Deformation measurement and analysis on related curved surfaces by holography

The technique with two holograms is investigated in case of large deformations of an opaque body. The recovering of invisible fringes by a modification and the strain determination are briefly outlined. Two conditions from the first derivative of the optical path difference should ensure locally a spacing and a contrast of the fringes. The three linear forms from this derivative are analysed with the polar decomposition of the deformation, some affine connections and the transverse ray aberration. The correlation for the fringe visibility, Frenet's relations of curvature, changes of geodesic curvature and the integrability are involved. The second derivative of the path difference contains three quadratic forms with the derivatives of the dilatation, the curvature changes of the object surface and the virtual deformation of the images besides a term with the fringe vector. A duality from the aberration permits the elimination of a bilinear form.