Laser multi-reflection differential confocal long focal-length measurement.

We propose a new laser multi-reflection differential confocal focal-length measurement (LDCFM) method to meet the requirements of high-precision measurements of long focal lengths. An optical flat and a reflector are placed behind a test lens for reflecting the measuring beam repeatedly. Then, LDCFM uses the property that the null points of differential confocal response curves precisely correspond to the convergence points of the multi-reflected measuring beam to exactly determine the positions of the convergence points accurately. Subsequently, the position variation of the reflector is measured with different reflection times by using a distance-measuring instrument, and thereby the long focal length is measured precisely. Theoretical analyses and preliminary experimental results indicate that the LDCFM method has a relative expanded standard uncertainty (k=2) of 0.04% for the test lens with a focal length of 9.76 m. The LDCFM method can provide a novel approach for high-precision focal-length measurements.