Methods and apparatuses for measurement of a parameter of a feature fabricated on a substrate

A method comprising:

• receiving, by a receiver, radiation scattered from one or more measured features on the substrate;
• generating, by a pupil generator, an unprocessed pupil representation based on the received radiation, the unprocessed pupil representation comprising a plurality of pixels each having an intensity indicative of at least one parameter of interest of a feature fabricated on a substrate and of one or more nuisance parameters of the feature;
• multiplying, by a matrix multiplier, a transformation matrix with the intensities of each of the plurality of pixels of the unprocessed pupil representation to determine a post-processed pupil representation in which the effects of the one or more nuisance parameters are mitigated;
• and
• estimating, by a parameter estimator, the at least one parameter of interest based on the post-processed pupil representation.

A non-transitory computer readable medium comprising instructions, that when executed by a computer system, are configured to cause the computer to at least:

• generate an unprocessed pupil representation based on signals representing measured radiation scattered from one or more measured features on a substrate, the unprocessed pupil representation comprising a plurality of pixels each having an intensity indicative of at least one parameter of interest of a feature fabricated on a substrate and of one or more nuisance parameters of the feature;
• multiply a transformation matrix with the intensities of each of the plurality of pixels of the unprocessed pupil representation to determine a post-processed pupil representation in which the effects of the one or more nuisance parameters are mitigated;
• and
• estimate the at least one parameter of interest based on the post-processed pupil representation.