In this work we report the design of a null screen for corneal topography. Here we assume that the corneal surface is an ellipsoid with a diameter of 12 mm and a curvature radius of 7.8 mm. To avoid the difficulties in the alignment of the test system due to the face contour (eyebrows, nose, or eyelids), we design a conical null-screen with spots (similar to ellipses) drawn on it in such a way that its image, which is formed by reflection on the test surface, becomes an exact radial array of circular spots if the surface is perfect. Additionally, we performed a numerical simulation introducing Gaussian random errors in the coordinates of the centroids of the spots on the image plane, and in the coordinates of the sources (spots on the null-screen) in order to obtain the conical null-screen that reduces the error in the evaluation of the topography.© (2011) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.