A novel specular surface reconstruction approach developed for and used in an experimental multi-camera corneal topographer arrangement is presented in the paper. The tear-film coated, and therefore specular, corneal surface is mathematically reconstructed from the corneal images taken simultaneously by the calibrated cameras of the arrangement. The surface reconstruction is achieved by the joint solution of partial differential equations (PDEs) that is derived from the mapping between the measurement-pattern and its virtual images taken by the cameras. The PDEs - each given in an advantageous form for one of the cameras - describe the phenomenon of light-reflection at the corneal surface. The portions of the corneal surface that reflect - possibly different - measurement-pattern points to more than one camera convey starting points for the mathematical reconstruction of the surface.