Multi-layer neural network applied to phase and depth recovery from fringe patterns

A multi-laver neural network (MLNN) is used to carry out calibration processes in fringe projection profilometry in which the explicit knowledge of the experimental set-up parameters is not required. The MLNN is trained by using the fringe pattern irradiance and the height directional gradients provided from a calibration object. After the MLNN has been trained, profilometric height data are estimated from the projected fringe patterns onto the test object. The MLNN method works adequately on an open fringe pattern, but it can be extended to closed fringe patterns. In the proposed technique, edge effects do not appear when the field view is limited in the fringe pattern. In order to show the application of the MLNN method, three different experiments are presented: (a) shape determination of a spherical optical surface; (b) optical phase calculation from a computer-simulated closed fringe pattern; and (c) height determination of a real surface target. An analysis is also made of how noise, spatial carrier frequencies, and different training sets affect the MLNN performance. (C) 2000 Elsevier Science B.V. All rights reserved.