Topographic profiling and refractive-index analysis by use of differential interference contrast with bright-field intensity and atomic force imaging

A methodology is described for phase restoration of an object function from differential interference contrast (DIC) images. The methodology involves collecting a set of DIC images in the same plane with different bias retardation between the two illuminating light components produced by a Wollaston prism. These images, together with one conventional bright-field image, allows for reduction of the phase deconvolution restoration problem from a highly complex nonlinear mathematical formulation to a set of linear equations that can be applied to resolve the phase for images with a relatively large number of pixels. Additionally, under certain conditions, an on-line atomic force imaging system that does not interfere with the standard DIC illumination modes resolves uncertainties in large topographical variations that generally lead to a basic problem in DIC imaging, i.e., phase unwrapping. Furthermore, the availability of confocal detection allows for a three-dimensional reconstruction with high accuracy of the refractive-index measurement of the object that is to be imaged. This has been applied to reconstruction of the refractive index of an arrayed waveguide in a region in which a defect in the sample is present. The results of this paper highlight the synergism of far-field microscopies integrated with scanned probe microscopies and restoration algorithms for phase reconstruction.