Bayesian approach for in Situ Numerical Aperture calibration and pitch determination in optical microscopy

The most important components in microscopy are the illumination and the numerical aperture (NA) of microscope objectives. Numerical aperture together with the wavelength set the final resolution limits and capabilities of an entire microscopy system. In optical measurement techniques such as scatterometry and ptychography, a precise knowledge of the NA is required for the geometry reconstruction algorithm where the provided NA value directly affects the final result. The tolerances of values supplied by the manufacturers are often too large, and therefore, impairing the measurement capability of the system. In this research, we demonstrate a novel method to measure the numerical aperture of microscope objectives with high precision, thereby improving optical microscopy, scatterometry and ptychography measurements. The method is based on fitting the Rayleigh lines, generated during the light interaction with traceable reference gratings, in the Fourier plane image using state of the art Least-Square and Bayesian methods. The Bayesian approach offers the possibility of including prior knowledge for the fitting of the Rayleigh lines, which may reduce the uncertainty. We also demonstrate that the calibrated microscope objectives may be used to find the pitch of unknown periodic structures. • Novel method is designed for NA measurements of all types of microscope objectives. • Intrinsic physics description and Fourier optics analysis for NA calibration is provided. • Bayesian least square approach-based traceable method provides accuracy of 10 -4 . • The method provides NA determination accuracy essential for the inverse modeling.