Moiré interferometry for out-of-plane displacement measurements

Abstract

Moiré interferometry is a relatively new branch of photomechanics that utilizes a diffraction grating on the specimen to determine surface displacements. To date, it has been used primarily to determine in-plane displacements of the specimen surface. The objective of this work is to demonstrate that the technique is capable of determining out-of-plane displacements as well.

A high-frequency phase grating on a specimen surface is illuminated by oblique beams; two diffracted beams are recorded by holographic interferometry. If the wavefront warpages of the two diffracted beams are characterized by fringe orders, Nₐ and N_b, it is demonstrated that the in-plane displacements are proportional to Nₐ - N_b, while out-of-plane displacements are proportional to Nₐ + N_b. Initially, these subtractive and additive parameters are determined numerically, and the resulting displacements are compared to displacements measured by well-accepted prior experimental methods. Excellent agreement with these proven methods is shown.

Using this remarkably simple relationship between wavefront warpages, an experimental procedure is developed which is capable of simultaneously determining the in-plane and out-of-plane displacements of a specimen surface. The method requires only one photographic exposure of the deformed specimen, with displacement information being extracted through the use of optical filtering. The fact that the information required to yield these patterns can be obtained from a single photographic recording not only makes this an experimentally simple technique to use, but provides the capability of analyzing dynamic events as well.

The sensitivity of measurements made by utilizing this technique are directly proportional to the frequency of the specimen grating. Therefore, it is desirable to obtain specimen gratings with frequencies on the order of 500-2000 lines/mm ( 12, 700 - 50,800 lines/in.). A technique is developed whereby high frequency moire gratings with highly reflective surfaces can be transferred to workpieces made from most engineering materials. Specimen gratings with frequencies as high as 2000 lines/mm (50,800 lines/in.) and exhibiting 10 percent diffraction efficiency in the first diffraction order have been applied to numerous specimens using simple laboratory techniques.