A refractive index field can be quantitatively visualized by using a background-oriented schlieren (BOS) technique to measure the displacements of background dot patterns of a 2D image captured by a camera. In BOS, the displacement is caused by the deflection of the light ray passing through the refractive index field. However, obtaining depth information of refractive index fields is often difficult because dot-pattern displacement results from deflection of light rays integrated over their path. A method of reconstructing depth information of the refractive index field using an inverse matrix method with the BOS technique is proposed here under the assumption of an axisymmetric refractive index field. A field, generated by laser irradiation inside a glass, is reconstructed by the proposed method and is also theoretically calculated using the heat diffusion equation and thermal stress theory. The reconstructed field agrees well with the theoretically calculated one, which validates the proposed method. The proposed method is a promising candidate for measuring axisymmetric refractive index fields of various media. (C) 2018 Optical Society of America
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