Modelling radially symmetric impact craters with Zernike polynomials

Wallis, D.; Solomon, C.J.; Kearsley, A.T.; Graham, G. and McBride, N. (2002). Modelling radially symmetric impact craters with Zernike polynomials. International Journal of Impact Engineering, 27(4) pp. 433–457.

DOI: https://doi.org/10.1016/S0734-743X(01)00148-8

Abstract

Crater morphology in a ductile target can reveal some properties of the impacting particle. Simple measurements alone, such as the crater depth and diameter are limited in potential because the complete morphology is not considered. Detailed shape measurements, made by comparing stereo Scanning Electron Micrographs, can be reduced to a parameter set based on an orthogonal expansion over a circular domain, allowing quantitative comparisons between craters that consider the complete morphology. Most high-velocity impact craters are circular (have a circular rim), enabling us to make a model using only the radially symmetric terms from the orthogonal functions set. Shape parameters can be plotted on a feature space diagram, where similar shaped craters form clusters which can be analysed statistically. The method has been applied to laboratory impacts using a two-stage light-gas gun to fire mineral grains at an aluminium alloy target and glass beads over the velocity range 1–6 kms−1. The minerals kamacite and enstatite can be distinguished from crater morphology by this method and we have shown that the shape of impact craters change over the velocity range 1–6 kms−1 as well as simply the depth to diameter ratio.

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