Lambda Physics

Optical Coatings Research Laboratory

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Single-Layer Optical Coating Reflectivity Calculator

Calculate the reflectance and transmittance of a single homogeneous optical coating at normal incidence, determine the quarter-wave coating thickness, and visualize the spectral response.

Input parameters

Optical media
Coating and wavelength
Spectral graph

Calculation results

Bare substrate R
–
%
Coated surface R
–
%
Coated surface T
–
%
Quarter-wave d
–
nm
R change vs bare
–
percentage points
Optimal n for zero R (ideal)
–
n
Optical phase thickness
–
°
Quarter-wave R
–
%
Model: homogeneous, isotropic, non-absorbing single layer on a plane-parallel substrate, normal incidence. The entered refractive indices are treated as constant over the displayed spectral range. For real coating design, material dispersion n(λ), absorption k(λ), substrate absorption and angle of incidence should be included where relevant.
Calculation method
r01 = (n0 − n1) / (n0 + n1)
r12 = (n1 − ns) / (n1 + ns)
δ = 2π n1d / λ
r = [r01 + r12 exp(2iδ)] / [1 + r01r12 exp(2iδ)]
R = |r|²
T = 1 − R   (lossless coating and substrate)

Quarter-wave thickness: d = λ / (4n1)

Single-layer thin-film coating calculation

This online optical coating calculator evaluates a single dielectric or transparent thin film deposited on a plane-parallel optical substrate at normal incidence. It is useful for exploring anti-reflection (AR) coatings, quarter-wave layers, surface reflectance and basic thin-film interference effects.

The calculator compares the coated surface with the bare substrate and plots reflectance and transmittance as a function of wavelength. It also reports the optical phase thickness and the ideal refractive index for zero reflection in the classical single-layer quarter-wave case.

Typical applications

  • Estimate the reflectance of a single-layer AR coating.
  • Find the quarter-wave physical thickness for a selected wavelength.
  • Visualize thin-film interference and the effect of coating thickness.
  • Compare coating materials with different refractive indices.

Optical coating reference

For a lossless quarter-wave layer at the design wavelength, the ideal single-layer AR condition is n1 = √(n0ns), with physical thickness d = λ/(4n1).

The simple model here assumes constant real refractive indices. Real thin-film design can require dispersion, extinction coefficient k, substrate absorption and oblique-incidence effects.

Lambda Physics also offers optical components, optical glass and coating materials in its General Stock catalog.