Analysis of the Inherent Error of the TMS-1 Topographic Modeling System in Mapping a Radially Aspheric Surface

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Abstract
The potential spherical bias of the Topographic Modeling System (TMS) in measuring a radially aspheric surface was investigated. The radii of curvature of an ellipsoidal surface were measured experimentally using the TMS, and calculated using both an instantaneous radius of curvature formula and a spherically biased algorithm for comparison. Measurements were made aligned and under four conditions of misalignment. A sphere with the same radius of curvature as the apex of the ellipsoid was used to document the fundamental performance of the system. The TMS demonstrated increasing error from center to periphery in measurement of an ellipsoid with 7.5 mm apical radius of curvature and 0.5 eccentricity. Greater than 3 D of error was present at 4 mm from the apex. The misalignment error was small compared to the inherent error in the system performance. The TMS does not accurately measure the instantaneous radii of curvature of an ellipsoidal surface due to an inherent spherical bias. In addition, the spherically biased system may not detect subtle shifts in curvature in the peripheral regions, causing potentially inaccurate reconstruction of patterns of curvature.

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