We propose the design of a conical null-screen with quasi-elliptical targets drawn on it so that its image, which is formed by reflection on a biconical convex surface, becomes a precise radial set of circular targets if the surface under test is perfect. This null-screen avoids alignment difficulties of the test system due to the contour of the face (eyebrows, nose or eyelids). In addition, the proposed method prevents the targets from overlapping and touching each other. We discuss how to integrate the system to calibrate it by testing a spherical and a biconical surface on which we obtain geometrical parameters such as radius of curvature and conic constant, as well as elevation, and sagittal and meridional curvature maps with a smartphone-based corneal topographer.
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