L'image tridimensionnelle du point en présence d'aberration sphérique primaire et de filtrage d'amplitude : unitaire ou modal

We investigate the point diffraction image arising from an objective lens in the vicinity of its paraxial focus, under the combined influence of spherical aberration, defocusing, and an amplitude filtering of modal TEM00 law. The previous literature pertaining to our subject is first reviewed thoroughly and then we outline a new hybrid formalism that permits an easy computation of the total diffraction image everywhere in the focal region. In this formalism the complex pupil amplitude is developed into a series of Zernike polynomials, the coefficients of which are obtained through the Gauss–Chebyshev method of numerical quadrature. A considerable amount of numerical information has thus been obtained, which will be presented here in graphical form and discussed. Notably we show that our modal filter, combined with an appropriate amount of defocusing, does compensate the existing spherical aberration beyond the supposedly ideal situation represented by the Airy pattern.