The anterior surface of the eye ('cornea') is extremely important for good sight. Instruments measuring corneal shape conventionally visualize the surface characteristics by mapping the instantaneous radius of curvature onto a rainbow colour scale. This technique is known to have important drawbacks. Firstly, not corneal shape itself is visualized, but rather second order surface properties. Secondly, the type of colouring produces well documented artifacts. We discuss visualization techniques for a more direct representation of the data. In a three part display, shape deviations are presented as a height surface in one window, height lines superimposed over the input image in another, and a colour mapped representation of the mean normal radius of curvature in a third. With the aid of some typical examples, it is shown that these visualizations are easy to interpret by the physician and overcome the limitations of the conventional techniques.