Computational Speckle Pattern Interferometry

Abstract

Visually imperceptible surface deformations encode rich information about a scene, from the mechanical properties of an object to the acoustic vibrations present in the surrounding environment. Optical interferometric techniques can reveal these subtle changes, typically by capturing a sequence of measurements to perform temporal phase shifting. In this paper, we introduce Computational Speckle Pattern Interferometry (CSPI), a novel single-shot approach to estimating per-pixel displacement and motion. Our key insight is that the image formation model for speckle pattern interferometry can be decomposed into spatial and temporal factors, each represented as a vector. After calibrating for the spatial term, we recover the scene dynamics using a reconstruction algorithm modeled after the classic Horn-Schunck method for estimating optical flow. Unlike traditional interferometric methods, CSPI requires no precision instrumentation to perform phase stepping. We demonstrate its effectiveness by measuring per-pixel displacements and motions at sub-micrometer scales, visualizing high-frequency vibrations of a tuning fork and a Chladni plate, and recovering sound indirectly from these vibrations.