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The instrument that measures the radius of curvature, or base curve, of a spectacle lens surface in diopters, is the Geneva lens clock. This tool is specifically designed to provide the curvature measurement of the front or back surface of the lens, which is critical for ensuring proper fitting and optical performance in eyewear.

The lens clock operates on the principle of an arc that corresponds to the curve of the lens surface. It typically has two contact points that touch the surface of the lens. The differences in height between these points help determine the curvature, which can then be converted into a diopter measurement. The result indicates how steep or flat a lens surface is, directly related to its prescription and optics.

In contrast, while the lensometer is used primarily to measure the prescription of finished spectacle lenses, and the refractometer measures the refractive index of materials, neither is designed to specifically measure the base curve of a lens. The cylinder gauge, typically used to measure the thickness of a lens, does not provide curvature information either. Thus, the Geneva lens clock stands out as the appropriate tool for this specific measurement.