Thin Film on Thick Substrate Calculator
Coherent Coating on a Thick Substrate
Real lab samples often pair a sub-micron coating with a millimeter-thick glass slide or polymer sheet. The coating keeps its resolved optical phase while the thick substrate is best modeled as incoherent — phase variations across its thickness exceed what any real source bandwidth or thickness uniformity can resolve.
Why This Distinction Matters
Each layer adds a number of round-trip phase cycles \(N = 2nd\cos\theta/\lambda\) to the reflected wave — where \(n\) is the layer refractive index, \(d\) is its physical thickness, \(\theta\) is the refracted ray angle inside the layer, and \(\lambda\) is the vacuum wavelength — and that number decides whether interference fringes survive. The thin coating accumulates a small fraction of a cycle, so its phase is well-defined and contributes coherently. A millimeter-thick substrate accumulates thousands of cycles in the visible, more than any real source bandwidth, beam divergence, or thickness variation can resolve — its phase is randomized, so it is treated incoherently: the dense Fabry–Pérot fringes wash out into a smooth intensity baseline.