## Abstract

We examined the influence of complex diffraction effects on low-coherence fringes created for high-aspect depth-to-width ratio structures called trenches. The coherence function was analyzed for these micrometer-wide trenches and was registered with a white-light interference microscope. For some types of surface structure we observed that additional low-coherence fringes that do not correspond directly to the surface topology are formed near the sharp edges of the structures. These additional coherence fringes were studied by rigorous numerical evaluations of vector diffractions, and these simulated interference fields were then compared with experimental results that were obtained with a white-light interference microscope.

© 2005 Optical Society of America

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### Equations (9)

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(1)
$$\mathrm{\gamma}=\mathit{\int}F(\mathrm{\lambda})F(\mathrm{\lambda}-{\mathrm{\Delta}}_{z})\text{d}\mathrm{\lambda},$$
(2)
$$\mathrm{\kappa}=\frac{{\text{NA}}_{\text{il}}}{{\text{NA}}_{\text{obj}}}.$$
(3)
$${\mathbf{\text{J}}}_{x,y,z}=\text{\u2211}_{\mathrm{\mu}}L({\mathbf{k}}_{\mathrm{\mu}})\times {\left\{\text{\u2211}_{\nu}H({\mathbf{k}}_{\nu ,\mathrm{\mu}})exp(i{\mathbf{k}}_{\nu ,\mathrm{\mu}}\cdot \mathbf{\text{r}}){cos}^{1/2}(\nu )\left[\begin{array}{l}{\stackrel{\sim}{E}}_{x}({\mathbf{k}}_{\nu ,\mathrm{\mu}})\hfill \\ {\stackrel{\sim}{E}}_{y}({\mathbf{k}}_{\nu ,\mathrm{\mu}})\hfill \end{array}\right]\right\}}^{2},$$
(4)
$$A={{\mathbf{\text{J}}}_{1}}^{\text{T}}{\mathbf{\text{J}}}_{2}*$$
(5)
$$=\frac{{I}_{0}\mathrm{\gamma}exp(i\mathrm{\phi})}{2},$$
(6)
$$\mathbf{\text{I}}={({\mathbf{\text{J}}}_{1}+{\mathbf{\text{J}}}_{2})}^{\text{T}}{({\mathbf{\text{J}}}_{1}+{\mathbf{\text{J}}}_{2})}^{*}$$
(7)
$$={I}_{0}[1+\mathrm{\gamma}cos(\mathrm{\phi})].$$
(8)
$${\mathbf{\text{J}}}_{2}=[cos(\mathrm{\Theta}),sin(\mathrm{\Theta})].$$
(9)
$${\mathbf{\text{J}}}_{2}=\frac{1}{\sqrt{2}}[1,i].$$