Laser triangulation: fundamental uncertainty in distance measurement

TLDR

The uncertainty in distance measurement of laser triangulation sensors and other coherent sensors is limited by speckle noise, which arises from coherent illumination interacting with rough surfaces. The study discusses the uncertainty limit in distance sensing by laser triangulation and introduces an uncertainty principle linking lateral resolution to distance uncertainty. The authors derive a minimum distance uncertainty from speckle statistics, introduce an uncertainty principle linking lateral resolution to distance uncertainty, and determine design criteria—small temporal and spatial coherence with a large observation aperture—for sensors achieving minimal uncertainty. The derived uncertainty depends on wavelength, observation aperture, and speckle contrast, matches the same value obtained from single‑photon experiments and Heisenberg's principle, and is confirmed by experiments.

Abstract

We discuss the uncertainty limit in distance sensing by laser triangulation. The uncertainty in distance measurement of laser triangulation sensors and other coherent sensors is limited by speckle noise. Speckle arises because of the coherent illumination in combination with rough surfaces. A minimum limit on the distance uncertainty is derived through speckle statistics. This uncertainty is a function of wavelength, observation aperture, and speckle contrast in the spot image. Surprisingly, it is the same distance uncertainty that we obtained from a single-photon experiment and from Heisenberg's uncertainty principle. Experiments confirm the theory. An uncertainty principle connecting lateral resolution and distance uncertainty is introduced. Design criteria for a sensor with minimum distanc uncertainty are determined: small temporal coherence, small spatial coherence, a large observation aperture.