Reconstruction of gratings from noisy reflection data

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. (C) 2002 Optical Society of America.