Automatic method to measure the numerical aperture of a propagating Gaussian light beam

Abstract

In this work, an automatic method to measure the numerical aperture (NA) of a propagating Gaussian light beam is presented. The proposed method uses two separated digital intensity recordings of the light beam along its propagation axis and a Levenberg–Marquardt minimization algorithm to find the standard deviation of the intensity profiles, needed for the accurate computation of the NA. The manuscript presents the mathematical basis, implementation and testing of the method, with both simulated and experimental light beams. The performance of the automatic method shows a R-square of 0.99 regarding the simulated data and a 3.72% of error with respect to the experimental Gaussian light beams produced by commercially NA graded optical systems.