The paraxial approximation is used in the development of a theory for the
visualization of monochromatic infrared point images using a cylindrical pump wave.
The theory is based on the application of the classical Green's functions. One of the
possible waves of efficient visualization is considered in detail. Expressions are obtained
for the converted image field and, in particular, for the plane of the best image along
two mutually perpendicular directions. These expressions describe qualitatively the
astigmatism of the visualized image field. Illustrative numerical calculations are given
for LiNbO3, LiIO3, and Ag3AsS3. Experimental investigations are reported of the
visualization, with the aid of a cylindrical pump wave, in LiNbO3 and LiIO3 crystals
under degenerate conditions, i.e., in the frequency doubling regime. In particular, a
study is made of the nature and degree of astigmatism of the visible image field. The
experimental results are in satisfactory agreement with the theoretical predictions.