Mathematical methods for shape analysis of double-shell inertial confinement fusion capsules

Implosion symmetry is a key requirement in achieving a robust burning plasma in inertial confinement fusion (ICF) experiments. In double shell capsule implosions we are interested in the shape of the inner shell as it pushes on the fuel. Shape analysis is a popular technique for studying said symmetry during implosion. Paired filtering and contour finding algorithms are studied for their promise in reliably recovering Legendre shape coefficients from synthetic radiographs of double-shell capsules with x-ray framing camera noise. What we call the maximum intensity marching squares and the non-local means max(slope) methods are able to recover p₀, p₂ and p₄ maxslope Legendre shape coefficients with mean pixel discrepancy errors of 2.16 and 2.18, respectively, over all noisy synthetic radiographs studied. This improves upon prior radial lineout methods paired with Gaussian filtering which we show to be unreliable and whose performance is highly dependent on input parameters that are difficult to estimate.