Evaluation of the depth of diffraction-limited high-NA focusing in media on the basis of aberration analysis

Spherical aberration caused by the flat boundary surface of the medium limits the quality of high-numerical-aperture light focusing. The main objective is to determine the achievable focusing depth as a function of the specified NA, wavelength, and medium refractive index for diffraction-limited focusing according to the Maréchal criterion. The wave aberration function and its root-mean-square value are obtained from the analysis of beam refraction on the flat medium surface. Main conclusions: wave aberration is directly proportional to the focusing depth, its maximum value is achieved at a refractive index of ∼1.75, and the effective focus is shifted from the paraxial focus by 0.46 of the maximum longitudinal spherical aberration. The proposed approach allows for determining optimal conditions for focusing in laser microprocessing and microscopy, and for formulating requirements for methods of compensating for spherical aberration using adaptive optics or special objectives.