Abstract <p>Estimation of an image quality has a decisive importance when designing optical systems with an enhanced depth of focus that involve axicons, which have two caustics, preserve the property of linearity, however, being spatially-variant, which creates difficulties for their analysis. We propose to consider the images formed by each of the caustics in terms of the linear systems theory. Theoretical analysis of constructing images is performed, the point spread function are found for three optical systems in which toroidal light waves are formed with the help of an axicon; numerous experiments on determining the resolving power of such systems are carried out. As a result, it is shown that the axicon constructs the image of a single object as a continuous set of ‘‘intermediate’’ images along the focal segment. The light beams arriving from the object to the central part of the axicon will create an ‘‘intermediate’’ image in the immediate vicinity of the axicon, while the beams arriving to the axicon periphery will produce an image at the periphery of the focal segment. At that, all these low-contrast images mask each other. The lens-axicon tandem simultaneously builds the object images in both the near-field diffraction zone in the form of a set of ‘‘intermediate’’ images and in the far-field diffraction zone in the geometrically transformed shape. Moreover, in the near-field diffraction zone, the space depth rendered by the tandem can exceed that rendered by a single objective. The experimental data confirm the theoretical conclusions.</p>