A full-field digital gradient sensing method is proposed for measuring small angular deflections of light rays due to local stresses in transparent planar solids. The working principle of the method is explained, and the governing equations are derived. The analysis shows that angular deflections of light rays can be linked to nonuniform changes in thickness and refractive index of the material. In mechanically loaded planar solids, the angular deflections can be further related to spatial gradients of first invariant of stresses under plane stress conditions. The proposed method is first demonstrated by capturing the angular deflection fields in two orthogonal directions for a thin plano-convex lens. The measured contours of constant angular deflection of light rays are in good agreement with the expected ones for a spherical wavefront. The method is also successfully implemented to study a stress concentration problem involving a line load acting on an edge of a large planar sheet. Again, the stress gradients, measured simultaneously along and perpendicular to the loading directions, are in good agreement with the analytical predictions. The measured stress gradients have also been used to estimate stresses in the load point vicinity where plane stress results hold.
© 2012 Optical Society of America
Instrumentation, Measurement, and Metrology
Original Manuscript: October 11, 2011
Manuscript Accepted: February 27, 2012
Published: April 18, 2012
Chandru Periasamy and Hareesh V. Tippur, "Full-field digital gradient sensing method for evaluating stress gradients in transparent solids," Appl. Opt. 51, 2088-2097 (2012)