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Proceedings Paper

Nondestructive measurement of two-dimensional refractive index profiles by deflectometry
Author(s): Di Lin; James R. Leger
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Paper Abstract

We present a method for calculating a two-dimensional refractive index field from measured boundary values of beam position and slope. By initially ignoring the dependence of beam trajectories on the index field and using cubic polynomials to approximate these trajectories, we show that the inverse problem can be reduced to set of linear algebraic equations and solved using a numerical algorithm suited for inverting sparse, ill-conditioned linear systems. The beam trajectories are subsequently corrected using an iterative ray trace procedure so that they are consistent with the ray equation inside the calculated index field. We demonstrate the efficacy of our method through computer simulation, where a hypothetical test index field is reconstructed on a 15 × 15 discrete grid using 800 interrogating rays and refractive index errors (RMS) less than 0.5% of the total index range (nmax-nmin) are achieved. In the subsequent error analysis, we identify three primary sources of error contributing to the reconstruction of the index field and assess the importance of data redundancy. The principles developed in our approach are fully extendable to three-dimensional index fields as well as more complex geometries.

Paper Details

Date Published: 21 June 2015
PDF: 11 pages
Proc. SPIE 9526, Modeling Aspects in Optical Metrology V, 95260Q (21 June 2015); doi: 10.1117/12.2184856
Show Author Affiliations
Di Lin, Univ. of Minnesota, Twin Cities (United States)
James R. Leger, Univ. of Minnesota, Twin Cities (United States)

Published in SPIE Proceedings Vol. 9526:
Modeling Aspects in Optical Metrology V
Bernd Bodermann; Karsten Frenner; Richard M. Silver, Editor(s)

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