Avenue for apertometer using spectral plane and Fourier correlation analysis

This Letter proposes a simple and practical approach for numerical aperture measurement of immersion objectives. The basic concept is to generate a reference on the spectral plane and then apply the Abbe sine condition to evaluate the numerical aperture. An extremely cheap, simple but effective and practical example is to locate a coverslip on the focal plane and then record the resulting back focal plane, on which the total internal reflection ring is applied as the reference. To achieve higher repeatability and impose fewer requirements on both the operation procedure and experiment conditions, we propose an algorithm mainly consisting of two-dimensional Fourier correlation analysis and grayscale statistics to automatically identify the radii of total internal reflection and clear aperture. The proposed approach is further applied in the measurement of an objective lens with adjustable pupils when surface plasmon is employed as reference. Experimental verification is provided.