Evaluating SMR Positioning with an Autostigmatic Microscope

An optical method of determining the location of the apex of a corner reflector mounted in a steel ball, commonly referred to as a Spherically Mounted Retroreflector (SMR), relative to the center of the ball to the 1-2 µm level was previously described by us. The method used an autostigmatic microscope focused on the apex and viewed the reflected spot image as the SMR was rotated about a normal to its entrance aperture. This measurement determined the lateral offset of the apex and tipping the SMR while viewing the spot gave an indication of the axial displacement. A related questions arose recently, could the distance between two SMRs be determined to the same level of precision if the SMRs were rigidly mounted in a fixture so they could not be moved. We show the answer is yes assuming the stage moving the pair of SMRs has the required precision. As a SMR is scanned under the autostigmatic microscope the spot motion seen by the microscope is identical to that seen when scanning a spherical ball under the microscope and we have already shown that balls centers can be found to 1 µm precision using a 10x objective. We show experimentally that we can determine the distance between 2 SMRs by repeated measurements with the balls in different azimuthal orientations, and show that by taking into account the orientation, the distance between SMRs remains the same within experimental errors.