Abstract

In the small deflection theory of thin plates, the bending stress is directly proportional to the curvature of the deflected plate surface. Most optical methods, such as holographic interferometry and shadow moire, give deflection contours which have to be differentiated twice to yield curvature values. Since numerical differentiation is intrinsically error prone, it is important that it be avoided whenever possible. In this paper we present a technique whereby real-time curvature fringes of a mirrored specimen surface can be obtained with a simple Ronchi grating through the use of shearing interferometry and the Talbot effect. It is done by illuminating the deflected specimen surface with a coherent beam through the grating and observing the resulting wave at a certain distance away. If the distance between the specimen surface and the observation plane is one of the Talbot distances and the resulting wave is the sum of only zeroth-order and two first-order diffraction waves, a high quality fringe pattern representing curvature contours is obtained. A sensitivity of 2 × 10⁻⁶/mm/ fringe has been achieved. Both theoretical analysis and experimental demonstration are presented.

© 1985 Optical Society of America