An overlay metrology target (T) is formed by a lithographic process. A first image (740(0)) of the target structure is obtained using with illuminating radiation having a first angular distribution, the first image being formed using radiation diffracted in a first direction (X) and radiation diffracted in a second direction (Y). A second image (740(R)) of the target structure using illuminating radiation having a second angular illumination distribution which the same as the first angular distribution, but rotated 90 degrees. The first image and the second image can be used together so as to discriminate between radiation diffracted in the first direction and radiation diffracted in the second direction by the same part of the target structure. This discrimination allows overlay and other asymmetry-related properties to be measured independently in X and Y, even in the presence of two-dimensional structures within the same part of the target structure.