Methods and apparatus for controlling a lithographic process

A method comprising:

• obtaining a substrate model for representing a process parameter fingerprint across a substrate, the substrate model being defined as a combination of basis functions including at least one basis function suitable for representing variation of the process parameter fingerprint between substrates and/or batches of substrates;
• receiving measurements of the process parameter across at least one substrate;
• determining substrate model parameters using the measurements and the basis functions;
• and
• determining a control parameter based on weighted values of the substrate model parameters, wherein values of substrate model parameters associated with the at least one basis function have a reduced weighting.

A method comprising:

• after a first step in a lithographic process involving a plurality of processing steps performed on a series of substrates, obtaining measurements of a measurement parameter across at least one substrate;
• applying the measurements to a model to determine a full fingerprint estimation of one or more operational parameters across the substrate;
• utilizing the full fingerprint estimation for applying the one or more operational parameters at a second processing step of the substrate;
• modifying the full fingerprint estimation to account for effects predetermined to have a distorting effect on at least one control parameter, to obtain a control parameter fingerprint estimation for the substrate;
• and
• at the first step in the processing of at least one subsequent substrate in the series of substrates, applying the control parameter fingerprint estimation.