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Appl Opt. 1994 Mar 1;33(7):1306-14. doi: 10.1364/AO.33.001306.

Laser triangulation: fundamental uncertainty in distance measurement.


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.

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