Degree Name

Doctor of Philosophy


School of Electrical, Computer and Telecommunications Engineering


This thesis focuses on improving the accuracy of using multiple-shot fringe projection profilometry (FPP) for three dimensional (3D) shape measurement of rigid objects with movement. By using information on the object movement, the errors caused by the object movement in the projection of the multiple fringe patterns are addressed. The author mathematically describes the movement of the rigid object using a rotation matrix and translation vector. The influence on the fringe patterns caused by the movement is then analysed. Because the movement of the object changes the height distribution of the object surface, and the height distribution is related to the captured fringe patterns, a new expression for fringe patterns with movement is obtained. Using the new expression, algorithms are proposed to address the errors caused by different types of movement. At last, the errors caused by the object movement are removed successfully.

At the beginning of this thesis, an algorithm based on phase-shifting profilometry (PSP) is proposed to address the errors caused by the two dimensional (2D) movement of the object. Firstly, the rotation matrix and the translation vector describing the movement of the object are estimated using a set of marks placed on the surface of the object. New expressions for the fringe patterns under the influence of the 2D object movement are then derived and used to determine the correct phase map, which leads to accurate measurement of the object profile.

Because the intensity ratio method with a triangular fringe pattern can be more efficiently calculated than the phase value in PSP, an algorithm based on the intensity ratio method is proposed to address the errors caused by 2D movement. The movement of the object is described by the rotation matrix and the translation vector. The influence on the fringe patterns caused by the 2D movement of the object is then analysed and then used to estimate the normalised fringe patterns from the object without movement. Finally, the object is reconstructed by using the existing intensity ratio algorithm and incorporating the estimated fringe patterns, which leads to improved measurement accuracy.

In practice, the movement of an object is not limited to two dimensions. Therefore, a third algorithm based on PSP is proposed to address the errors when the object is subject to 3D movement. Because 3D movement introduces unknown height variation of the object, the algorithms used to account for 2D movement become invalid. An iterative least-squares algorithm is proposed to address the errors caused by the 3D movement. The object is limited to be a rigid object, and the movement consists of a translation in the direction of height and a 2D movement in the plane perpendicular to the direction of height. The proposed method does not require the height variation caused by the movement to be known in advance.

The thesis also addresses the errors caused by the shadow in PSP. Because the shadow areas in the captured image do not include the information of the fringe patterns, errors will be introduced to the measurement results. To remove the influence caused by the shadow, the reconstructed 3D results are mapped on a pointby- point basis to the corresponding positions on the digital micro-mirror device (DMD) of the projector. A set of rules are then presented to detect the shadow points based on their mapped positions on the DMD.

Experimental results are given to verify the proposed algorithms above. These proposed algorithms not only have the advantages of the multiple-shot technique, but also improve the accuracy of the 3D reconstruction for an object with movement. The invalid points caused by the shadow are also removed and a high-quality result can be obtained. A 3D shape measurement system that can reconstruct a moving object with high accuracy is then built. Finally, the thesis is concluded and future work is proposed.



Unless otherwise indicated, the views expressed in this thesis are those of the author and do not necessarily represent the views of the University of Wollongong.