Predict interference colors for clear oxide films by thickness, density, and substrate. Transfer matrix optics and CIE 1931 color science, plus a PVD coating color reference.
Select a material, set density and substrate, then drag the thickness slider — or click the spectrum map — to see live reflected color.
Standard — typical ALD / sputtered film, f ≈ 0.85
Slider range adjusts to material's interesting window. Type larger values to explore higher orders.
As film thickness increases, the two reflected beams (from the top and bottom of the film) cycle in and out of phase. At phase difference δ = π, the wavelength is maximally reflected and defines the perceived color. Thicker films produce longer-wavelength (redder) colors, then repeat the color sequence in higher orders — but with lower contrast.
Amorphous or porous films (sputter-deposited at high pressure, PECVD) incorporate void space, reducing effective refractive index via effective medium theory. A TiO₂ film at n = 2.10 (porous) needs ~17% more thickness to produce the same color as a dense rutile film at n = 2.70. Optical measurements of n are a practical indicator of film quality and packing density.
Reflection at the film/substrate interface (r₁₂) depends on the index contrast. A metallic substrate (silver, gold) produces a large, complex r₁₂ that modulates the interference deeply. Gold's absorption onset at ~520 nm imparts a warm tint to films on gold, even at zero thickness. Porous or Lambertian white/black substrates reduce interference contrast while adding a background tint.