Method and apparatus for measuring a structure on a substrate, models for error correction, computer program products for implementing such methods & apparatus

A reconstruction process includes measuring structures formed on a substrate by a lithographic process, determining a reconstruction model for generating modeled patterns, computing and minimizing a multi- variable cost function including model errors. Errors induced by nuisance parameters are modeled based on statistical description of the nuisance parameters' behavior, described by probability density functions. From the statistical description model errors are calculated expressed in terms of average model errors and weighing matrices. These are used to modify the cost function so as to reduce the influence of the nuisance parameters in the reconstruction, without increasing the complexity of the reconstruction model. The nuisance parameters may be parameters of the modeled structure, and/or parameters of an inspection apparatus used in the reconstruction. 种重构过程包括测量通过光刻工艺形成在衬底上的结构，确定用于生成模型化图案的重构模型，计算并最小化包括模型误差的多变量成本函数。由讨厌参数导致的误差基于通过概率密度函数描述的讨厌参数的行为的统计描述被建模。从统计描述计算在平均模型误差和加权矩阵方面所表示的模型误差。这些被用于修改成本函数以便减少重构中的讨