## Abstract

The refractive index and the thickness of a transparent pellicle are determined when the pellicle is placed between two vertical crossed polarizers and rotated in the horizontal plane. The transmission axes of the polarizers are neither parallel nor perpendicular to the plane of incidence. The light transmitted through the crossed polarizers reaches a minimum when the pellicle satisfies the absentee-layer condition. The refractive index and the film thickness are obtained from the pellicle orientation angles under such a condition.

© 1996 Optical Society of America

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### Equations (4)

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(1)
$${R}_{\mathrm{\nu}}=\frac{{r}_{01\mathrm{\nu}}+{r}_{12\mathrm{\nu}}\hspace{0.17em}\text{exp}(-j2\mathrm{\pi}d/{D}_{\mathrm{\phi}})}{1+{r}_{01\mathrm{\nu}}{r}_{12\mathrm{\nu}}\hspace{0.17em}\text{exp}(-j2\mathrm{\pi}d/{D}_{\mathrm{\phi}})},$$
(2)
$${{N}_{1}}^{2}={{N}_{0}}^{2}\hspace{0.17em}{\text{sin}}^{2}\hspace{0.17em}{\mathrm{\phi}}_{m}+{m}^{2}{\left(\frac{\mathrm{\lambda}}{2d}\right)}^{2},$$
(3)
$$\begin{array}{l}{N}_{1}={\left[{\text{sin}}^{2}\hspace{0.17em}{\mathrm{\phi}}_{m}+{m}^{2}\left(\frac{{\text{sin}}^{2}\hspace{0.17em}{\mathrm{\phi}}_{{m}^{\u2033}}-{\text{sin}}^{2}\hspace{0.17em}{\mathrm{\phi}}_{{m}^{\prime}}}{{{m}^{\prime}}^{2}-{{m}^{\u2033}}^{2}}\right)\right]}^{1/2}\\ (m={m}^{\prime}\hspace{0.17em}\text{or}\hspace{0.17em}{m}^{\u2033}),\hspace{0.17em}d=\frac{\mathrm{\lambda}}{2}{\left(\frac{{{m}^{\prime}}^{2}-{{m}^{\u2033}}^{2}}{{\text{sin}}^{2}\hspace{0.17em}{\mathrm{\phi}}_{{m}^{\u2033}}-{\text{sin}}^{2}\hspace{0.17em}{\mathrm{\phi}}_{{m}^{\prime}}}\right)}^{1/2}.\end{array}$$
(4)
$$m=\frac{{\text{sin}}^{2}\hspace{0.17em}{\mathrm{\phi}}_{m-1}-{\text{sin}}^{2}\hspace{0.17em}{\mathrm{\phi}}_{m+1}}{4\hspace{0.17em}{\text{sin}}^{2}\hspace{0.17em}{\mathrm{\phi}}_{m}-2({\text{sin}}^{2}\hspace{0.17em}{\mathrm{\phi}}_{m-1}+{\text{sin}}^{2}\hspace{0.17em}{\mathrm{\phi}}_{m+1})}.$$