Thin-film reflectance and transmittance calculator
Transfer-matrix calculation of a thin-film stack: choose or edit the layers, set the design wavelength, substrate and angle of incidence, and read s, p and average reflectance and transmittance with the coating color.
- SiO₂n 1.461
- TiO₂n 2.668
- Fused silican 1.461
Indices at λ₀ = 532 nm. Layers are drawn to scale with each other; the substrate is cut short.
- Transmittance at 532 nm
- 96.5%
- s and p
- s 96.5%p 96.5%
- Reflectance
- 3.51%
- Peak T, 432 to 562 nm
- 96.5%at 532.0nm
- Stack
- 15layers1.13µm
Reflectance 3.51 percent and transmittance 96.5 percent at 532 nm, 0 degrees, average of s and p. Narrow bandpass at 532 nm, 15 layers on fused silica.
Reflected color
Y 97.1 %
x 0.324 y 0.347
Transmitted color
Y 2.91 %
x 0.184 y 0.122
Seen in D65 daylight by the CIE 1931 2° observer, shown in sRGB. Dim colors are drawn brighter so the hue shows; Y is the true luminous value.
Layers, air side first
Air
- 1.00 QW
- 1.00 QW
- 1.00 QW
- 1.00 QW
- 1.00 QW
- 1.00 QW
- 1.00 QW
- 2.00 QW
- 1.00 QW
- 1.00 QW
- 1.00 QW
- 1.00 QW
- 1.00 QW
- 1.00 QW
- 1.00 QW
Fused silica substrate
A single cavity with no blocking stack. Outside the mirrors' stop band it passes light again, and that leak sets most of the transmitted color.
Indices: fused silica, Malitson (1965); MgF₂, Dodge (1984); TiO₂, DeVore (1951), bulk rutile, so evaporated films run lower; Ta₂O₅, Rodríguez-de Marcos et al. (2016); N-BK7, the SCHOTT catalog.
At 13.5 nm the same calculation matches the Mo/Si mirror model on the EUV and DUV optics page to nine decimal places.
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Illustrative sample · coating designs · coated face only, the back face of the substrate is left out
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