## Abstract

This paper describes a study of the absorptance of thin films with the aim of
elucidating the region of validity for a direct relationship between the
absorptance and the absorption coefficient. The calculations are performed for
an unsupported film, a film on a transparent or metallic substrate, and for the
absorptance as a function of polarization.

© 1977 Optical Society of America

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### Equations (8)

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(1)
$$R={\left|\frac{{r}_{1}+{r}_{2}\hspace{0.17em}\text{exp}(-2i\gamma d)}{1+{r}_{1}{r}_{2}\hspace{0.17em}\text{exp}(-2i\gamma d)}\right|}^{2},$$
(2)
$$T={\left|\frac{{t}_{1}{t}_{2}\hspace{0.17em}\text{exp}(-i\gamma d)}{1+{r}_{1}{r}_{2}\hspace{0.17em}\text{exp}(-2i\gamma d)}\right|}^{2},$$
(3)
$${\u3008A(\theta )\u3009}_{\beta}=\frac{{\int}_{0}^{\pi /2}{A}_{\beta}(\theta )\hspace{0.17em}\text{cos}\theta \hspace{0.17em}\text{sin}\theta d\theta}{{\int}_{0}^{\pi /2}\text{cos}\theta \hspace{0.17em}\text{sin}\theta d\theta}.$$
(4)
$$\mathcal{R}=R+\frac{{T}^{2}{R}_{0}}{1-{R}_{0}{R}^{\prime}},$$
(5)
$$\mathcal{T}=\frac{T(1-{R}_{0})}{1-{R}_{0}{R}^{\prime}},$$
(6)
$${R}^{\prime}={\left|\frac{{r}_{2}+{r}_{1}\hspace{0.17em}\text{exp}(-2i\gamma d)}{1+{r}_{1}{r}_{2}\hspace{0.17em}\text{exp}(-2i\gamma d)}\right|}^{2}.$$
(7)
$$A\approx n\eta d\left[\frac{4{R}_{0}}{1-{{n}_{s}}^{2}}+\frac{2{{T}_{0}}^{2}}{(1+{n}_{s})(1-{R}_{0})}\right],$$
(8)
$$E(x)=(1-r)\hspace{0.17em}\text{exp}(-i\gamma x)\left\{\frac{1-r\hspace{0.17em}\text{exp}[-i\gamma 2(d-x)]}{1-{r}^{2}\text{exp}(-i\gamma 2d)}\right\}.$$