Speckle Projection Profilometry Using a Diffractive Telecentric Arrangement

Abstract

A modified approach to 3-D shape measurement using the Speckle Projection technique is proposed and demonstrated. Images of a random speckle pattern are obliquely projected onto a reference plane and then onto the specimen surface. The apparent local in-plane image displacements determined by two-dimensional Digital Image Correlation (2-D DIC) combined with triangulation to provide the surface height or shape of the specimen. Here, the projected pattern is created using a custom telecentric projector. This enables the physical projection to follow closely the theoretical assumptions typically used in triangulation and to avoid the artifacts introduced when using the expanding projection created by a typical projector arrangement. In addition, the apparent size of the telecentric projected image remains constant within a significant range of out-of-plane displacements or non-zero surface heights. This feature aligns the apparent in-plane image displacement due to specimen shape to a single direction. Therefore, measurements of any displacements in the second in-plane direction provide an independent measure of changes in camera perspective, effectively reducing the need for pre-measurement calibration. Finally, the use of a diffraction grating creates a parallelogram projection, equalizing the optical path lengths of the entire projected pattern. This maximizes the range of telecentricity or nearly parallel focus of the projected speckle, allowing objects with large surface height variation to be measured accurately. An example optical system is presented and the practical features are explained. Experimental results for a cylinder specimen and also a complex shaped specimen show that the method is effective and accurate. This approach allows for shape measurements to be made efficiently, with minimal calibration and reduced mathematical complexity.