An inspection apparatus measures a property of a substrate including a periodic structure. An illumination system provides a beam of radiation with an illumination profile including a plurality of illuminated portions. A radiation projector projects the beam of radiation onto the substrate. A detector detects radiation scattered from the periodic structure and separately detects first order diffracted radiation and at least one higher order of diffracted radiation of each of the illuminated portions. A processor determines the property of the substrate from the detected radiation. The plurality of illuminated portions are arranged such that first order diffracted radiation arising from one or more of the illuminated portions are not overlapped by zeroth order or first order diffracted radiation arising from any other of the illuminated portions. Furthermore, the plurality of illuminated portions are arranged such that first order diffracted radiation arising from the one or more of the illuminated portions are overlapped by at least one of the higher orders of diffracted radiation arising from any other of the illuminated portions.