framework. By acquiring more data than the minimum required, our method forms an overdetermined system that mitigates the effects of noise during vector reconstruction. The system uses a gradient-index (GRIN) lens to create a fan-shaped scanning geometry that enables flexible angular sampling from a single-beam configuration. This method is validated with a piezoelectric phantom for quantitative accuracy and then applied to in vivo gerbil middle ear structures, demonstrating assessment of the magnitude and direction of vibrational vectors in confined anatomical regions.