A system includes a light pattern generator having light spots for illuminating front and back surfaces of a cornea with polarized light; one or more detectors for receiving one or more of first spot images from light reflected off the front surface, and second spot images from light reflected off the back surface, the light reflected off the front surface having a first polarization and the light reflected off the back surface having a second polarization; a polarization element in an optical path between the back surface and the one or more detectors, the polarization element being configured to attenuate an intensity of the light reflected off the front surface by an amount greater than an amount by which it attenuates the light reflected off the back surface; and a processor for determining a geometric characteristic of the cornea using at least the second plurality of spot images.