Moiré method for determining bending moments from hologram interferometry

Abstract

Interferograms obtained in hologram interferometry provide the observer with ‘contour maps’ of more or less constant displacement of an object surface. The contours are presented in the form of fringes, often sinusoidal or approximately so. In many applications, however, it is important to determine the bending moments of the surface, which are related to the second partial derivatives of the surface deformation with respect to the surface coordinates. It is shown that bending moments can be evaluated at any point on the interferogram by moiré interference between two transparencies of the interferogram, rotated 180° about the point in question. This method not only yields the bending moments but also indicates the principal axes of bending and the relative sign between the two principal components. One application of the technique is in the design of certain musical instruments, guitars in particular, where analysis of vibration modes of braces is helpful.