Disclosed is an inspection apparatus for use in lithography. It comprises a support for a substrate carrying a plurality of metrology targets; an optical system for illuminating the targets under predetermined illumination conditions and for detecting predetermined portions of radiation diffracted by the targets under the illumination conditions; a processor arranged to calculate from said detected portions of diffracted radiation a measurement of asymmetry for a specific target; and a controller for causing the optical system and processor to measure asymmetry in at least two of said targets which have different known components of positional offset between structures and smaller sub-structures within a layer on the substrate and calculate from the results of said asymmetry measurements a measurement of a performance parameter of the lithographic process for structures of said smaller size. Also disclosed are substrates provided with a plurality of novel metrology targets formed by a lithographic process.