With analog scanning, time-domain low-coherence interferometry lacks precise depth information, and optical carrier generation demands a linear scanning speed. Full-field heterodyne low-coherence interferometry that uses a logarithmic complementary metal-oxide semiconductor camera, acousto-optic modulation, and digital depth stepping is reported, with which random regions of interest, lateral and axial, can be accessed. Furthermore, nanometer profilometry is possible through heterodyne phase retrieval of the interference signal. The approach demonstrates inexpensive yet high-precision functional machine vision offering true digital random access in three dimensions. (c) 2006 Optical Society of America.