By using the matrix-theory approach, an exact formula for the reflectance of light incident normally on a nonabsorbing, thin-film combination made of homogeneous and inhomogeneous films is derived. The refractive indexes of the inhomogeneous layers change exponentially with film thickness, and the combination is bounded on either side by nonabsorbing, homogeneous, semi-infinite media. The formula, which is valid for any wavelength, has been analyzed at short and long wavelengths.
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Sebastiano F. Monaco (1961) studied this question.
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