High-resolution microscopy with transition from continuous to discrete diffraction

An optical approach aiming at the selection of a finite number of wave vector projections is employed to interpret the diffraction pattern of a microscope useful to probe matter at the nanoscale level. Despite the approximation, we show that accurate three-dimensional analytical description of linear microscopy is still possible and a comparison with the ordinary numerical reconstruction of the focal zone is quantified by tiny relative deviations of about 10−6. The advantageous use of the proposed analytical description is further considered in the vectorial analysis of an example of non-linear microscopy. In any optical regime (either linear or non-linear), the calculation speed increases significantly with respect to the traditional approach based on purely numerical methods.