## Abstract

The grating division-of-amplitude photopolarimeter (G-DOAP) is an instrument that exploits the multiple-beam-splitting, polarizing, and dispersive properties of diffraction gratings for the time-resolved measurement of the complete state of polarization of collimated broadband incident light, as represented by the four Stokes parameters as a function of wavelength across the spectrum. It is a compact, high-speed sensor that has no moving parts and is simple to install and operate. These characteristics make the G-DOAP well suited for *in situ* spectroscopic ellipsometry (SE) applications for monitoring and controlling thin-film processes. The design and performance of a prototype instrument are presented. Precise SE measurements, to ±0.04° in ψ and ±0.1° in Δ, are demonstrated in the 550–940-nm wavelength range.

© 2003 Optical Society of America

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### Equations (15)

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(1)
$$sin\left({\mathrm{\theta}}_{i}\right)=sin\left(\mathrm{\theta}\right)-i\mathrm{\lambda}/g.$$
(2)
$$\mathbf{\text{I}}=\mathbf{\text{FS}},$$
(3)
$$\mathbf{\text{S}}={\mathbf{\text{F}}}^{-1}\mathbf{\text{I}}.$$
(4)
$$\mathbf{\text{I}}\left(P\right)={\mathbf{\text{F}}}_{0}+{\mathbf{\text{F}}}_{1}cos\left(2P\right)+{\mathbf{\text{F}}}_{2}sin\left(2P\right).$$
(5)
$$\mathbf{\text{I}}\left(\mathrm{RCP}\right)={\mathbf{\text{F}}}_{0}+{\mathbf{\text{F}}}_{3},\hspace{1em}\mathbf{\text{I}}\left(\mathrm{LCP}\right)={\mathbf{\text{F}}}_{0}-{\mathbf{\text{F}}}_{3},$$
(6)
$${\mathbf{\text{F}}}_{3}=0.5\left[\mathbf{\text{I}}\left(\mathrm{RCP}\right)-\mathbf{\text{I}}\left(\mathrm{LCP}\right)\right].$$
(7)
$${\mathbf{\text{F}}}_{0}=0.5\left[\mathbf{\text{I}}\left(\mathrm{RCP}\right)+\mathbf{\text{I}}\left(\mathrm{LCP}\right)\right].$$
(8)
$${\mathbf{\text{F}}}_{n}=\left[\begin{array}{cccc}1& {F}_{01}& {F}_{02}& {F}_{03}\\ 1& {F}_{11}& {F}_{12}& {F}_{13}\\ 1& {F}_{21}& {F}_{22}& {F}_{23}\\ 1& {F}_{31}& {F}_{32}& {F}_{33}\end{array}\right].$$
(9)
$${S}_{1}=0.5+0.5cos\left(4C\right),{S}_{2}=0.5sin\left(4C\right),{S}_{3}=sin\left(2C\right).$$
(10)
$$\mathrm{\Psi}=\frac{1}{2}{tan}^{-1}\left[\frac{{\left(S_{3}{}^{2}+S_{2}{}^{2}\right)}^{1/2}}{-{S}_{1}}\right],$$
(11)
$$\mathrm{\Delta}={tan}^{-1}\left[\frac{-{S}_{3}}{{S}_{2}}\right].$$
(12)
$$D=\left|\begin{array}{cccc}1& {x}_{0}& {y}_{0}& {z}_{0}\\ 1& {x}_{1}& {y}_{1}& {z}_{1}\\ 1& {x}_{2}& {y}_{2}& {z}_{2}\\ 1& {x}_{3}& {y}_{3}& {z}_{3}\end{array}\right|.$$
(13)
$$D=\left|\begin{array}{ccc}{x}_{1}-{x}_{0}& {y}_{1}-{y}_{0}& {z}_{1}-{z}_{0}\\ {x}_{2}-{x}_{0}& {y}_{2}-{y}_{0}& {z}_{2}-{z}_{0}\\ {x}_{3}-{x}_{0}& {y}_{3}-{y}_{0}& {z}_{3}-{z}_{0}\end{array}\right|.$$
(14)
$$D=\mathbf{\text{A}}\xb7\left(\mathbf{\text{B}}\times \mathbf{\text{C}}\right),$$
(15)
$${D}_{max}=\frac{16}{{3}^{1.5}}=3.0792.$$