Inspection apparatus (100) is used for measuring parameters of targets on a substrate. Coherent radiation follows an illumination path (solid rays) for illuminating target (T). A collection path (dashed rays) collects diffracted radiation from the target and delivers it to a lock-in image detector (112). A reference beam following a reference path (dotted rays). An acousto-optical modulator (108) shifts the optical frequency of the reference beam so that the intensity of radiation at the lock-in detector includes a time-varying component having a characteristic frequency corresponding to a difference between the frequencies of the diffracted radiation and the reference radiation. The lock-in image detector records two-dimensional image information representing both amplitude and phase of the time-varying component. A second reference beam with a different shift (110) follows a second reference path (dot-dash rays). Interference between the two reference beams can be used for intensity normalization.