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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 19, Iss. 11 — Nov. 1, 2002
  • pp: 2229–2237

Reconstruction of gratings from noisy reflection data

Johannes Skaar and Ricardo Feced  »View Author Affiliations


JOSA A, Vol. 19, Issue 11, pp. 2229-2237 (2002)
http://dx.doi.org/10.1364/JOSAA.19.002229


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Abstract

The worst-case error amplification factor in reconstructing a grating from its complex reflection spectrum is shown to be of the order 1/T<sub>min</sub>, where T<sub>min</sub> is the minimum transmissivity through the grating. For a uniform grating with coupling coefficient–length product κL, the error amplification is exp(2κL). The exponential dependence on the grating strength shows that spatial characterization of gratings from a measured reflection spectrum is impossible if the grating is sufficiently strong. For moderately strong gratings, a simple regularization technique is proposed to stabilize the solution of the inverse-scattering problem of computing the grating structure from the reflection spectrum.

© 2002 Optical Society of America

OCIS Codes
(050.2770) Diffraction and gratings : Gratings
(060.2340) Fiber optics and optical communications : Fiber optics components

Citation
Johannes Skaar and Ricardo Feced, "Reconstruction of gratings from noisy reflection data," J. Opt. Soc. Am. A 19, 2229-2237 (2002)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-19-11-2229


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