Abstract: A method and apparatus of detection, registration and quantification of an image. The method may include obtaining an image of a lithographically created structure, and applying a level set method to an object, representing the structure, of the image to create a mathematical representation of the structure. The method may include obtaining a first dataset representative of a reference image object of a structure at a nominal condition of a parameter, and obtaining second dataset representative of a template image object of the structure at a non-nominal condition of the parameter. The method may further include obtaining a deformation field representative of changes between the first dataset and the second dataset. The deformation field may be generated by transforming the second dataset to project the template image object onto the reference image object. A dependence relationship between the deformation field and change in the parameter may be obtained.

Abstract: A defect prediction method for a device manufacturing process involving production substrates processed by a lithographic apparatus, the method including training a classification model using a training set including measured or determined values of a process parameter associated with the production substrates processed by the device manufacturing process and an indication regarding existence of defects associated with the production substrates processed in the device manufacturing process under the values of the process parameter, and producing an output from the classification model that indicates a prediction of a defect for a substrate.

Abstract: In a lithographic process, product units such as semiconductor wafers are subjected to lithographic patterning operations and chemical and physical processing operations. Alignment data or other measurements are made at stages during the performance of the process to obtain object data representing positional deviation or other parameters measured at points spatially distributed across each unit. This object data is used to obtain diagnostic information by performing a multivariate analysis to decompose a set of vectors representing the units in said multidimensional space into one or more component vectors. Diagnostic information about the industrial process is extracted using the component vectors. The performance of the industrial process for subsequent product units can be controlled based on the extracted diagnostic information.