A sphere mount for a ball mounted retro-reflector having a perimeter recess and a base shank. The sphere mount is configured to receive a ball mounted retro-reflector in a centrally disposed conical nest, such as a three-point conical nest, and to position it with a high degree of precision over the central axis of the base shank to within .+-.0.0005 of an inch. The perimeter recess is in the form of a single oblique scallop, orientated from the upper surface to the lower surface, and permits a maximum negative acceptance angle for incident light to a mounted spherical retro-reflector with no occlusion by the sphere mount perimeter.