Model-based shape from shading for microelectronics applications

Model-based shape from shading (SFS) is a promising paradigm introduced by Atick et al. [Neural Comput 8 (1996), 1321– 1340 ] in 1996 for solving inverse problems when we happen to have a lot of prior information on the depth profiles to be recovered. In the present work we adopt this approach to address the problem of recovering wafer profiles from images taken using a scanning electron microscope (SEM). This problem arises naturally in the microelectronics inspection industry. A low-dimensional model, based on our prior knowledge on the types of depth profiles of wafer surfaces, has been developed, and based on it the SFS problem becomes an optimal parameter estimation. Wavelet techniques were then employed to calculate a good initial guess to be used in a minimization process that yields the desired profile parametrization. A Levenberg–Marguardt (LM) optimization procedure has been adopted to address ill-posedness of the SFS problem and to ensure stable numerical convergence. The proposed algorithm has been tested on synthetic images, using both Lambertian and SEM imaging models. VC 2006 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 16, 65–76, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.20065