Placement sensitivity to aberration in optical imaging

Theories are developed to quantify the shift of image intensity extremum (Δx) due to aberration. The theory on real, one-dimensional mask spectrum has been extended to complex, two-dimensional mask spectrum under coherent and partially coherent imaging. Verification of the formulae was performed on alternating phase-shifting mask (PSM) and contact array. Balanced third-order coma was used to illustrate the validity of the theories. It is found that the image shift due to aberration of alternating PSM decreases when the partial coherence factor increases. In general, the theories can be applied to any mask spectra and aberration functions.