## Extension of the fringe projection method to large objects for shape and deformation measurement

There is a real need for methods to allow the measurement of the form and deformation of large objects. For example, for maintenance and production costs as well as for security. Even though there are many methods of measuring the form and deformation of small objects (up to 1 m2), currently none of them are able to quickly measure larger objects (i.e. at a large number of points at the same time). Among the existing techniques, the fringe projection seem to us one of the most adequate to deal with these kinds of problems. In its classical form, this technique is very simple, since it consists of projecting equispaced rectilinear fringes on an object from one direction and of observing the scene from another with a CCD camera. The displacement of the fringes distorted by the object contains the desired shape information. The phase shifting and phase unwrapping procedures allow automatic, rapid acquisition of an optical print (called a "phase map") of the object. In the case of small objects (the classical approach), the extraction of the shape information from this optical print is quite simple. A phase map of the object as well as a phase map of a reference surface plane is acquired. Then, basically, the desired shape information is obtained by subtracting these two maps from each other. For larger objects, this approach is not possible anymore. On the one hand, such a reference surface does not exist. On the other hand, in order to measure the whole surface at once, it must be fully illuminated. This suggests the use of interferometrically generated fringes, in divergent beams, which implies that the fringes are no longer rectilinear and equispaced. For these reasons the classical approach is no longer valid. It is therefore necessary to find another method to be able to extract the object shape information from the optical print. In the frame of this work, three methods have been conceived and developed in order to extract the shape information of large objects from their optical print. The first two methods proposed here are dedicated to quasi-planar objects that are parallel to the imaging plane of the camera. These assumptions allow the simplification of the equations describing the system to "mimic" the classical approach, where the desired shape information is proportional to the difference between the measured and reference phase maps. The next step is to determine the parameters of the projection head. The first method is based on two coupled interferometers (of the Mach-Zehnder and Young's type), and the other uses least squares calculations with a small number of calibration points, aiming at minimizing the difference between the theoretical and measured phase at more than four calibration points. Finally, the desired reference phase map is artificially generated. These two techniques are simple but their application is limited only to planar object parallel to the imaging plane of the camera. In the last technique, which is based on a new approach, the system is described by the interferometric equation and the central perspective equations. Solving them simultaneously allows the determination of the coordinates (x,y,z) of all measured points from the optical print. This approach is general and offers the advantage of allowing the measurement of the shape and deformation of large objects. In addition, it also makes the system more flexible. In this report, these different techniques are presented and their feasibility is shown; examples of measurements give a first evaluation of their precision, and assess the new possibilities offered in terms of object shape and configuration of the measurement system, as well as their limitations. Finally, the three methods are compared one to another and advice for their optimization is proposed.

Jacquot, Pierre
Year:
2003
Publisher:
Lausanne, EPFL
Laboratories: