An optical system delivers illuminating radiation and collects radiation after interaction with a target structure on a substrate. A measurement intensity profile is used to calculate a measurement of the property of the structure. The optical system may include a solid immersion lens. In a method, the optical system is controlled to obtain a first intensity profile using a first illumination profile and a second intensity profile using a second illumination profile. The profiles are used to derive a correction for mitigating the effect of, e.g., ghost reflections. Using, e.g., half-moon illumination profiles in different orientations, the method can measure ghost reflections even where a solid immersion lens would cause total internal reflection. The optical system may include a contaminant detection system to control a movement based on received scattered detection radiation. The optical system may include an optical component having a dielectric coating to enhance evanescent wave interaction.