Reconstruction of refractive index maps using photogrammetry

Miller, A. and Mullholland, A. J. and Tant, K.M.M. and Pierce, S.G. and Hughes, B. and Forbes, A.B. (2021) Reconstruction of refractive index maps using photogrammetry. Inverse Problems in Science and Engineering, 29 (13). pp. 2696-2718. ISSN 1741-5977 (

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Large volume metrology is a key enabler of autonomous precision manufacturing. For component positioning, the optical-based metrology technique of photogrammetry could be used more widely if its accuracy was improved. These positional measurements are subject to uncertainties which can be greater than manufacturing tolerances. One source of uncertainty is due to thermal gradients, which cause the refraction of the light rays in large-scale industrial environments. This paper uses light-based sensor data to reconstruct a heterogeneous spatial map of the refractive index in air. We use this reconstructed refractive index map to discount the refractive effects and thereby reduce the uncertainty of this positioning problem. This new inverse problem employs Voronoi tessellations to spatially parameterize the refractive index map, the Fast Marching Method to solve the forward problem of calculating the light rays through this medium, and a Bayesian approach in the inversion. Using simulated data, this methodology leads to positioning improvements of up to 37 (Formula presented.).