Nondestructive measurement of two-dimensional refractive index profiles by deflectometry

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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 x 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.

Original languageEnglish (US)
Title of host publicationModeling Aspects in Optical Metrology V
EditorsRichard M. Silver, Bernd Bodermann, Karsten Frenner
ISBN (Electronic)9781628416862
StatePublished - 2015
EventModeling Aspects in Optical Metrology V - Munich, Germany
Duration: Jun 23 2015Jun 25 2015

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
ISSN (Print)0277-786X
ISSN (Electronic)1996-756X


OtherModeling Aspects in Optical Metrology V

Bibliographical note

Publisher Copyright:
© 2015 Copyright SPIE.


  • deflectometry
  • geometrical optics
  • gradient-index
  • inhomogeneous media
  • metrology
  • refractive index


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