Many industrial applications require accurate and rapid measurement of the 3-D shapes of physical objects. Representative applications of 3-D shape measurement include mechanical reverse engineering, 3-D digital replication, and part inspection. Traditional 3-D measurement techniques, such as coordinate measurement machines (CMM) and laser scanning, provide high accuracy but are generally slow and expensive. In recent years, shape measurement based on digital fringe projection (SMDFP) has been developed for non-contact shape measurements. Systems based on SMDFP are promising due to low cost, fast speed, and flexibility. However, the existing models and algorithms for SMDFP systems need to be significantly improved to fully exploit the potentials of this technique.

This dissertation presents a new mathematical model for SMDFP that provides an accurate modeling of the optical geometry of SMDFP systems. Based on this model, three related algorithms for shape measurements were developed, namely the algorithm for construction of absolute phase map, algorithm for construction of point cloud, and algorithm for estimation of sensor parameters. With the new model and algorithms, the measurement speed of existing SMDFP systems is improved and the calibration procedure is made easier. At the same time, high measurement accuracy is ensured. This dissertation also provides a framework for using adaptive projection patterns in SMDFP technique. A new algorithm was developed for automatic generation of projection patterns with variable fringe pitches to achieve improved measurement performance. This capability is particularly important for ensuring the accuracy and speed when measuring surfaces with a large range of normal directions. Finally, this dissertation presents a comprehensive uncertainty model for describing the relations between various error sources and the resulting uncertainties in shape measurements. Based on this model, measurement uncertainties can be estimated from the image data acquired in a measurement.

The research results reported in this dissertation can be used to improve the performance and features of existing SMDFP systems in the following aspect: measurement accuracy, speed, ease of calibration, and estimation of measurement uncertainties. These improvements could make SMDFP technique more attractive to industrial 3-D shape measurement applications and to stimulate the wide spread use of this technique.