Single-shot depth-resolved displacement field measurement using phase-contrast polychromatic speckle interferometry

We describe a system for measuring sub-surface displacement fields within a scattering medium using a broadband super-luminescent light emitting diode (SLED) source and spectral imaging. The use of phase information in the backscattered speckle pattern offers displacement sensitivity in the range of a few tens of nm, some two to three orders of magnitude better than the depth resolution of state-of-the-art Optical Coherence Tomography systems. The system is based on low cost components and has no moving parts. It provides displacement maps within a 2-D slice extending into the sample, and the fact that all the data for a given deformation state are acquired in a single shot is a highly attractive feature for in-vivo investigations in the biological sciences. The theoretical basis for the system is presented along with experimental results from a simple well-controlled geometry consisting of independently-tilting glass sheets. Results are validated using standard two-beam interferometry. Scattering samples were also studied and we show a wrapped phase map through the thickness of a pig ex-vivo cornea. The phase change was due to viscoelastic creep in the cornea after a change in the intraocular pressure.