Methods, apparatuses, and software are disclosed for optimization of a source and/or mask as used in lithographic manufacturing and patterning processes. One method includes determining a first pupil having a central obscuration (CO), determining a diffraction order (DO) based on a target design and a mask model, determining a first diffraction pattern (DP) based on the DO and the first pupil, the first DP including overlapping regions of diffracted light, determining a second DP based on the DO and the first pupil, and determining an initial pupil based on the first DP and the second DP, the initial pupil including at least some of the overlapping regions.

In one embodiment, an aperture correction amount calculation method is for calculating a correction amount for positions or dimensions of a plurality of apertures formed in an aperture array substrate through which multiple charged particle beams pass. The method includes measuring a shift amount distribution on an irradiation surface, which is a distribution of shift amounts from a predetermined position or a predetermined current density of each beam within a beam array of the multiple charged particle beams, dividing the beam array into a predetermined number of block regions based on the shift amount distribution, and calculating a representative value of the shift amounts corresponding to each block region, and calculating, for each of the block regions, correction amounts for positions or dimensions of the corresponding apertures of the aperture array substrate based on the representative values.

Methods and systems for compensating for uncertainty in illumination angle of incidence to enable accurate measurements of semiconductor structures are described herein. In one aspect, measurements are performed at one or more nominal angles of incidence, an actual angle of incidence corresponding to each measurement is estimated, and a value of a parameter of interest characterizing a measured structure is estimated based at least in part on the collected measurement data and the actual angle of incidence. In some examples, an actual angle of incidence is directly measured. In some other examples, an actual angle of incidence is estimated from measurement data collected over a range of nominal illumination angles of incidence. In some other examples, an actual angle of incidence with respect to a tilted structure is estimated from measurement data collected over a range of nominal illumination angles of incidence.

A method for improving imaging of a feature on a mask to a substrate during scanning operation of a lithographic apparatus. The method includes obtaining a dynamic pupil representing evolution of an angular distribution of radiation exposing a mask during a scanning operation of a lithographic apparatus and determining a variation of shift of a feature at a substrate during the scanning operation due to interaction of the dynamic pupil with the mask. The method includes configuring a mask parameter and/or or a control parameter of the lithographic apparatus to reduce the variation of shift of the feature.