Quantitative determination of out-of-plane displacements by endoscopic electronic-speckle-pattern interferometry

The combination of endoscopes and electronic-speckle-pattern interferometry requires a more detailed consideration of their imaging properties with respect to interferometric fringe formation, if a quantitative analysis of the observed deformation is desired. Due to a relatively small distance between the illuminating and the imaging optical elements and to strongly divergent beams, the sensitivity vector may not be regarded as constant, and image distortions caused by the endoscope optics must be taken into account. A simplified model that deals with the situation of a plane object perpendicular to the optical axes of the endoscope is presented and verified by experimental results.