Vectorial 3D modeling of coherence scanning interferometry

Electromagnetic modeling of interference, confocal, and focus variation microscopy

“…are the minimum and maximum diffraction orders limited by the NA of the objective lens, 19 c n is the Fourier coefficient related to the diffraction order n, 15 and the square root term considers energy conservation. 39…”

“…22 In the previous studies, quasianalytic models are developed based on Fourier optics or scalar Kirchhoff theory to analyze systematic deviations and the transfer characteristics of CSI systems, 15,[23][24][25][26] confocal microscopes, 12,14,27 as well as conventional or FVM. [28][29][30] It should be noted that with respect to the scattering surface, the so-called phase object approximation 15,19,27 and foil model 23,25,29 are based on the same scalar Kirchhoff scattering theory 31 and thus show similar results. 19,32 Generally, the phase object approximation is more flexible regarding incidence angle and surface material dependence of reflection coefficients and is less affected by numerical artifacts.…”

“…[28][29][30] It should be noted that with respect to the scattering surface, the so-called phase object approximation 15,19,27 and foil model 23,25,29 are based on the same scalar Kirchhoff scattering theory 31 and thus show similar results. 19,32 Generally, the phase object approximation is more flexible regarding incidence angle and surface material dependence of reflection coefficients and is less affected by numerical artifacts. As an additional advantage, the phase object approach can be simply exchanged by a rigorous method in the modeling of surface topography instruments if required, since both may be considered by a pupil integration.…”

“…[9][10][11][12][13][14][15][16][17][18] In order to predict and analyze these deviations, numerical models are developed. In this study, we present an extension of the vectorial Kirchhoff model introduced in former publications, 19,20 where inconsistencies are fixed and local reflection coefficients depending on the local surface slope are considered. The extended model is unified in a sense that it applies to CSI, CM, and FVM.…”

“…Nonetheless, the model presented by Xie only considers the zeroth order of diffraction for depth scan, leading to significant disadvantages compared to the conventional Kirchhoff model as demonstrated in a previous study. 19 A vectorial extension of the scalar Kirchhoff model for CSI has been presented by Pahl et al 19 However, the model shows inconsistencies, since the electric field is not perpendicular to the wave vector after the scattering process anymore. These inconsistencies are partially fixed in a recent publication.…”