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On page 756 of [2] there are expressions for transmittance:

[tex]T = \frac{n_3 \cos \theta _3}{n_1 \cos \theta _1} \left| t \right| ^2 \qquad \qquad \mbox{(TE)}[/tex]

[tex]T = \frac{(\cos \theta _3) / n_3}{(\cos \theta _1)/ n_1} \left| t \right| ^2 \qquad \qquad \mbox{(TM)}[/tex]

__In other words, I'm trying to find the transmittance (using the amplitude transmittance value I already know) for a system that consists of a semi-infinite incidence medium (dielectric), many thin-films (absorbing), and a semi-infinite substrate (absorbing)__. In comparison, the reflectance is easy to find, because you just multiply the reflectivity by its complex conjugate; this is not the case. If you use the expressions above, replacing [tex](n_3)[/tex] and [tex](\theta_3)[/tex] by the substrate complex refractive index and the complex angle on the exit side, respectively, the results will be complex as well.

Any ideas? Thanks.

[1] J. Eastman,

*Surface scattering in optical interference coatings*. PhD thesis, University of Rochester, 1974.

[2] M. Born and E. Wolf,

*Principles of Optics*. Cambridge, UK: Cambridge University Press, 7th ed., 1999.