Abstract: Methods and associated apparatus for reconstructing a free-form geometry of a substrate, the method including: positioning the substrate on a substrate holder configured to retain the substrate under a retaining force that deforms the substrate from its free-form geometry; measuring a height map of the deformed substrate; and reconstructing the free-form geometry of the deformed substrate based on an expected deformation of the substrate by the retaining force and the measured height map.

Abstract: Methods and associated apparatus for reconstructing a free-form geometry of a substrate, the method including: positioning the substrate on a substrate holder configured to retain the substrate under a retaining force that deforms the substrate from its free-form geometry; measuring a height map of the deformed substrate; and reconstructing the free-form geometry of the deformed substrate based on an expected deformation of the substrate by the retaining force and the measured height map.

Abstract: A method for determining a mechanical property of a layer applied to a substrate and associated control system for controlling a lithographic process. The method includes obtaining measured out-of-plane deformation of the substrate, the out-of-plane deformation including deformation normal to a substrate plane defined by, or parallel to, a substrate surface. The measured out-of-plane deformation is fitted to a second order polynomial in two coordinates associated with the substrate plane and the mechanical property (e.g. anisotropic Young's moduli) of the layer is determined based on characteristics of the fitted second order polynomial. The mechanical property of the layer can be used to calibrate an in-plane distortion model of the substrate for predicting in-plane distortion based on the measured out-of-plane deformation.