Diffraction-based self-calibration method for defocused speckle imaging

Abstract

Defocused speckle imaging (DSI) is an optical technique where a diffuse object surface is illuminated by a laser source, and the scattered interference speckle field is sampled by a defocused camera. The recorded image contains a speckle pattern that characterizes the surface; if the object displaces or rotates, the speckles move within the camera view. Non-contact surface motion measurements are thus possible by simply tracking the speckle movements. The observed speckle motion magnitude scales proportional to the object distance, which makes DSI attractive for remote measurement applications. However, because DSI measurement sensitivity depends on the specific geometric arrangement, object range and orientation must be known to properly scale the measured speckle motions. In field conditions, manual extraction of the geometric parameters is challenging and time-consuming due to large distances and harsh conditions.To solve the scaling problem, a diffraction-based self-calibration method is proposed here to extract the geometric parameters from the captured speckle patterns directly with no additional sensors. The solution utilizes multi-longitudinal mode laser illumination combined with speckle pattern diffraction analysis. A laser with a multi-wavelength spectrum creates several copies of partially overlapping speckle patterns that propagate at slightly different directions. The related spatial speckle offset measured on the image sensor depends on the surface angle and scales proportional to the sampling distance. Therefore, all calibration parameters can be explicitly determined from a pair of speckle patterns recorded at axially separated focal planes.The speckle offset equations are derived from the general diffraction equation using simple geometric treatment. The speckle pattern dependence on the laser source spectrum is experimentally studied, and the proposed self-calibration method is demonstrated. The diffraction analysis can extract 500–1000 mm sampling distances at a 1.7% accuracy and determine 15–45˚ oblique surface angles at a 0.7˚ accuracy.