Measurement of planar refractive index profiles with rapid variations in glass using interferometry and total variation regularized differentiation

Abstract

Planar refractive index profiles with rapid variations, formed in glass, are measured with interferometry. This involves forming a bevel in the glass and orientating the fringe pattern to be normal to the bevel edge. The index profile is determined by differentiation of the phase function of the fringe pattern. The differentiation has been performed using the total variation regularization method in order to preserve rapid changes in the derivative. This new approach avoids the necessity of filtering, in order to reduce noise, in the direction perpendicular to the bevel, which would otherwise smooth out the rapid index changes. The method is assessed using a model refractive index profile that contains an index gradient of 0.24 μm-1 and is then applied practically to measure the refractive index profile of electrically poled BK7 glass. The new approach allows the sharp transition in the index between poled and unpoled glass to be observed as well as the accumulation of potassium ions beyond the poled glass region.