In order to determine the external profile of a diamond, particularly a large diamond which has re-entrant features, an elongate and thin beam is projected onto the diamond while the diamond is rotated about an axis normal to the beam; an imaging system is used to image from one side the line along which the beam strikes the diamond, this image being formed on a diffraction grating which is tilted in accordance with the Scheimpflug condition and in order to employ the first order beam of the diffraction grating. The image on the diffraction grating is viewed with a second imaging system. Furthermore, there may be a substantial improvement in light capture. The arrangement is applicable to systems other than those for determining profile.