We compare different inverse scattering (IS) algorithms used to calculate profiles of fibre Bragg gratings (FBGs) and analyse their robustness, speed and implementation difficulties. We analyse sources of IS algorithm errors and discuss their relative importance. We discuss the optimal choice of IS algorithm for inverse-direct iterative optimisation schemes for grating design. We find that our time-domain layer-peeling method is an order of magnitude faster and more robust than the spectral domain algorithms considered here. We demonstrate that our method is essential to solving highly complex FBG designs demanded by astronomical applications.
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