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Provided herein is a corneal topography system that utilizes a prism placed in optical alignment between the pattern image generator, such as a Placido disk, and the eye. The corneal topography system may be a prismatic triangulating corneal topography system that utilizes light rays of angle θ at the edge of the prism not passing through the prism, light rays that deviate from angle θ passing through the prism and light rays of angle a calculated from the reflection image to determine the corneal reflection point on the corneal surface. Also provided is a method for mapping a corneal surface of an eye of a subject utilizing an optical prism to produce a reflection image from a corneal surface reflection point on the corneal surface of the eye.