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
Johannes Skaar and Ricardo Feced, "Reconstruction of gratings from noisy reflection data," J. Opt. Soc. Am. A 19, 2229-2237 (2002)