## Abstract

A far-field setup based on the fast and simultaneous recording of 1 million intensity angle-resolved-light-scattering patterns allows both to reconstruct surface topography and to cancel local defects in this topography. A spectral analysis is performed on measured data and allows to extract roughness and slopes mapping of a surface taking into account the spectral bandpass.

© 2014 Optical Society of America

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### Equations (19)

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(1)
$$\delta =\sqrt{\frac{1}{S}{\int}_{\mathbf{r}}{h}^{2}(\mathbf{r})\mathrm{d}\mathbf{r}}\ll \lambda $$
(2)
$$\hat{h}(\mathit{\sigma})=\frac{1}{4{\pi}^{2}}{\int}_{\mathbf{r}}h(\mathbf{r})\mathrm{exp}(j\mathit{\sigma}\xb7\mathbf{r})\mathrm{d}\mathbf{r}$$
(3)
$$\mathit{\sigma}=k\text{\hspace{0.17em}}\mathrm{cos}\text{\hspace{0.17em}}\theta |\begin{array}{c}\mathrm{cos}\text{\hspace{0.17em}}\phi \\ \mathrm{sin}\text{\hspace{0.17em}}\phi \end{array}$$
(4)
$$E(\mathit{\sigma},{\mathit{\sigma}}_{\mathbf{0}})=C(\mathit{\sigma},{\mathit{\sigma}}_{\mathbf{0}})\xb7\hat{h}(\mathit{\sigma}-{\mathit{\sigma}}_{\mathbf{0}}),$$
(5)
$$E(\theta ,i)=C(\theta ,i)\xb7\widehat{h}(\theta ,i).$$
(6)
$$I(\mathit{\sigma},{\mathit{\sigma}}_{\mathbf{0}})=D(\mathit{\sigma},{\mathit{\sigma}}_{\mathbf{0}})\xb7\gamma (\mathit{\sigma}-{\mathit{\sigma}}_{\mathbf{0}})$$
(7)
$$\gamma (\mathit{\sigma})=\frac{4{\pi}^{2}}{S}{|\widehat{h}(\mathit{\sigma})|}^{2}.$$
(8)
$$\gamma (\mathit{\sigma}-{\mathit{\sigma}}_{\mathbf{0}})=I(\mathit{\sigma},{\mathit{\sigma}}_{\mathbf{0}})/D(\mathit{\sigma},{\mathit{\sigma}}_{\mathbf{0}}).$$
(9)
$${\delta}^{2}={\int}_{\mathit{\beta}}\gamma (\mathit{\beta})\mathrm{d}\mathit{\beta}.$$
(10)
$$\mathit{\beta}=\mathit{\sigma}-{\mathit{\sigma}}_{\mathbf{0}}.$$
(11)
$$-k(1+\mathrm{sin}\text{\hspace{0.17em}}i)\le \beta =k\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}\theta -k\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}i\le k(1-\mathrm{sin}\text{\hspace{0.17em}}i),$$
(12)
$$i=\frac{\pi}{2}\Rightarrow 0\le |\beta |\le 2k.$$
(13)
$${\delta}^{2}={\int}_{\mathit{\sigma}}\gamma (\mathit{\sigma})\mathrm{d}\mathit{\sigma}={\int}_{\sigma ,\phi}\sigma \gamma (\sigma ,\phi )\mathrm{d}\sigma \mathrm{d}\phi \phantom{\rule{0ex}{0ex}}=2\pi {\int}_{\sigma}\sigma {\gamma}^{*}(\sigma )\mathrm{d}\sigma $$
(14)
$${\delta}^{2}=2\pi {k}^{2}{\int}_{\theta}{\gamma}^{*}(\theta )\mathrm{cos}\text{\hspace{0.17em}}\theta \text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}\theta \mathrm{d}\theta .$$
(15)
$${\delta}_{ij}^{2}=2\pi {k}^{2}{\int}_{\theta}{\gamma}_{ij}^{*}(\theta )\mathrm{cos}\text{\hspace{0.17em}}\theta \text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}\theta \mathrm{d}\theta .$$
(16)
$$\mathit{\beta}=(\sigma -{\sigma}_{0})\mathbf{x}=-{\sigma}_{0}\mathbf{x}$$
(17)
$$k\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}{i}_{\mathrm{min}}\le \beta \le \mathrm{sin}\text{\hspace{0.17em}}{i}_{\mathrm{max}}.$$
(18)
$$\frac{1}{\lambda}\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}{i}_{\mathrm{min}}\le \beta \le \frac{1}{\lambda}\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}{i}_{\mathrm{max}}\Rightarrow 2\xb7{10}^{-4}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\mathrm{nm}}^{-1}\le \beta \le 1\xb7{10}^{-1}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\mathrm{nm}}^{-1}\mathrm{.}$$
(19)
$${s}_{ij}^{2}=\frac{1}{{S}_{ij}}{\int}_{x,y}[{\left(\frac{\partial h}{\partial x}\right)}^{2}+{\left(\frac{\partial h}{\partial y}\right)}^{2}]\mathrm{d}x\mathrm{d}y\phantom{\rule{0ex}{0ex}}=2\pi {\int}_{\sigma}{\sigma}^{3}{\gamma}_{ij}^{*}(\sigma )\mathrm{d}\sigma .$$