An exact vector expression for the deformations of a wavefront from any chosen reference surface, as a function of the directions of the real and reference rays, is deduced. It can be used with slope measuring test methods, such as Hartmann or Ronchi tests, but the need for a spherical reference is removed. We present simulated and experimental results to show the feasibility of this proposal.

To measure the shape of the fast corneal surface of the human eye, we propose the design and characterization of a compact corneal topographer using the capabilities of a smartphone. The performance evaluation of the compact corneal topographer includes the calculation and compensation of the distortion introduced by the smartphone lens used to acquire the images and the evaluation of a reference surface. To demonstrate the feasibility of our proposal, we performed surface topography measurements on some human corneas and compared the results with those obtained by a commercial corneal topographer. We showed that the results obtained with our algorithms were consistent with other methods that analyze the corneal surface.

In order to measure the shape of fast convex aspherics, such as the corneal surface of the human eye, we propose the design of a conical null-screen with a radial point distribution (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 array of circular spots if the surface is perfect. Any departure from this geometry is indicative of defects on the evaluated surface. We present the target array design and the surface evaluation algorithm. The precision of the test is increased by performing an iterative process to calculate the surface normals, reducing the numerical errors during the integration. We show the applicability of the null-screen based topographer by testing a spherical calibration surface of 7.8 mm radius of curvature and 11 mm in diameter. Here we obtain an rms difference in sagitta between the evaluated surface and the best-fitting sphere less than 1 μm.

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