Optimizing the parameters of spherical harmonic reconstruction of the 3D morphology of manufactured aggregate with different particle sizes

The optimal reconstruction parameters of spherical harmonic (SH) series for the aggregates with different morphologies and sizes were not clear. In this paper, manufactured aggregates with different sizes (1.18–2.36 mm, 2.36–4.75 mm, 4.75–9.50 mm), and natural aggregate with size >1.18 mm were scanned using the digital light projection (DLP), and reconstructed using SH series. The effect of maximum number of SH functions (N) used in the reconstruction series and the number of terms in the Gaussian quadrature (G) used for solving the SH expansion coefficients on the reconstruction errors were studied. The optimal reconstruction parameters for different particle sizes and morphologies were proposed, via a derived relationship between N and G. The reconstruction errors decreased when the N and G values increased. The relationship between N and G was derived to be G ≥ 1.84 N + 3.60, which is probably caused by the issue of the algebraic precision of the Gaussian integral.