title: Reconstruction of gratings from noisy reflection data.
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(min), where T(min) is the minimum transmissivity through the grating. For a uniform grating with coupling coefficient-length product kappaL, the error amplification is exp(2kappaL). 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.
authors.affiliation: johannes.skaar@fysel.ntnu.no
authors.forename: Johannes
authors.initials: J
authors.lastname: Skaar
authors.forename: Ricardo
authors.initials: R
authors.lastname: Feced