Deformation measurement and analysis on related curved surfaces

In holographic Interferometry the technique with two holograms and modifications at the reconstruction is investigated in case of large deformations of an opaque body. The recovering of previously invisible fringes and the strain determination is outlined. Two conditions for the smallness of the first derivative of the optical path difference should ensure locally a proper spacing and a sufficient contrast of the fringes. The linear forms from the first derivative are analysed with the polar decomposition, some affine connections and the transverse ray aberration. The principal subject is the second derivative of the path difference to analyse the fringe curvature. Frenet's curvature relations, an involution from the shell theory, the changes of geodesic curvature and the integrability are used. The latter points to the dislocation theory. Three quadratic forms appear besides terms with the fringe and visibility vectors. They contain the derivatives of the dilatation and the curvature change of the object surface and the virtual deformation of the images. The duality of the aberration permits the elimination of some bilinear forms. In the appendix the previous relations of curvature change are illustrated by a short extension to the Ricci tensor and geodesics in general. An interpretation by a virtual deformation of Schwarzschild's solution of the field of gravitation is added as simple example.