Accurate determination of fractional retardations in photoelasticity through digital fringe multiplication

Abstract

Digital fringe multiplication is a useful technique for obtaining fractional fringe orders in photoelasticity at regions with very feeble retardations. In this paper, the effectiveness of the existing fringe multiplication techniques is investigated theoretically and experimentally. A new approach for fringe multiplication, using background nullified fringes, is developed to overcome the prevailing issues. Three options for obtaining background nullified fringe patterns are explained. Further, quadrature transformation of these fringe patterns is carried out to fetch uniform modulation. Moreover, a simplified fringe multiplication method is worked out to obtain fractional fringes from the uniformly modulated fringe patterns. The proposed procedures have been demonstrated through simulated as well as experimental images. A parametric study is carried out to understand the influence of pixel resolution and bit depth of the images on fringe multiplication. A criterion is established for finding out the maximum possible fringe multiplication for a given initial pixel/fringe resolution. It is observed that, for higher levels of fringe multiplication, larger bit depth of the image in conjunction with sufficient fringe resolution would be essential. The same also holds for fringe multiplication at areas with stress concentrations.