Robust motion-free and error-correcting method of estimating the focal length of a lens

This paper presents a motion-free technique to characterize the focal length of any spherical convex or concave lens. The measurement test-bench uses a Gaussian laser beam, an electronically controlled variable focus lens (ECVFL), a digital micro-mirror device (DMD), and a standard photo-detector (PD). The method requires measuring beam spot sizes for different focal length settings of the ECVFL and using the measurement data to obtain a focal length estimate through an iterative least-squares-based curve-fitting algorithm. The method is also shown to overcome potential measurement errors that arise due to inaccurate placement of optical components on the test-bench as well as unknown principal plane locations of asymmetric lens samples such as plano-convex lenses. Contrary to the commercially deployed and other proposed methods of focal length characterization, this method does not involve any bulk mechanical motion of optical elements. This approach eliminates measurement errors due to gradual mechanical wear and tear and improves measurement repeatability by minimizing mechanical hysteresis. The compact and fully automated method delivers fast, repeatable, and reliable measurements, which we believe makes it ideal for deployment in industrial lens production units and characterizing lenses used in sensitive imaging systems and various other optical experiments and systems. Measured focal lengths are within the 1% manufacturer-provided tolerance values showing excellent agreement between theory and experiments. We also demonstrate measurement robustness by rectifying discrepancies between known and actual separation distances on the measurement test bench.