## Abstract

At compact monolayer coverage the anisotropic rodlike molecules of palmitic acid, aligned parallel to each other and perpendicular to the monolayer film, are insensitive to wavelength dispersion relative to a water substrate. The relative absence of dispersion of the monolayer film makes it possible to obtain sufficient data to characterize the three unknowns of palmitic acid: the real refractive indices parallel and perpendicular to the plane of the film and the film thickness. Other nonabsorbing thin-film–substrate systems should lend themselves to similar analysis (where the dispersion of the film is relatively less than that of the substrate); particularly since automated, wavelength-tracking ellipsometers are coming into greater use.

© 1978 Optical Society of America

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### Equations (6)

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(1)
$$\begin{array}{c}\delta \mathrm{\Delta}=\delta -\overline{\mathrm{\Delta}}\\ =-4\pi d/\mathrm{\lambda}[\text{sin}{\varphi}_{i}\hspace{0.17em}\text{tan}{\varphi}_{i}{n}_{1}]/[1-({n}_{1}^{2}/{n}_{3}^{2})\hspace{0.17em}{\text{tan}}^{2}{\varphi}_{i}]\times [({n}_{x}^{2}-{n}_{3}^{2})/({n}_{1}^{2}-{n}_{3}^{2})][1-{n}_{1}^{2}/{\alpha}_{3}{n}_{x}^{2}],\end{array}$$
(2)
$${\alpha}_{3}=({n}_{z}^{2}/{n}_{x}^{2})[({n}_{x}^{2}-{n}_{3}^{2})/({n}_{z}^{2}-{n}_{3}^{2})].$$
(3)
$${\left(\frac{\partial n}{\partial d}\right)}_{{\varphi}_{1}}={\left(\frac{\partial n}{\partial d}\right)}_{{\varphi}_{2}}={\left(\frac{\partial n}{\partial d}\right)}_{{\varphi}_{3}}.$$
(4)
$${\left[\left(\frac{\partial \mathrm{\Delta}}{\partial d}\right)/\left(\frac{\partial \mathrm{\Delta}}{\partial n}\right)\right]}_{{\varphi}_{1}}={\left[\left(\frac{\partial \mathrm{\Delta}}{\partial d}\right)/\left(\frac{\partial \mathrm{\Delta}}{\partial n}\right)\right]}_{{\varphi}_{2}}={\left[\left(\frac{\partial \mathrm{\Delta}}{\partial d}\right)/\left(\frac{\partial \mathrm{\Delta}}{\partial n}\right)\right]}_{{\varphi}_{3}}$$
(5)
$$\text{tan}(\mathrm{\Delta}/2)=\text{cos}{\varphi}_{i}{({\text{sin}}^{2}{\varphi}_{i}-1/{n}^{2})}^{1/2}/{\text{sin}}^{2}{\varphi}_{i}.$$
(6)
$$\text{tan}({\mathrm{\Delta}}_{m}/2)=({n}^{2}-1)/2n.$$