Abstract: A system for indirectly measuring a geometric dimension related to an opening in an apertured exterior surface of a part such as an ammunition case based on direct measurements of the part when fixtured at a measurement station is provided. The system includes first and second holding devices for holding the part therebetween in a part-retaining position in which the part is firmly held between the devices at its end surfaces. In one embodiment, a portion of each of the holding devices extends into its respective opening in the part-retaining position. The system also includes a head apparatus which has a plurality of radiation sources for successively directing arrays of planes of radiation at the holding devices and at the part, and a plurality of receiver modules for measuring the amount of radiation present in unobstructed planar portions of the planes to obtain holding device and part signals.