3D displacement measurements using a single camera

• 3D displacements are measured using a single camera.
• Magnification changes as well as blurring effects induced by out-of-plane displacements are accounted for.
• The method is based on digital image correlation.
• The method is not limited to large depth of field optical systems.
• Demonstrative examples illustrate the capabilities of the method.

Measuring 3D displacements usually requires at least two cameras or 3D images. However, in some especially constrained experimental circumstances, it is only possible to use a single camera. The present paper develops a methodology, based on digital image correlation that is able to measure the homogeneous 3D displacement of a plane surface using a single camera. Based on Descartes' theory, a model is elaborated that accounts not only for the magnification change due to the out-of-plane displacement but also for the unfocusing of the object. Several examples are provided that show the ability of the technique to track 3D displacements with various optical setups with different depths of field.