A fundamental limit for the distance uncertainty of coherent 3D-sensors is presented. The minimum distance uncertainty is given by (delta) z equals 1/2(pi) (DOT) (lambda) /sin²u, with the aperture of observation sinu and wavelength (lambda) . This distance uncertainty can be derived via speckle statistics for different sensing principles, and surprisingly the same result can be obtained directly from Heisenberg's uncertainty, principle for a single photon. Because speckles are the main reason for distance uncertainty, possibilities to overcome the speckle problem are discussed. This leads to an uncertainty principle between lateral resolution and longitudinal distance uncertainty. A way to improve the distance uncertainty without sacrificing lateral resolution is the use of temporally incoherent light.

Date Published: 23 March 1993
PDF: 9 pages
Proc. SPIE 1822, Optics, Illumination, and Image Sensing for Machine Vision VII, (23 March 1993); doi: 10.1117/12.141937

Published in SPIE Proceedings Vol. 1822:
Optics, Illumination, and Image Sensing for Machine Vision VII
Donald J. Svetkoff, Editor(s)