A scatterometer for overlay measurement, the scatterometer comprising: an illumination system configured to deliver at least one beam of radiation; an objective optical system (417, L3) configured to focus the at least one beam onto the substrate, the objective optical system having a pupil aperture; and a detection system configured to detect light reflected from the substrate; wherein the illumination system comprises an optical pupil symmetrization OPS system configured to symmetrize the at least one beam at the pupil aperture, the OPS system comprising: at least one beam splitter configured to split the at least one beam into a first sub-beam and a second sub-beam and recombine the first and second sub-beams; and at least two optical branches configured to (i) respectively receive and reflect the first and second sub-beams , (ii) rotate at least the second sub-beam such that an intensity distribution of the second sub-beam is inverted, and (iii) recombine the first sub-beam with the second sub-beam such that the second sub-beam is symmetric relative to the first sub-beam ; wherein the OPS system is further configured such that the first and second sub-beams have an optical path difference characterized in that the optical path difference is greater than a temporal coherence length of the at least one beam of radiation and less than a depth of focus in the pupil plane of the objective optical system (417, L3). an illumination system configured to deliver at least one beam of radiation; an objective optical system (417, L3) configured to focus the at least one beam onto the substrate, the objective optical system having a pupil aperture; and a detection system configured to detect light reflected from the substrate; wherein the illumination system comprises an optical pupil symmetrization OPS system configured to symmetrize the at least one beam at the pupil aperture, the OPS system comprising: at least one beam splitter configured to split the at least one beam into a first sub-beam and a second sub-beam and recombine the first and second sub-beams; and at least two optical branches configured to (i) respectively receive and reflect the first and second sub-beams , (ii) rotate at least the second sub-beam such that an intensity distribution of the second sub-beam is inverted, and (iii) recombine the first sub-beam with the second sub-beam such that the second sub-beam is symmetric relative to the first sub-beam ; at least one beam splitter configured to split the at least one beam into a first sub-beam and a second sub-beam and recombine the first and second sub-beams; and at least two optical branches configured to (i) respectively receive and reflect the first and second sub-beams , (ii) rotate at least the second sub-beam such that an intensity distribution of the second sub-beam is inverted, and (iii) recombine the first sub-beam with the second sub-beam such that the second sub-beam is symmetric relative to the first sub-beam ; wherein the OPS system is further configured such that the first and second sub-beams have an optical path difference characterized in that the optical path difference is greater than a temporal coherence length of the at least one beam of radiation and less than a depth of focus in the pupil plane of the objective optical system (417, L3). <EOS>