A lithographic apparatus is described, the apparatus comprising: an illumination
system configured to condition a
radiation beam; a support constructed to support a patterning device, the patterning device being capable of imparting the
radiation beam with a pattern in its cross-section to form a patterned
radiation beam; a substrate table constructed to hold a substrate; and a
projection system configured to project the patterned
radiation beam onto a target portion of the substrate, wherein the apparatus further comprises an alignment
system configured to perform, for one or more alignment marks that are present on the substrate: —a plurality of alignment mark position measurements for the alignment mark by applying a respective plurality of different alignment measurement parameters, thereby obtaining a plurality of measured alignment mark positions for the alignment mark; the apparatus further comprising a
processing unit, the
processing unit being configured to: —determine, for each of the plurality of alignment mark position measurements, a positional deviation as a difference between an expected alignment mark position and a measured alignment mark position, the measured alignment mark position being determined based on the respective alignment mark position measurement; —define a set of functions as possible causes for the positional deviations, the set of functions including a
substrate deformation function representing a deformation of the substrate, and at least one mark deformation function representing a deformation of the one or more alignment marks; —generating a matrix equation PD=M*F whereby a vector PD comprising the positional deviations is set equal to a weighted combination, represented by a
weight coefficient matrix M, of a vector F comprising the
substrate deformation function and the at least one mark deformation function, whereby weight coefficients associated with the at least one mark deformation function vary depending on applied alignment measurement; —determining a value for the weight coefficients of the matrix M; —determining an inverse or pseudo-inverse matrix of the matrix M, thereby obtaining a value for the
substrate deformation function as a weighted combination of the positional deviations. —applying the value of the substrate deformation function to perform an alignment of the target portion with the patterned
radiation beam.