Methods are disclosed for measuring target structures (32-35) formed by a lithographic process on a substrate (W). A grating structure within said target is smaller than an illumination spot (31) and field of view of a measurement optical system. The optical system has a first branch leading to a pupil plane imaging sensor (19) and a second branch leading to a substrate plane imaging sensor (23). A spatial light modulator (SLM) (24, 124, 224, 324) is arranged in an intermediate pupil plane of the second branch of the optical system. The SLM imparts a programmable pattern of attenuation that may be used to correct for asymmetries between the first and second modes of illumination or imaging. By use of specific target designs and machine-learning processes, the attenuation patterns may also be programmed to act as filter functions, enhancing sensitivity to specific parameters of interest, such as focus.