  In this work we report a theoretical study of the lateral resolution granted
by a simple glass microcylinder. In this 2D study, we had in mind the 3D
analogue -- a microsphere whose ability to form a deeply subwavelength and
strongly magnified image of submicron objects has been known since 2011.
Conventionally, the microscope in which such the image is observed is tuned so
that to see the areas behind the microsphere. This corresponds to the location
of the virtual source formed by the microsphere at a distance longer than the
distance of the real source to the miscroscope. Recently, we theoretically
found a new scenario of superresolution, when the virtual source is formed in
the wave beam transmitted through the microsphere. However, in this work we
concentrated on the case when the superresolution is achieved in the
impractical imaging system, in which the microscope objective lens is replaced
by a microlens located at a distance smaller than the Rayleigh range. The
present paper theoretically answers an important question: which scenario of
far-field nanoimaging by a microsphere grants the finest spatial at very large
distances. We found that the novel scenario (corresponding to higher refractive
indices) promises further enhancement of the resolution.
