WASHES · REFERENCE GALLERY · OPTICS
Kubelka–Munk glazing playground
Kubelka & Munk, 1931. "Ein Beitrag zur Optik der Farbanstriche," Zeitschrift für Technische Physik 12, 593–601. The two-flux model behind the Washes renderer.
Each pigment is characterized by an absorption coefficient K and a scattering coefficient S per channel. A layer of thickness x has a closed-form reflectance R and transmittance T; stacking a layer over a background of reflectance Rb composites optically as R + T²Rb / (1 − RRb) — light passes down through the glaze, bounces, and passes back up, attenuated twice.
The two large swatches render the same two layers both ways: physically, via Kubelka–Munk, and naively, via sRGB alpha compositing. The chart plots the top pigment's reflectance per channel as its thickness grows, flattening toward the asymptote R∞.
Kubelka–Munk
Naive alpha blend
Cross-section, glaze → paper
Try this
1. Asymmetry. Titanium white over ivory black, then swap. White over black scatters light back before it reaches the black and reads pale gray; black over white goes nearly black. Order matters in K–M because R and T are not symmetric roles — alpha blending has no equivalent.
2. Glazing luminosity. A thin ultramarine glaze (x ≈ 0.4) over a hansa yellow wash on white paper yields a green the alpha-blend swatch renders duller and grayer. This is "blue + yellow = green" — the effect Sochorová & Jamriška built Mixbox to recover — falling straight out of the 1931 math.
3. Black paper. Any transparent pigment (rose, ultramarine) over black paper nearly vanishes at any thickness — nothing scatters light back. Titanium white still reads. Watch the chart: for transparent pigments over black, the curves barely lift off zero. That is the K-versus-S distinction made visible.
Coefficient caveat: the K and S values here are representative numbers chosen to behave like their namesakes, not the measured coefficients from Figure 5 of Curtis et al. 1997. Swap in the paper's values for the published gallery.