Determination of slopes of microscopic surface features by Nomarski polarization interferometry

Abstract

The two images produced by each feature in a Nomarski polarization interferogram are in general not equivalent. In the case of an etch pit or other isolated, sloped feature, the angle ϑ between the feature and the flat background surface can be computed from the fringe spacing l in the feature by the relationship sin[ϑapp−(ε/2) cosα] =λ/2l. The angle ε/2 is calculated from the background fringe spacing l0 and the relation sin(ε/2) =λ/2l0. The angle α is the orientation of the feature with respect to the background interference fringes on the flat surface. An additional correction is necessary to calculate ϑ from ϑapp because of the distortion of the fringe spacings which occurs in microinterferometers when using microscope objectives of large numerical aperture. Empirical observation shows that this obliquity correction can be calculated accurately by a formula first derived by Ingelstam. The method of determining slopes from fringe spacings in Nomarski polarization interferometry is described in detail. This description may be of interest to investigators who study crystal surfaces or changes in their topography during chemical reactions, because the Nomarski microinterferometer is suitable for continuous observation of surface changes which accompany reactions in a controlled-atmosphere heating stage.

Theory for double beam interference microscopes with coherence effects and verification using the Linnik microscope

“…Dependence of the fringe size and contrast on the NA It has been known for a long time [7][8][9][10][11][12][13][14][15][16][17] that the NA of an interferometric microscope can aVect the fringe size (spacing) and therefore the surface heights measured with that objective. For a Michelson interferometer (NA5 0) the fringe size (FS) is ¶=2 but as the NA gets larger the FS becomes larger.…”

“…By scanning and using phase shifting interferometry techniques three-dimensional images could be constructed [2][3][4][5][6]. A number of models [7][8][9][10][11][12][13][14][15][16][17] have been proposed to explain the dependence of the fringe size on the numerical aperture of the microscope objective but none of these gave a satisfactory explanation. The most, but not completely, accurate expression for the correction factor at high numerical aperture (NA) is the one derived by Ingelstam and Johansson [8], who used an eVective NA determined by the shape of the back aperture, the spatial coherence and the uniformity of the illumination.…”

Effect of numerical aperture on interference fringe spacing

“…Various presentations of experimental investigations have also been given. [7][8][9][10][11] An interferometric image consists of three terms. In addition to the interferometric term, there is a conventional intensity image and a constant reference beam term.…”