ISO 4287 on Mineral Surfaces
Published:
ISO 4287 on mineral surfaces
Implemented the standard surface roughness metrics (ISO 4287) for the depth profiler. These are the same parameters used in precision manufacturing to characterize machined surfaces, now applied to mineral samples to quantify particle size and texture.
Ra = (1/N) Σ |zi - z̄|, arithmetic mean deviation
Rq = √((1/N) Σ (zi - z̄)²), root mean square roughness
Rz = max(peaks) - min(valleys), maximum height
Rsk = (1/N·Rq³) Σ (zi - z̄)³, skewness (asymmetry)
Rku = (1/N·Rq⁴) Σ (zi - z̄)⁴, kurtosis (peakedness)
The interesting finding: Ra and Rq correlate well with the coarser size fractions from sieve analysis, but for fine particles the relationship breaks down because the depth camera resolution becomes a limiting factor. We need sub-millimeter depth accuracy for the finer fractions, and the current setup gives us about 0.5mm, fine for coarse characterization but not for complete granulometry replacement.
Also added cross-section profile extraction, draw a line on the depth map and get a 1D height profile with bilinear interpolation. This is surprisingly useful for identifying particle boundaries and measuring individual grain sizes.
The Gaussian curvature analysis K = (f_xx · f_yy - f_xy²) / (1+fx²+fy²)² helps identify flat regions (K≈0, bulk material), convex peaks (K>0, particle tops), and saddle points (K<0, particle boundaries). This topological classification could feed directly into an automated particle counter.
